If \(\int\frac{dx}{\sqrt{\sin^{3}x\left(\sin x+2\cos x\right)}}=f\left(x\right)+C\), then \(f\left(\frac{\pi}{4}\right)\) is equal to
Answer & explanation
Correct answer: option 3
\(\frac{1}{\sqrt{\sin^3 x\left(\sin x+2 \cos x\right)}}=\frac{\csc^2 x}{\sqrt{1+2\cot x}}\), put \(1+2\cot x=t^{2}\)