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Question

[log(1+cosx)xtan(x2)]dx

A
xlog(1+tanx)
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B
xlog(1+sinx)
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C
log(1+sinx)
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D
xlog(1+cosx)
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Solution

The correct option is C xlog(1+cosx)
I=log(1+cosx)dxxtan(x/2)dx
I=xlog(1+cosx)+xsinx1+cosxdxxtanx2.
=xlog(1+cosx) second term gets cancel [sinx1+cosx=tanx2]
=xlog(1+cosx)

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