This is a list with the formulas and proofs in GR.

The table of integrals by Gradshteyn and Ryzhik is one of the most widely used ones.
It is our goal to present proofs of these formulas and put them in some context.

The whole collection of proofs will appear published in SCIENTIA, Series A.

If you want to help, please send the details to vhm at math.tulane.edu

If you experience a problem downloading a formula/proof email me at vhm at math.tulane.edu


Directory of notes on the integrals in GR.

Index of the papers with formulas in GR.

Thanks to those who contribute with a proof:

M. Albano, T. Amdeberhan, E. Beyerstedt, S. Boettner, K. Boyadzhiev, L. Glasser, M. Knight, K. Kohl, A. MacLeod, L. Medina, R. Posey, A. Straub

The notation not yet means that either I have not written the proof or I do not know how to do it.


2.01: The basic integrals

Section 2.01 contains 26 formulas:




2.14: Forms containing the binomial 1+x^n

Section 2.148 contains 4 formulas:


Section 2.311 contains a single formula:


Section 2.312 contains a single formula:


Section 2.313 contains 2 formulas:


Section 2.314 contains a single formula:


Section 2.315 contains a single formula:


2.32: The exponential combined with a rational function of x

Section 2.321 contains 2 formulas. Proofs completed

Section 2.322 contains 4 formulas. Proofs completed


Section 2.323 contains a single formula. Proof completed


Section 2.324 contains $2$ formulas. Proofs completed


Section 2.325 contains $13$ formulas:


Section 2.326 contains a single formula. Proof completed


Section 2.33 contains 23 formulas:

Section 2.423 contains 64 formulas:



3.19-3.23: Combinations of powers of x and powers of binomials of the form a+bx

Section 3.191 contains 3 formulas. Proofs completed

Section 3.192 contains 4 formulas. Proofs completed

Section 3.193 contains a single formula. Proof completed

Section 3.194 contains 8 formulas. Proofs completed

Section 3.195 contains a single formula. Proof completed

Section 3.196 contains 5 formulas. Proofs completed

Section 3.197 contains 12 formulas. Proofs completed

Section 3.198 contains a single formula. Proof completed

Section 3.199 contains a single formula. Proof completed

Section 3.211 contains a single formula:

Section 3.212 contains a single formula:

Section 3.213 contains a single formula:

Section 3.214 contains a single formula:

Section 3.215 contains a single formula:

Section 3.216 contains 2 formulas. Proofs completed

Section 3.217 contains a single formula. Proof completed

Section 3.218 contains a single formula. Proof completed

Section 3.219 contains a single formula. Proof completed

Section 3.221 contains 2 formulas. Proofs completed

Section 3.222 contains 2 formulas. Proofs completed

Section 3.223 contains 3 formulas:

Section 3.224 contains a single formula. Proof completed

Section 3.225 contains 3 formulas. Proofs completed

Section 3.226 contains 2 formulas. Proofs completed

Section 3.227 contains 2 formulas:


Section 3.228 contains 6 formulas:

Section 3.229 contains a single formula. Proof completed

Section 3.231 contains 6 formulas. Proofs completed


Section 3.232 contains a single formula. Proof completed


Section 3.233 contains a single formula. Proof completed


Section 3.234 contains 2 formulas. Proofs completed


Section 3.235 contains a single formula. Proof completed


Section 3.236 contains a single formula:

Section 3.237 contains a single formula:

Section 3.238 contains 3 formulas:


3.24-3.27: Powers of x, binomials of the form .... and of polynomials in x

Section 3.241 contains 6 formulas. Proofs completed

Section 3.242 contains two formulas:

    3.242.2 appeared in SIAM Review 40(1998).

Section 3.243 contains a single formula:

Section 3.244 contains 4 formulas. Proofs completed

Section 3.245 contains a single formula. Proof completed

Section 3.246 contains a single formula. Proof completed

Section 3.247 contains 2 formulas. Proof completed

Section 3.248 contains 6 formulas:

Section 3.249 contains 8 formulas:

Section 3.251 contains 11 formulas. Proofs completed

Section 3.252 contains 14 formulas:

Section 3.253 contains a single formula:

Section 3.254 contains 2 formulas:

Section 3.255 contains a single formula:

Section 3.256 contains 2 formulas:

Section 3.257 contains a single formula:

    3.257 paper appeared in SIAM Review 40(1998).

