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Question

Primitive of f(x)=x.2ln(x2+1) w.r.t x is

A
2ln(x2+1)2(x2+1)+C
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B
(x2+1)2ln(x2+1)ln2+1+C
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C
(x2+1)(ln2+1)2(ln2+1)+C
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D
(x2+1)ln22(ln2+1)+C
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Solution

The correct option is B (x2+1)(ln2+1)2(ln2+1)+C
By logarithmic property,2ln(x2+1)=(x2+1)ln2
=>x.(x2+1)ln2dx
Let,
x2+1=t
=>2xdx=dt=>xdx=dt2
=>12(t)ln2dt
=t(ln2+1)2(ln2+1)+c
=(x2+1)(ln2+1)2(ln2+1)+c

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