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

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ex+c

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detailed solution

Correct option is D

I=∫xex1+x2dx=∫exx+1−1(x+1)2dx∵∫exf(x)+f′(x)dx=exf(x)+cI=∫ex1x+1−1(x+1)2dx=ex1x+1+c=exx+1+c

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