Question

Solve for the indefinite integral
e^x/(1+e^(2x))

Answer 1

\[\int\limits_{}^{}(e^x/(1+e ^{2x})dx \]
let u = e^x, then du = e^x dx. And note e^(2x) = (e^x)^2, or with the substitution, u^2:
\[= \int\limits_{}^{}(1/(1+u^2))du = \arctan(u) + C = \arctan(e^x) + C\]