Q. $\int_{}^{}\frac{dx}{\sqrt[4]{(x + 1)^{5}(x + 2)^{3}}}$ is equal to
A) $4\left( \ \frac{x + 1}{x + 2}\ \right)^{1/4} + c$
B) $- 4\ \left( \ \frac{x + 1}{x + 2}\ \right)^{- 1/4} + c$
C) $- 4\ \left( \ \frac{x + 2}{x + 1}\ \right)^{1/4} + c$
D) None of these
Explanation
(c)
Let $I = \int_{}^{}\frac{dx}{\sqrt[4]{(x + 1)^{5}(x + 2)^{3}}}$
Put $\frac{x + 1}{x + 2} = t\ \Rightarrow \ \frac{1}{(x + 2)^{2}}dx = dt$
$\therefore I = \int_{}^{}{\frac{dt}{t^{5/4}}\ \Rightarrow I = \frac{t^{- 1/4}}{\left( \ - \frac{1}{4}\ \right)} + c}$
$\Rightarrow I = - 4\ \left( \ \frac{x + 2}{x + 1}\ \right)^{1/4} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.