Q113 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics

$\int e^x(x+1)^2 d x=$

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

Solution

$\begin{aligned} & \text { } \int e^x(x+1)^2 d x=(x+1)^2 e^x-\int 2(x+1) e^x d x \\ & =(x+1)^2 e^x-2\left[\int x e^x d x+\int e^x d x\right] \\ & =(x+1)^2 e^x-2\left[x e^x-e^x+e^x\right]+c=\left(x^2+1\right) e^x+c\end{aligned}$

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

Relevant Questions