Evaluate the indefinite integral. $\int x \cos 9 x d x$
A) $\frac{1}{81} \sin 9 x+\frac{x}{9} \cos 9 x+C$
B) $\frac{1}{81} \cos 9 x+\frac{x}{9} \sin 9 x+C$
C) $\frac{1}{9} \cos 9 x+\frac{x}{9} \sin 9 x+C$
D) $\frac{x}{81} \cos 9 x+\frac{x}{9} \sin 9 x+C$
E) $\text { None of these }$

Question

Quizplus · Accepted Answer

We can apply integration by parts with $u=x$ and $dv=\cos(9x)dx$. Then $du=dx$ and $v=\frac{1}{9}\sin(9x)$.
\begin{align*}
\int x\cos(9x)dx&=x\cdot\frac{1}{9}\sin(9x)-\int \frac{1}{9}\sin(9x)dx\
&=\frac{x}{9}\sin(9x)+\frac{1}{81}\cos(9x)+C
\end{align*}
Thus, the answer is $\boxed{	extbf{(B)}}$.

Evaluate the Indefinite Integral ∫xcos⁡9xdx\int x \cos 9 x d x∫xcos9xdx

Evaluate the Indefinite Integral $\int x \cos 9 x d x$