Thread: Integration

$\displaystyle \int \frac{e^x}{1+e^{2x}}$

Could someone explain how to solve this?

Make the sub $\displaystyle u=e^{x}, \;\ du=e^{x}dx$

After making the subs, the resulting integral should look familiar and a cakewalk from there on out.

Originally Posted by Haris

$\displaystyle \int \frac{e^x}{1+e^{2x}}\, $

Could someone explain how to solve this?

$\displaystyle \int \frac{e^x}{1+e^{2x}}\,dx $ (note the dx - it's important)

Try letting $\displaystyle u = e^x$

$\displaystyle I=tan^{-1}(e^x)$

Is that correct?

Originally Posted by Haris

$\displaystyle I=tan^{-1}(e^x) + c$

Is that correct?