Section 3.258 contains 7 formulas:


Section 3.259 contains 3 formulas:


Section 3.261 contains 4 formulas:

Section 3.262 contains a single formula:

Section 3.263 contains a single formula:


Section 3.264 contains 7 formulas:

Section 3.265 contains a single formula. Proof completed


Section 3.266 contains a single formula:


Section 3.267 contains 3 formulas. Proofs completed


Section 3.268 contains 3 formulas:


Section 3.269 contains 3 formulas. Proofs completed


Section 3.271 contains 5 formulas:


Section 3.272 contains 2 formulas. Proofs completed


Section 3.273 contains 4 formulas:


Section 3.274 contains 3 formulas:

Section 3.275 contains 4 formulas:

Section 3.276 contains 2 formulas:

Section 3.277 contains 7 formulas:

Section 3.278 contains a single formula:


3.31: Exponential functions.

Section 3.310 contains a single formula. Proof completed

Section 3.311 contains 13 formulas. Proofs completed

Section 3.312 contains 3 formulas. Proofs completed

Section 3.313 contains 2 formulas. Proofs completed

Section 3.314 contains a single formula. Proof completed

Section 3.315 contains 2 formulas:

Section 3.316 contains a single formula. Proof completed

Section 3.317 contains 2 formulas. Proofs completed

Section 3.318 contains 2 formulas:


3.32-3.34: Exponentials of more complicated arguments.

Section 3.321 contains 7 formulas:


Section 3.322 contains 3 formulas:


Section 3.323 contains 3 formulas:


Section 3.324 contains 2 formulas. Proofs completed


Section 3.325 contains a single formula. Proof completed


Section 3.326 contains 5 formulas:



Exponentials of exponentials.

Section 3.327 contains a single formula. Proof completed


Section 3.328 contains a single formula. Proof completed


Section 3.329 contains a single formula. Proof completed


Section 3.331 contains 4 formulas. Proofs completed


Section 3.332 contains a single formula:


Section 3.333 contains 3 formulas:


Section 3.334 contains a single formula. Proof completed



Exponentials of hyperbolic functions.

Section 3.335 contains a single formula:


Section 3.336 contains 3 formulas:


Section 3.337 contains 3 formulas:



Exponentials of trigonometric functions and logarithms.

Section 3.338 contains 5 formulas:


Section 3.339 contains a single formula. Proof completed


Section 3.341 contains a single formula:

Section 3.342 contains a single formula. Proof completed


3.35: Combinations of exponentials and rational functions.

Section 3.351 contains 9 formulas. Proofs completed

Section 3.352 contains 7 formulas:



Section 3.353 contains 5 formulas:


Section 3.354 contains 5 formulas:


Section 3.355 contains 4 formulas:


Section 3.356 contains 4 formulas:


Section 3.357 contains 6 formulas:


Section 3.358 contains 8 formulas:


Section 3.359 contains a single formula:



3.36-3.37: Combinations of exponentials and algebraic functions.

Section 3.361 contains 3 formulas. Proofs completed


Section 3.362 contains 2 formulas. Proofs completed


Section 3.363 contains 2 formulas. Proofs completed


Section 3.364 contains 3 formulas. Proofs completed


Section 3.365 contains 2 formulas:


Section 3.366 contains 3 formulas:


Section 3.367 contains a single formula:


Section 3.368 contains a single formula:


Section 3.369 contains a single formula. Proof completed


Section 3.371 contains a single formula. Proof completed



Section 3.372 contains a single formula. Proof completed


Section 3.373 contains a single formula:


Section 3.374 contains two formulas:



3.38-3.39: Combinations of exponentials and arbitrary powers.

