Question

The integral $\displaystyle\int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}}\,dx$ is equal to: (where $C$ is a constant of integration)}

• A. $\dfrac{3}{4}\left(\dfrac{x+2}{x-1}\right)^{1/4} + C$
• B. $\dfrac{3}{4}\left(\dfrac{x+2}{x-1}\right)^{5/4} + C$
• C. $\dfrac{4}{3}\left(\dfrac{x-1}{x+2}\right)^{1/4} + C$
• D. $\dfrac{4}{3}\left(\dfrac{x-1}{x+2}\right)^{5/4} + C$

Hint:

For integrals with fractional powers of two linear factors, try the substitution $t = \dfrac{ax+b}{cx+d}$, which turns the integral into a simple power function.

Answer 1

The Correct Option is C