need help with two integral problems

[slinky2004]

I've been trying to figure these two out and i'm just stumped.
1. S(x^5)/(13+x^12)

i've tried using trig substitution and the parts formula and i can't evaluate it.

2. S(e^-x)/(1+e^-2x)

it's an improper integral and the integral is from -infinity to infinity. so far, i've broken it into two integrals, one from -infinity to c and one from c to infinity. can somebody show me how to work this one out?

 

[soroban]

Hello, slinky2004!

\(\displaystyle 1)\;\;\L\int \frac{x^5}{13\,+\,x^{12}}\,dx\)

\(\displaystyle \text{Let }u\,=\,x^6\)

\(\displaystyle 2)\;\;\L\int \frac{e^{-x}}{1\,+\,e^{-2x}}\,dx\)

\(\displaystyle \text{Let }u\,=\,e^{-x}\)


Both turn out to be of the \(\displaystyle \arctan\) form.

 

[slinky2004]

so for #1, i would make the 13 into the square root of 13, squared?