Integration of $\int \frac{e^x}{e^{2x} + 1}dx$ I came across this question and I was unable to solve it. I know a bit about integrating linear functions, but I don't know how to integrate when two functions are divided. Please explain. I'm new to calculus. 
Question: $$\int \frac{e^x}{e^{2x} + 1}dx$$
Thanks in advance. 

You may write
$$
\int \frac{e^x}{e^{2x} + 1}dx=\int \frac{d(e^x)}{(e^{x})^2 + 1}=\arctan (e^x)+C
$$ since
$$
\int \frac{1}{u^2 + 1}du=\arctan u+C.
$$
