Question

$\int \frac{cotx}{\sqrt[3]{sinx}}dx=$

• A. $\frac{-3}{\sqrt[3]{sinx}}+C$
• B. $\frac{-2}{si{n}^{3}x}+C$
• C. $\frac{3}{si{n}^{\frac{1}{3}}x}+C$
• D. None of these

Answer 1

Answer: (A)

$I=\int \frac{cotx}{\sqrt[3]{sinx}}dx=\int \frac{cosx}{si{n}^{\frac{1}{3}}x\cdot sinx}dx$

$=\int \frac{cosx}{si{n}^{\frac{4}{3}}x}dx=\int si{n}^{-\frac{4}{3}}x\cdot cosx$dx

Put $sinx=t\Rightarrow cosxdx=dt$

$\Rightarrow I=\int t^{-\frac{4}{3}}dt=\frac{t^{-\frac{1}{3}}}{-\frac{1}{3}}+C=\frac{-3}{\sqrt[3]{sinx}}+C$