Section 3.381 contains 11 formulas:


Section 3.382 contains 7 formulas:


Section 3.383 contains 10 formulas:


Section 3.384 contains 9 formulas:


Section 3.385 contains a single formula:


Section 3.386 contains two formulas:


Section 3.387 contains 7 formulas:


Section 3.388 contains 4 formulas:


Section 3.389 contains 9 formulas:


Section 3.391 contains a single formula:


Section 3.392 contains 4 formulas:


Section 3.393 contains a single formula:


Section 3.394 contains a single formula:


Section 3.395 contains 3 formulas:



3.41-3.44: Combinations of rational functions of powers and exponentials.

Section 3.411 contains 32 formulas. Proofs completed


Section 3.412 contains a single formula:


Section 3.413 contains 3 formulas:


Section 3.414 contains a single formula:


Section 3.415 contains 4 formulas:


Section 3.416 contains 3 formulas:


Section 3.417 contains 2 formulas. Proofs completed


Section 3.418 contains 3 formulas:


Section 3.419 contains 7 formulas:


Section 3.421 contains 5 formulas:


Section 3.422 contains a single formula:


Section 3.423 contains 6 formulas:



Section 3.424 contains 5 formulas:



Section 3.425 contains 2 formulas:



Section 3.426 contains 2 formulas:


Section 3.427 contains 11 formulas:


Section 3.428 contains 7 formulas:



Section 3.429 contains a single formula. Proofs completed


Section 3.431 contains 2 formulas:


Section 3.432 contains 2 formulas:


Section 3.433 contains a single formula. Proof completed


Section 3.434 contains 2 formulas. Proofs completed


Section 3.435 contains 4 formulas. Proofs completed



Section 3.436 contains a single formula. Proof completed


Section 3.437 contains a single formula:


Section 3.438 contains 4 formulas:


Section 3.439 contains a single formula:


Section 3.441 contains a single formula:


Section 3.442 contains 3 formulas:


Section 3.443 contains 3 formulas:




3.45: Combinations of powers and algebraic functions of exponentials.

Section 3.451 contains 2 formulas. Proof completed

Section 3.452 contains 5 formulas. Proof completed

Section 3.453 contains 2 formulas:

Section 3.454 contains 2 formulas:

Section 3.455 contains 2 formulas:

Section 3.456 contains 2 formulas:

Section 3.457 contains 3 formulas. Proofs completed

Section 3.458 contains 2 formulas:


3.46-3.48: Combinations of exponentials of more complicated arguments and powers.


3.46-3.48: Combinations of exponentials of more complicated arguments and powers.

Section 3.461 contains 9 formulas:

Section 3.462 contains 25 formulas:


Section 3.463 contains a single formula. Proof completed


Section 3.464 contains a single formula. Proof completed


Section 3.465 contains a single formula. Proof completed


Section 3.466 contains 3 formulas. Proofs completed


Section 3.467 contains a single formula. Proof completed


Section 3.468 contains 2 formulas. Proofs completed


Section 3.469 contains 3 formulas:


Section 3.471 contains 16 formulas:


Section 3.472 contains 5 formulas. Proofs completed


Section 3.473 contains a single formula. Proof completed


Section 3.474 contains 2 formulas:



Section 3.475 contains 3 formulas. Proofs completed


Section 3.476 contains 2 formulas. Proofs completed


Section 3.477 contains 2 formulas:


Section 3.478 contains 4 formulas:


Section 3.479 contains 2 formulas:


Section 3.481 contains 2 formulas. Proofs completed


Section 3.482 contains 3 formulas:


Section 3.483 contains a single formula:


Section 3.484 contains a single formula. Proof completed


Section 3.485 contains a single formula:


Section 3.486 contains a single formula:


Section 3.487 contains a single formula:


Section 3.511 contains 10 formulas. Proofs completed


Section 3.512 contains 2 formulas. Proofs completed


Section 3.513 contains 4 formulas:


Section 3.514 contains 4 formulas:


Section 3.515 contains a single formula. Proof completed


Section 3.516 contains 3 formulas:


Section 3.517 contains 2 formulas:


Section 3.518 contains 6 formulas:


Section 3.519 contains a single formula:


Section 3.521 contains 4 formulas. Proofs completed


Section 3.522 contains 10 formulas. Proofs completed


Section 3.523 contains 12 formulas. Proofs completed


Section 3.524 contains 23 formulas. Proofs completed


Section 3.525 contains 8 formulas:


