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What is int sin ^(3) x cos x dx equal to...

What is `int sin ^(3) x cos x dx` equal to ?
Where c is the constant of integration

A

`cos^(4) x + c`

B

`sin^(4) x + c`

C

`((1 - sin^(2)x)^(2))/(4) + c`

D

`((1 - cos^(2) x)^(2))/(4) + c`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `t = sin x rArr dt = cos x dx`
`int sin^(3) x cos x dx = int t^(3) dt = (t^(4))/(4) + c = (sin^(4)x)/(4) + c`
`= ((1 - cos^(2)x)^(2))/(4) + c`
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