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Question

cosx+xsinxx(x+cosx)dx=

A
log|xx+cosx|+c
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B
log|xx+cosx|+c
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C
log|x+cosx2x|+c
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D
log|x+cosx2x|+c
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Solution

The correct option is D log|xx+cosx|+c
x+cosx+xsinxxx(x+cosx)dx=x+cosxx(x+cosx)dxxxsinxx(x+cosx)dx=lnxln|x+cosx|=log|xx+cosx|+c

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