Section 3.526 contains 3 formulas:


Section 3.527 contains 16 formulas:


Section 3.528 contains 2 formulas:


Section 3.529 contains 3 formulas:


Section 3.531 contains 8 formulas:



Section 3.532 contains 2 formulas:



Section 3.533 contains 4 formulas:



Section 3.534 contains 2 formulas:



Section 3.535 contains a single formula:



Section 3.536 contains 4 formulas:



Section 3.541 contains 10 formulas:


Section 3.542 contains 2 formulas:



Section 3.543 contains 4 formulas:



Section 3.544 contains a single formula:


Section 3.545 contains 2 formulas:


Section 3.546 contains 4 formulas. Proofs completed


Section 3.547 contains 20 formulas:



Section 3.548 contains 2 formulas:



Section 3.549 contains 4 formulas:



Section 3.551 contains 10 formulas. Proofs completed



Section 3.552 contains 6 formulas. Proofs completed



Section 3.553 contains 2 formulas. Proofs completed



Section 3.554 contains 6 formulas:



Section 3.555 contains 2 formulas:



Section 3.556 contains 2 formulas:



Section 3.557 contains 7 formulas:


Section 3.558 contains 7 formulas:


Section 3.559 contains a single formula:


Section 3.561 contains a single formula:


Section 3.562 contains 6 formulas:


Section 3.611 contains 3 formulas:


Section 3.612 contains 7 formulas:


Section 3.613 contains 13 formulas:


Section 3.614 contains a single formula:


Section 3.615 contains 3 formulas:


Section 3.616 contains 8 formulas:


Section 3.617 contains a single formula:



3.62: Powers of trigonometric functions.

Section 3.621 contains 7 formulas:


Section 3.622 contains 4 formulas. Proofs completed


Section 3.623 contains 3 formulas. Proofs completed


Section 3.624 contains 6 formulas:


Section 3.625 contains 4 formulas. Proofs completed


Section 3.626 contains 2 formulas. Proofs completed


Section 3.627 contains a single formula. Proof completed


Section 3.628 contains a single formula. Proof completed


Section 3.631 contains 20 formulas:


Section 3.632 contains 5 formulas:



Section 3.633 contains 5 formulas:


Section 3.634 contains 3 formulas:


Section 3.635 contains 3 formulas:


Section 3.636 contains 3 formulas. Proofs completed


Section 3.637 contains 4 formulas:



Section 3.638 contains 3 formulas:


Section 3.641 contains 2 formulas:


Section 3.642 contains 4 formulas:


Section 3.643 contains 2 formulas:


Section 3.644 contains 5 formulas:


Section 3.645 contains a single formula:


Section 3.646 contains 2 formulas:


Section 3.647 contains a single formula:


Section 3.648 contains 2 formulas:


Section 3.649 contains 2 formulas:


Section 3.651 contains 2 formulas:


Section 3.652 contains 3 formulas:


Section 3.653 contains 6 formulas:


Section 3.654 contains 3 formulas:


Section 3.655 contains a single formula:


Section 3.656 contains 2 formulas:


3.66: Forms containing powers of linear functions of trigonometric functions.

Section 3.661 contains 4 formulas:


Section 3.662 contains 5 formulas:


Section 3.663 contains 2 formulas:


Section 3.664 contains 5 formulas:


Section 3.665 contains 2 formulas:


Section 3.666 contains 5 formulas:



Section 3.667 contains 7 formulas:


Section 3.668 contains 2 formulas:


Section 3.669 contains a single formula:


Section 3.670 contains 2 formulas:



Section 3.671 contains 5 formulas:



Section 3.672 contains 2 formulas:


Section 3.673 contains a single formula:



Section 3.674 contains 3 formulas:



Section 3.675 contains 2 formulas:



Section 3.676 contains 3 formulas:



Section 3.677 contains 2 formulas:



Section 3.678 contains 5 formulas:



Section 3.679 contains 3 formulas:


Section 3.681 contains 4 formulas:


Section 3.682 contains a single formula:


Section 3.683 contains 4 formulas:


Section 3.684 contains a single formula:


Section 3.685 contains 7 formulas:


Section 3.686 contains a single formula:


Section 3.687 contains 6 formulas:


Section 3.688 contains 20 formulas:


Section 3.689 contains 2 formulas:



3.69-3.71: Trigonometric functions of more complicated arguments.

