Integral Gallery

Here is a gallery of interesting integrals I've found. To me, they are the most beautiful mathematical equations, mainly because they would more likely than not not have been possible without CAM. One has to understand that it took about 300 years to develop the math of calculus to where it is and several decades to impliment it into Mathematica or Maple and yet only a few seconds to crank them out. It would take a human several hours or days or weeks to compute these and then again only a gifted few could do it in the first place. Software packages like these are the culmination of the greatest minds in mathematics. Its like asking the world of mathematics a question and getting back a definite answer. What's most suprising in my exploration of integrals is that most integrals that teachers and professors mention as impossible can actually be done in known functions, but usually not elementary trancendental ones. Most of these integrals include special functions and so have no real use until late undergraduate study. Then again, most have absolutely no use except to look nice. All of these were calculated with Mathematica 4.1.

Integrals involving trigonometric functions.

Here are some integrals involving the natural logarithm and e.

Here are some integrals involving radicals.

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