Question

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

• 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)

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