Find the indefinite integral.
$$\int x ^ { - 2 / 3 } \sqrt { x ^ { 1 / 3 } - 2 } d x$$
A) $2 \left( x ^ { 1 / 3 } - 2 \right) ^ { 3 / 2 } + C$
B) $2 x ^ { 1 / 3 } \left( x ^ { 1 / 3 } - 2 \right) ^ { 3 / 2 } + C$
C) $\frac { 1 } { 2 } \left( x ^ { 1 / 3 } - 2 \right) ^ { 3 / 2 } + C$
D) $x ^ { 1 / 3 } \left( x ^ { 1 / 3 } - 2 \right) ^ { 3 / 2 } + C$

Question

Quizplus · Accepted Answer

Using substitution $ u = x^{1/3} - 2 $, the integral simplifies to a form where the antiderivative is $ 2(u)^{3/2} + C $.

Find the Indefinite Integral ∫x−2/3x1/3−2dx\int x ^ { - 2 / 3 } \sqrt { x ^ { 1 / 3 } - 2 } d x∫x−2/3x1/3−2​dx

Find the Indefinite Integral $\int x ^ { - 2 / 3 } \sqrt { x ^ { 1 / 3 } - 2 } d x$