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Question

The integral dx(1+x)xx2 is equal to: (where C is a constant of integration).

A
21x1+x+C
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B
21+x1x+C
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C
1x1+x+C
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D
21+x1x+C
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Solution

The correct option is A 21x1+x+C
I=dx(1+x)xx2
Put x=cos2θdx=2cosθsinθdθI=2cosθsinθdθ(1+cosθ)cosθsinθ=2dθ2cos2θ2=sec2(θ2)dθ=2tanθ2+Ccosθ=x,and tanθ2=1cosθ1+cosθI=21x1+x+C

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