Question

$\int \frac{d x}{\sqrt[3]{x^{5 / 2}(x+1)^{7 / 2}}}$

• A. $-\left(\frac{ x +1}{ x }\right)^{1 / 6}+ C$
• B. $6\left(\frac{ x +1}{ x }\right)^{-1 / 6}+ C$
• C. $\left(\frac{x}{x+1}\right)^{5 / 6}+C$
• D. $-\left(\frac{x}{x+1}\right)^{5 / 6}+C$

Answer 1

Answer: (B)

$\int \frac{d x}{\left[x^6\left(1+\frac{1}{x}\right)^{7 / 2}\right]^{1 / 3}}=\int \frac{d x}{x^2\left(1+\frac{1}{x}\right)^{7 / 6}} $
now put $1+\frac{1}{x}=t^6$