AP EAMCET · Maths · Indefinite Integration
\(\int e^x(x+1)^2 d x=\)
- A \(x e^{\mathrm{x}}+c\)
- B \(e^2 x^2+c\)
- C \(e^x\left(x^2+1\right)+c\)
- D \(e^{\mathrm{x}}(x+1)+c\)
Answer & Solution
Correct Answer
(C) \(e^x\left(x^2+1\right)+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \int e^x(x+1)^2 d x=(x+1)^2 e^x-\int 2(x+1) e^x d x \\ & =(x+1)^2 e^x-2\left[\int x e^x d x+\int e^x d x\right] \\ & =(x+1)^2 e^x-2\left[x e^x-e^x+e^x\right]+c=\left(x^2+1\right) e^x+c\end{aligned}\)
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