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Question

Evaluate x1(x+1)x3+x2+xdx

A
tan1(x+1x+1)+c
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B
2tan1(x+1x+1)+c
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C
tan1(x+1x1)
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D
tan1(x1x+1)+c
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Solution

The correct option is B 2tan1(x+1x+1)+c
I=(x1)dx(x+1)x3+x2+x
=(x21)(x2+2x+1)x3+x2+x
=(11x2)dx(x+1x+2)x+1x+1
Substitute x+1x+1=μ2,
I=2μdu(μ2+1)μ=2tan1μ+c
=2tan1(x+1x+1)+c

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