Question

$\int_{}^{}\sqrt{\frac{\cos^{3}x}{\sin^{11}x}}$ dx is equal to –

• A. $\frac{- 2}{5}$cot^3/2 x –$\frac{2}{9}$cot^9/2 x + c
• B. $\frac{- 2}{5}$cot^5/2 x – $\frac{2}{9}$cot^9/2 x + c
• C. $\frac{- 2}{5}$ cot^5/2 x – $\frac{2}{9}$cot^3/2 x + c
• D. None of these

Answer 1

Answer: (B)

$\frac{- 2}{5}$cot^5/2 x – $\frac{2}{9}$cot^9/2 x + c

Answer 2

Since sum of powers of

cos x and sin x = $\frac{3}{2}$ + $\left( - \frac{11}{2} \right)$ = – 4,

we will put tan x = t