मान निकालें : ∫ xe^x / (x+1)^2 dx

Question

मान निकालें : \(\int \frac {x e ^x}{(x+1)^2}dx\)

Answer 1

\(\mathrm{I}=\int \frac{x e^{x}}{(x+1)^{2}} d x=\int \frac{x}{(x+1)^{2}} e^{x} d x\)

\(\int\left[\frac{1}{(1+x)}-\frac{1}{1+x / 2}\right] e^{x} d x=\frac{1}{1+x} e^{x}+c\)

\(I = \frac {e ^x}{1+x} +c\)