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Question

Primitive of f(x)=x.2In(x2+1) with respect to x is

A
2In(x2+1)(x2+1)+C
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B
(x2+1)2In(x2+1)In2+1+C
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C
(x2+1)In2+12(In2+1)+C
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D
(x2+1)In22(In2+1)+C
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Solution

The correct option is C (x2+1)In2+12(In2+1)+C
I=x2In(x2+1)dx let x2+1=t;xdx=dt2
Hence I=122Intdt=12tIn2dt=12.tIn2+1In2+1+C=12.(x2+1)In2+1In2+1+C

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