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Question

Find (3sinθ2)cosθ5cos2θ4sinθdθ.

A
I=ln|sinθ2|4sinθ2+C
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B
I=3ln|sinθ2|4sinθ2+C
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C
I=3ln|cosθ2|4sinθ2+C
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D
None of these
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Solution

The correct option is C I=3ln|sinθ2|4sinθ2+C
(3sinθ2)cosθ5cos2θ4sinθdθ
(3sinθ2)cosθsin2θ4sinθ+4dθ
Putting sinθ=m
cosθdθ=dm
3m2m24m+4dm
3(m2)+4(m2)2dm
3m2dm+4(m2)2dm
3ln|m2|4m2+C
I=3ln|sinθ2|4sinθ2+C

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