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

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

A

`(1)/(32)[-(3)/(2)cos 2x+(1)/(6)cos 6x]+C`

B

`(1)/(16)[-(3)/(2)cos 2x+(1)/(6)cos 6x]+C`

C

`(1)/(64)[-(3)/(2)cos 2x +(1)/(6)cos 6x]+C`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
`intsin^(3)x cos^(3)x dx=(1)/(8)int(2sin x cosx)^(3)dx`
`=(1)/(8)intsin^(3)2xdx`
`=(1)/(8)int(3sin2x-sin6x)/(4)dx`
`=(1)/(32)int(3sin2x-sin6x)dx`
`=(1)/(32)[-(3)/(2)cos2x+(1)/(6)cos 6x]+C`
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