Question

hi can any maths pro integrate sqrt(1+e^2x) dx?

Answer 1

http://www.wolframalpha.com/input/?i=+sqrt%281%2Be%5E%282x%29%29+dx

Click show steps. It's a bit early for me to see a better way of doing it.

Answer 2

\[\int\limits {\sqrt{1+ (e^x)^2}} dx\]

set

\[\tan u = e^x\]

now just use the trig identity sec^2 u = tan^2 u + 1