The integral $\int \frac { 1 } { \left( x ^ { 2 } - 1 \right) ^ { \frac { 3 } { 2 } } } d x$ is

A) $\frac { - x } { 2 \sqrt { x ^ { 2 } - 1 } } + C$
B) $\frac { 2 x } { \sqrt { x ^ { 2 } - 1 } } + C$
C) $\frac { - 2 x } { \sqrt { x ^ { 2 } - 1 } } + C$
D) $\frac { x } { \sqrt { x ^ { 2 } - 1 } } + C$
E) $\frac { - x } { \sqrt { x ^ { 2 } - 1 } } + C$

Question

The integral $\int \frac { 1 } { \left( x ^ { 2 } - 1 \right) ^ { \frac { 3 } { 2 } } } d x$ is

A) $\frac { - x } { 2 \sqrt { x ^ { 2 } - 1 } } + C$
B) $\frac { 2 x } { \sqrt { x ^ { 2 } - 1 } } + C$
C) $\frac { - 2 x } { \sqrt { x ^ { 2 } - 1 } } + C$
D) $\frac { x } { \sqrt { x ^ { 2 } - 1 } } + C$
E) $\frac { - x } { \sqrt { x ^ { 2 } - 1 } } + C$

Quizplus · Accepted Answer

This integral can be solved using a trigonometric substitution, such as $x = \sec(\theta)$, which simplifies the integral into a form that can be directly integrated. The correct answer, after simplifying and substituting back for $x$, is $\frac{-x}{\sqrt{x^2 - 1}} + C$.

The Integral ∫1(x2−1)32dx\int \frac { 1 } { \left( x ^ { 2 } - 1 \right) ^ { \frac { 3 } { 2 } } } d x∫(x2−1)23​1​dx

The Integral $\int \frac { 1 } { \left( x ^ { 2 } - 1 \right) ^ { \frac { 3 } { 2 } } } d x$