Section 3.691 contains 22 formulas:


Section 3.692 contains 6 formulas:


Section 3.693 contains 2 formulas:



Section 3.694 contains 2 formulas:


Section 3.695 contains 2 formulas:


Section 3.696 contains 4 formulas:



Section 3.697 contains a single formula:


Section 3.698 contains 4 formulas:


Section 3.699 contains 5 formulas:


Section 3.711 contains a single formula:


Section 3.712 contains 2 formulas:


Section 3.713 contains 2 formulas:


Section 3.714 contains 4 formulas:



Section 3.715 contains 21 formulas:



Section 3.716 contains 13 formulas:


Section 3.717 contains a single formula:


Section 3.718 contains 7 formulas:



Section 3.719 contains 3 formulas:


Section 3.721 contains 3 formulas:


Section 3.722 contains 8 formulas:


Section 3.723 contains 12 formulas:


Section 3.724 contains 3 formulas:


Section 3.725 contains 3 formulas:


Section 3.726 contains 3 formulas:


Section 3.727 contains 14 formulas:


Section 3.728 contains 9 formulas:


Section 3.729 contains 4 formulas:


Section 3.731 contains 4 formulas:



Section 3.732 contains 4 formulas:



Section 3.733 contains 5 formulas:



Section 3.734 contains 2 formulas:



Section 3.735 contains a single formula:



Section 3.736 contains 6 formulas:



Section 3.737 contains 6 formulas:


Section 3.738 contains 2 formulas:


Section 3.739 contains 4 formulas:


Section 3.741 contains 3 formulas:


Section 3.742 contains 8 formulas:


Section 3.743 contains 5 formulas:


Section 3.744 contains a single formula:


Section 3.745 contains a single formula:


Section 3.746 contains 2 formulas:


Section 3.747 contains 11 formulas:


Section 3.748 contains 3 formulas:


Section 3.749 contains 3 formulas:



3.75: Combinations of trigonometric and algebraic functions.

Section 3.751 contains 4 formulas:


Section 3.752 contains 2 formulas:


Section 3.753 contains 5 formulas:


Section 3.754 contains 3 formulas:


Section 3.755 contains 2 formulas:


Section 3.756 contains 2 formulas:


Section 3.757 contains 2 formulas. Proofs completed



3.76-3.77: Combinations of trigonometric and powers

Section 3.761 contains 12 formulas:



Section 3.762 contains 3 formulas.



Section 3.763 contains 4 formulas.


Section 3.764 contains 2 formulas:


Section 3.765 contains 2 formulas:


Section 3.766 contains 4 formulas:


Section 3.767 contains 4 formulas:


Section 3.768 contains 14 formulas:


Section 3.769 contains 7 formulas.



Section 3.771 contains 13 formulas.



Section 3.772 contains 6 formulas.



Section 3.773 contains 6 formulas.



Section 3.774 contains 6 formulas.



Section 3.775 contains 11 formulas.


Section 3.776 contains 2 formulas:


Section 3.781 contains 2 formulas:


Section 3.782 contains 3 formulas:


Section 3.783 contains 2 formulas:



Section 3.784 contains 9 formulas:


Section 3.785 contains a single formula:


Section 3.786 contains 3 formulas:



Section 3.787 contains 4 formulas:



Section 3.788 contains a single formula:



Section 3.789 contains a single formula:



Section 3.791 contains 12 formulas:



Section 3.792 contains 21 formulas:



Section 3.793 contains 2 formulas:



Section 3.794 contains 6 formulas:



Section 3.795 contains a single formula:



Section 3.796 contains 2 formulas:



Section 3.797 contains 3 formulas:



Section 3.798 contains 2 formulas:



Section 3.799 contains 3 formulas:



Section 3.811 contains 5 formulas:



Section 3.812 contains 15 formulas:



Section 3.813 contains 11 formulas:



Section 3.814 contains 15 formulas:



Section 3.815 contains 4 formulas:



Section 3.816 contains 4 formulas:



Section 3.817 contains 8 formulas:



Section 3.818 contains 9 formulas:



Section 3.819 contains 16 formulas:



3.82-3.83: Powers of trigonometric functions combined with other powers.

