# Fun integrals to try

1. Nov 10, 2015

### LAZYANGEL

Hey folks,

found a couple of interesting integrals and was able to solve one of them ANALYTICALLY! That means no numerical solutions needed.

$$\int_{0}^{\frac{\pi}{2}} \frac{1}{1+(tan(x))^{\sqrt{2}}} dx$$

$$\int \frac{1}{1+e^{\frac{1}{x}}} dx$$

The first one I solved and will reveal analytic solution if no one can get it (it should be $$\frac{\pi}{4}$$).

Have fun!

To moderators: These are not homework or test problems, both of them are either from an old math olympiad and an old research paper.

2. Nov 11, 2015

### Staff: Mentor

Interesting integral, I tend to use my math handbook and just look these things up. However a method I learned recently was parametric integration. I don't know if that's what you used but I'll share a reference on it here in the interest of learning about new things:

http://www.maa.org/sites/default/files/268948443847.pdf