How come the antiderivative of e^(2x+x^2) isn't e^(2x+x^2)/(x+2x)??
I know the anti derivative of e^(x^2) cannot be defined using elem. functions, so i guess e^(2x+x^2) is kinda like that, but it seemed to make sense to me when I antiderived it using substitution like this :
S e^u = e^u + C
let u= 2x+x^2
du = 2+2x dx
S e^(2x+x^2) dx= S e^u * du/2+2x = e^(2x+x^2)/2+2x
Doesn't that make sense? what am I doing wrong? or is that the antiderivative of e^(2x+x^2) altho I'm pretty sure it isn't?? does this have something to do with chain rule??