Section 3.821 contains 14 formulas:


Section 3.822 contains 2 formulas:


Section 3.882 contains 3 formulas:


Section 3.936 contains 5 formulas:


Section 3.941 contains 2 formulas:


Section 3.942 contains 2 formulas:



3.98-3.99: Combinations of trigonometric and hyperbolic functions.

Section 3.981 contains 12 formulas:


Section 3.996 contains 5 formulas:



Section 3.997 contains 4 formulas:


Section 4.112 contains 2 formulas:


Section 4.116 contains 2 formulas:


Section 4.117 contains 9 formulas:


Section 4.118 contains a single formula:


Section 4.119 contains a single formula:


Section 4.121 contains 2 formulas:


Section 4.122 contains 2 formulas:


Section 4.123 contains 7 formulas:


4.21: Logarithmic functions.

Section 4.211 contains 2 formulas. Proofs completed


Section 4.212 contains 9 formulas. Proofs completed


Section 4.215 contains 4 formulas. Proofs completed



4.22: Logarithms of more complicated arguments.

Section 4.221 contains 3 formulas. Proofs completed


Section 4.222 contains 8 formulas:

Section 4.223 contains 3 formulas. Proof completed

Section 4.224 contains 15 formulas:


Section 4.225 contains 4 formulas:


Section 4.226 contains 7 formulas:

Section 4.227 contains 17 formulas. Proof completed


Section 4.229 contains 7 formulas:



4.23: Combinations of logarithms and rational functions.

Section 4.231 contains 20 formulas:


Section 4.232 contains 3 formulas. Proof completed


Section 4.233 contains 5 formulas:


Section 4.234 contains 8 formulas. Proof completed



Section 4.235 contains 4 formulas. Proof completed


Section 4.236 contains 2 formulas. Proof completed



4.24: Combinations of logarithms and algebraic functions.

Section 4.241 contains 11 formulas. Proof completed


Section 4.242 contains 6 formulas:



Section 4.243 contains a single formula. Proof completed


Section 4.244 contains 3 formulas. Proof completed


Section 4.245 contains 2 formulas. Proof completed


Section 4.246 contains a single formula. Proof completed


Section 4.247 contains 2 formulas. Proof completed


4.25: Combinations of logarithms and powers.

Section 4.251 contains 6 formulas. Proofs completed


Section 4.252 contains 4 formulas. Proofs completed


Section 4.253 contains 7 formulas. Proofs completed


Section 4.254 contains 6 formulas. Proofs completed


Section 4.255 contains 3 formulas. Proofs completed


Section 4.256 contains a single formula. Proof completed


Section 4.257 contains 5 formulas:



4.26-4.27: Combinations involving powers of the logarithm and other powers.

Section 4.261 contains 21 formulas:


Section 4.262 contains 9 formulas. Proofs completed


Section 4.263 contains 3 formulas:


Section 4.264 contains 3 formulas. Proofs completed


Section 4.265 contains a single formula. Proof completed


Section 4.266 contains 2 formulas. Proofs completed


Section 4.267 contains 43 formulas:


Section 4.268 contains 7 formulas:


Section 4.269 contains 7 formulas:


Section 4.271 contains 16 formulas. Proofs completed


Section 4.272 contains 19 formulas:


Section 4.273 contains a single formula. Proof completed


Section 4.274 contains a single formula. Proof completed


Section 4.275 contains 2 formulas. Proofs completed


4.28: Combinations of rational functions of ln x and powers.

Section 4.281 contains 7 formulas:


Section 4.282 contains 13 formulas:


Section 4.283 contains 14 formulas:


Section 4.284 contains 2 formulas:


Section 4.285 contains a single formula:



4.29-4.32: Combinations of logarithmic functions of more complicated arguments and powers.

