Q218 / 270 · NDA 2015 (Phase 1) · Mathematics

What is $\int \frac{x e^x d x}{(x+1)^2}$ equal to? where $c$ is the constant integration.

  • A
    $(x+1)^2 e^x+c$
  • B
    $(x+1) e^x+c$
  • Correct answer
    C
    $\frac{e^x}{x+1}+c$
  • D
    $\frac{e^x}{(x+1)^2}+c$

Solution

$\begin{aligned} & \int \frac{x e^x}{(1+x)^2} d x \\ & =\int e^x\left[\frac{1}{1+x}-\frac{1}{(1+x)^2}\right] d x \\ & =\frac{e^x}{1+x}+C \quad\left\{\int e^x\left(f(x)+f^{\prime}(x)\right) d x=e^x f(x)\right\}\end{aligned}$

Hence, the correct answer is option: 'C'.

Relevant Questions