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Q.

∫xex(1+x)2dx is equal to

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a

ex1+x+C

b

−11+x+C

c

−ex(1+x)+C

d

ex(1+x)2+C

answer is A.

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Detailed Solution

Let I=∫xex(1+x)2dx=∫ex(x+1)−1(1+x)2dx=∫ex1(1+x)−1(1+x)2dxLet f(x)=11+x⇒f′(x)=−1(1+x)2we know that ∫exf(x)+f′(x)dx=exf(x)⇒ I=∫ex11+x−1(1+x)2dx=ex1+x+C

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∫xex(1+x)2dx is equal to