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Question

Integrate cosxsinx1+sin2x

A
1sinx+cosx+C
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B
1sinx+cosx+C
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C
1sinxcosx+C
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D
1sinx+C
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Solution

The correct option is B 1sinx+cosx+C

I=(cosxsinx1+2sinxcosx)dx=(cosxsinxsin2x+cos2x+2sinxcosx)dx=cosxsinx(sinx+cosx)2dxletsinx+cosx=t(cosxsinx)dx=dt=(dtt2)=(1t)+c=(1(sinx+cosx))+c


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