Question

How to take integral:
(xe power X)dx/Sq of (1+e power X)

Answer 1

\[\Large \int\limits \frac{x e^x\;dx}{\sqrt{1+e^x}}\quad=\quad \int\limits \frac{e^x\;dx}{\sqrt{1+e^x}}\cdot x\]Hmm from this form I think we can successfully apply `Integration by Parts`.
You are familiar with this technique, yes?

Answer 2

The x isn't outside of the integral.
I shouldn't have written it AFTER the dx, sorry that was sloppy of me :)

Answer 3

\[\Large =\quad \int\limits\limits x\cdot\frac{e^x\;dx}{\sqrt{1+e^x}}\]

Answer 4

\[\Large\bf u=x,\qquad\qquad dv=\frac{e^x\;dx}{\sqrt{1+e^x}}\]
\[\Large\bf du=?, \qquad\qquad v=?\]