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Question

The value of cos3xsin2x+sinxdx is equal to

A
loge|sinx|+sinx+C
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B
loge|sinx|sinx+C
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C
loge|sinx|=sinx+C
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D
loge|sinx|+sinx+C
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Solution

The correct option is B loge|sinx|sinx+C
Let I=cos3xsin2x+sinxdx

I=cos2x.cosxsin2x+sinxdx

I=(1sin2x).cosxsin2x+sinxdx

Let sinx=t
cosxdx=dt
I=(1t2)t2+tdt

I=(1t)(1+t)t(1+t)dt

I=(1t)tdt

I=1tdt(1)dt

I=loge|t|t+c
Now, re-substituting value of t, we get:
I=loge|sinx|sinx+c




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