Q101 / 200 · TS EAMCET 2001 · Mathematics

$\int(x+1)^2 e^x d x$ is equal to

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

Solution

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

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

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