And, yes, I mean what you think it means: antidifferentiating. Finding a primative. Whatever...

At my school, we're conducting an integration bee not unlike similar bees done elsewhere.

The purpose of this thread is two-fold:
1. To compile a list of non-routine integrals
2. To discuss how these integrals are done

Here is the list I came up with. Please add to the list. I'm not looking for 300 integrals no one at a community college can solve (and, yes, by "solve", I mean to antidifferentiate). They should stump a significant percentage of those who would get an A in Integral Calculus though not 100%.

A few of these are downright easy but they can stump the woefully inexperienced.

One or two of them are potentially very difficult if you're not clever enough.

The first one is a fairly trivial change of variable trick, and the second is found by contour integration. In addition to having these down pat, an integrator champ should be able to pull all the tricks: differentiating under the integral sign, direct integration of differential eq corresponding to the function, etc.

They all have one thing in common: when integrating by parts, you have to recognize that you eventually get the same integral you started with, and you have to add a multiple of it to both sides to finish the problem.

The integral of sqrt(sinx) is not exactly solvable. You will need elliptic integrals or when you use the substitution t=sinx, you will get a beta-function...

holy... geez talk about scaring a Calc 1 student... I don't even know how to approach some of those integrals... geez. The only thing that comes close that I can solve is probably applying an arctangent rule to no. 9 from my knowledge, but as marlon said I probably have to review partial fractions.