Use a CAS to perform the integration.
-$$\int x ^ { 6 } \ln x d x$$
A) $\frac { x ^ { 7 } } { 7 } \ln x + \frac { x ^ { 7 } } { 49 } + C$
B) $\frac { x ^ { 7 } } { 7 } \ln x - \frac { x ^ { 8 } } { 56 } + C$
C) $\frac { x ^ { 7 } } { 7 } \ln x - \frac { x ^ { 7 } } { 7 } + C$
D) $\frac { x ^ { 7 } } { 7 } \ln x - \frac { x ^ { 7 } } { 49 } + C$

Question

Quizplus · Accepted Answer

Using integration by parts, let $u=\ln x$ and $dv=x^6 dx$. Then $du = \frac{1}{x} dx$ and $v = \frac{1}{7}x^7$. Thus, 
\begin{align*}
\int x^6 \ln x dx &= \frac{1}{7}x^7 \ln x - \int \frac{1}{7}x^7 \cdot \frac{1}{x} dx \
&= \frac{1}{7}x^7 \ln x - \frac{1}{49} x^7 + C.
\end{align*}
Thus, the best choice is $\boxed{	ext{(D)}}$.

Use a CAS to Perform the Integration ∫x6ln⁡xdx\int x ^ { 6 } \ln x d x∫x6lnxdx

Use a CAS to Perform the Integration $\int x ^ { 6 } \ln x d x$