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Question

cosx+xsinxx(x+cosx)dx is equal to

A
logxx+cosx+c
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B
logx+cosxx+c
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C
log1x+cosx+c
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D
log|x+cosx|+c
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Solution

The correct option is B logxx+cosx+c
cosx+xsinxx(x+cosx)dx=(x+cosx)x(1sinx)x(x+cosx)dx

=(1x1sinxx+cosx)dx=log|x|log|x+cosx|+c

=logxx+cosx+c

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