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Question

e(sinx1x)(1+x cosx+1x)dx is

A
cosx.e(sinx1x)+c
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B
1x.e(sin1x)+c
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C
x.e(sin x1x)+c
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D
e(sinx1x)+x+c
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Solution

The correct option is C x.e(sin x1x)+c
e(sinx1x)(1+x cosx+1x)dx
=e(sinx1x)dx+x.e(sinx1x)(cosx+1x2)dx
=1e(sinx1x)dx+x.e(sinx1x)(cosx+1x2)dx
=x.e(sinx1x)x.e(sinx1x)(cosx+1x2)dx+x.e(sinx1x)(cosx+1x2)dx+c
=x.e(sinx1x)+c

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