Section 4.291 contains 30 formulas:

Section 4.292 contains 5 formulas:

Section 4.293 contains 14 formulas. Proofs completed

Section 4.294 contains 13 formulas:

Section 4.295 contains 41 formulas:


Section 4.296 contains 4 formulas:


Section 4.297 contains 10 formulas:


Section 4.298 contains 23 formulas:


Section 4.299 contains 4 formulas:


Section 4.311 contains 6 formulas:



Section 4.312 contains 2 formulas:



Section 4.313 contains 7 formulas:


Section 4.314 contains 4 formulas:


Section 4.315 contains 4 formulas:



Section 4.316 contains 2 formulas:


Section 4.317 contains 11 formulas:


Section 4.318 contains 2 formulas:


Section 4.319 contains 3 formulas:


Section 4.321 contains 2 formulas:


Section 4.322 contains 10 formulas:


Section 4.323 contains 3 formulas:


Section 4.324 contains 3 formulas:


Section 4.325 contains 12 formulas:


Section 4.326 contains 2 formulas:


Section 4.327 contains 3 formulas:



4.33-4.34: Combinations of logarithms and exponentials.

Section 4.331 contains 3 formulas. Proofs completed


Section 4.332 contains 2 formulas:


Section 4.333 contains a single formula. Proof completed


Section 4.334 contains a single formula:


Section 4.335 contains 3 formulas. Proofs completed


Section 4.336 contains 2 formulas:


Section 4.337 contains 5 formulas:


Section 4.338 contains 2 formulas:


Section 4.339 contains a single formula:


Section 4.341 contains a single formula:


Section 4.342 contains 3 formulas:


Section 4.343 contains a single formula:



4.35-4.36: Combinations of logarithms, exponentials and powers.

Section 4.351 contains 3 formulas. Proofs completed

Section 4.352 contains 4 formulas. Proofs completed


Section 4.353 contains 3 formulas. Proofs completed


Section 4.354 contains 5 formulas:


Section 4.355 contains 4 formulas. Proofs completed


Section 4.356 contains 5 formulas:


Section 4.357 contains 3 formulas:




Section 4.358 contains 5 formulas:


Section 4.359 contains 2 formulas:



Section 4.361 contains 2 formulas:



Section 4.362 contains 2 formulas:



Section 4.369 contains 2 formulas:




4.38-4.41: Logarithms and trigonometric functions.

Section 4.381 contains 4 formulas:

Section 4.382 contains 5 formulas:

Section 4.383 contains 2 formulas:


Section 4.384 contains 26 formulas:



Section 4.385 contains 5 formulas:


Section 4.386 contains 4 formulas:


Section 4.387 contains 10 formulas:


Section 4.388 contains 6 formulas:


Section 4.389 contains 6 formulas:


Section 4.391 contains 4 formulas:


Section 4.392 contains 2 formulas:


Section 4.393 contains 5 formulas:


Section 4.394 contains 9 formulas:


Section 4.395 contains 2 formulas:


Section 4.396 contains 7 formulas:


Section 4.397 contains 16 formulas:


Section 4.398 contains 3 formulas:


Section 4.399 contains 3 formulas:


Section 4.411 contains 3 formulas:


Section 4.412 contains 5 formulas:


Section 4.413 contains 5 formulas:


Section 4.414 contains 10 formulas:


Section 4.415 contains 2 formulas:


Section 4.416 contains 4 formulas:


Section 4.432 contains 26 formulas:


Section 4.441 contains 2 formulas:



4.52: Combinations of arcsines, arccosines, and powers.

Section 4.521 contains 8 formulas:


4.53-4.54: Combinations of arctangents, arccotangents, and powers.

Section 4.531 contains 13 formulas:


Section 4.536 contains 3 formulas:



Section 4.539 contains a single formula:



6.28 - 6.31: The probability integral.

Section 6.281 contains 2 formulas:


Section 6.282 contains 2 formulas:


Section 6.283 contains 2 formulas:



8.258: Integrals involving the complementary error function.

Section 8.258 contains 5 formulas: