Question

How can I solve the integral of: x*e^x/(1+x)^2 ? Thanks.

Answer 1

look at a quotient rule

observe if \[f(x) = e^{x}\] and \[g(x) = x +1\] so that \[h(x) = f(x)/g(x)\]

if you take the derivative of h(x) you will get exactly what you have. then just rewrite it as
\[\int\limits (e ^{x}/(x+1)) d/dx\]

and integral negates the derivative and you have the answer plus a constant of integration C