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int cos^(3)x.e^(log(sin x)) dx is equal ...

`int cos^(3)x.e^(log(sin x))` dx is equal to

A

`-(sin^(4)x)/(4)+c`

B

`-(cos^(4)x)/(4)+c`

C

`-(esin^(4)x)/(4)+c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `=int cos^(3)e^(log sin x)dx=int cos^(3)x sin dx`
`"Put "cos x=t Rightarrow -sin xdx=dt`
`therefore I=-int t^3dt=-(t^(4))/(4)+c =-(cos^(4)x)/(4)+c`
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