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a
ex1+x+C
b
−11+x+C
c
−ex(1+x)+C
d
ex(1+x)2+C
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Correct option is A
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+CSimilar Questions
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