Let I(x) = ((x+1))/(x(1+xe^x)^2),dx, x0.

Question

Let $I(x) = \displaystyle\int\frac{(x+1)}{x(1+xe^x)^2}\,dx$, $x>0$. If $\displaystyle\lim_{x	o\infty}I(x)=0$, then $I(1)$ is equal to:

Accepted Answer

*(The full partial-fraction / substitution steps were not fully recoverable from the source text; the boundary condition at infinity fixes the constant of integration, and evaluating at $x=1$ yields the stated answer.)*

Solutions · 1