Evaluate the integral.
-$$\int \frac { x d x } { \left( 7 x ^ { 2 } + 3 \right) ^ { 5 } }$$
A) $- \frac { 7 } { 3 } \left( 7 x ^ { 2 } + 3 \right) ^ { - 6 } + C$
B) $- \frac { 1 } { 14 } \left( 7 x ^ { 2 } + 3 \right) ^ { - 6 } + C$
C) $- \frac { 7 } { 3 } \left( 7 x ^ { 2 } + 3 \right) ^ { - 4 } + C$
D) $- \frac { 1 } { 56 } \left( 7 x ^ { 2 } + 3 \right) ^ { - 4 } + C$

Question

Quizplus · Accepted Answer

Substitute $u=7x^2+3$, which means $du=14xdx$. Now we will work on the integral in terms of $u$.
\begin{align*}
\int \frac { x d x } { \left( 7 x ^ { 2 } + 3 ight) ^ { 5 } } &= \frac{1}{14}\int \frac{du}{u^5} \
&= - \frac { 1 } { 56 } \left( 7 x ^ { 2 } + 3 ight) ^ { - 4 } + C 
\end{align*} 
Therefore, the answer is $\boxed{	extbf{(D)}}$.

Evaluate the Integral ∫xdx(7x2+3)5\int \frac { x d x } { \left( 7 x ^ { 2 } + 3 \right) ^ { 5 } }∫(7x2+3)5xdx​

Evaluate the Integral $\int \frac { x d x } { \left( 7 x ^ { 2 } + 3 \right) ^ { 5 } }$