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Question

Evaluate 101x1+x.dxx+x2+x3

A
π3
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B
π6
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C
π12
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D
π4
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Solution

The correct option is A π3
l=101x1+xdxx+x2+x3
=10(1x2)(x2+2x+1)x+x2+x3
=101x21dx(x+1x+2)x+1x+1
Put x+1x+1=t2(11x2dx)=2tdt
l=32tdt(t2+1)t=23dtt2+1=2[tan1]3=π3

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