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Question

If sinxsin(xα) dx=Ax+Blogsin(xα)+c then value of (A,B) is:

A
(sinα,cosα)
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B
(cosα,sinα)
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C
(sinα,cosα)
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D
(cosα,sinα)
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Solution

The correct option is B (cosα,sinα)
Let I=sinxsin(xα)dx

Put xα=tdx=dt

I=sin(t+α)sintdt=sintcosα+costsinαsintdt

=cosαdt+sinαcostsintdt

=tcosα+sinαlogsint+c

=cosα(xα)+sinαlogsin(xα)+c

=xcosα+αcosα+sinαlogsin(xα)+c

=xcosα+sinαlogsin(xα)+C

A=cosα,B=sinα

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