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int(sinxcosx)/(sqrt(1-sin^(4)x)dx is equ...

`int(sinxcosx)/(sqrt(1-sin^(4)x)dx` is equal to

A

`(1)/(2)sin^(-1)(sin^(2)x)+C`

B

`(1)/(2)cos^(-1)(sin^(2)x)+C`

C

`tan^(-1)(sin^(2)x)+C`

D

`tan^(-1)(2sin^(2)x)+C`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int(sinx cos x)/(sqrt(1-sin^(4)x))dx`
Put`" "Sin^(2)x=t rArr 2 sin x cos x dx=dt`
`therefore" "l=int(dt)/(2sqrt(1-t^(2)))=(1)/(2)sin^(-1)t+C`
`=(1)/(2)sin^(-1)(sin^(2)x)+C`
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