Question

does this have a simple solution?

Answer 1

\[\int\limits_{ }^{ } \frac{e^x+xe^x}{\sqrt{1-\left(x+e^x \right)^2}}dx\]and darn it, I am 100% in parenthesis is a plus, not a multiplication sign.

Answer 2

100% *sure*

Answer 3

u=e^x fails, I guess. I tried that 4 times, but I get
\[\int\limits_{ }^{ } \frac{1+\ln(u)}{\sqrt{1-\left(\ln(u)+u \right)^2}}du\] which is even worse.

Answer 4

what makes you think there exists an elementary solution ?
http://www.wolframalpha.com/input/?s=32&_=1423536355565&fp=1&i=%5cint+%5cfrac%7be%5ex%2bxe%5ex%7d%7b%5csqrt%7b1-%5cleft(x%2be%5ex+%5cright)%5e2%7d%7ddx&incTime=true

Answer 5

Is that a proof by Wolfram Alpha lol?

Answer 6

lol, it didn't get the interpretation of how you copy pasted my latex

Answer 7

http://www.wolframalpha.com/input/?i=integral+%28e%5Ex%2Bxe%5Ex%29%2F √%281-%28x%2Be%5Ex%29%5E2%29+dx

Answer 8

but I guess, no then....

Answer 9

yeah for most complicated integrals, you shouldn't expect... actually existence of elementary function is an excuse most of the times, not a rule :P