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Question

If I=dx(1+x)xx2, then I equals

A
2(x+1)1x+C
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B
2(x1)1x+C
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C
2(1x)x(1x)+C
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D
2(x1)x(1x)+C
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Solution

The correct option is B 2(x1)1x+C
I=dx(1+x)xx2
Substitute x=sin2t

Then, dx=2sintcostdt=sin2tdt
I=2sintcost(1+sint)sintcostdt

=2(tantsect)+c

=2sint1cost+c

=2sint11sin2t+c

I=2(x1)1x+c

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