Question

`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`

Answer 1

Correct Answer - 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`