The value of $\int\frac{\sin x\cos x}{\sqrt{1-\sin^4x}}$ is equal to:
Answer & explanation
Correct answer: option 2
Put $\sin^2 x = t⇒2\sin x.\cos x\,dx=dt$ $⇒I=\frac{1}{2}\int\frac{dt}{\sqrt{1-t^2}}=\frac{1}{2}\sin^{-1}(t)+C=\frac{1}{2}\sin^{-1}(\sin^2x)+C$