Help me to find the antiderivative, please!?

Question

How to find the antiderivative of this : e^(x+sin x). Thanks

Answer 1

Who's asking you to do this? There is no closed form solution to this guy. Even if you break it down into a series to try to find some general recursion, if you take

e^x=1+x+x^2/2 + . . . and

sin(x) =x+x^3/6 . . ..

then you end up with x^x, which itself doesn't exist in closed form. I'm not saying that it can't be done, just that it hasn't. Good luck!

Answer 2

there is no solution to this problem.