Evaluate the integral using integration by parts.
-$\int x e ^ { 3 x } d x$
A) $\frac { 1 } { 6 }$ $x ^ { 2 }$ $e ^ { 3 x }$ + C
B) $e ^ { 3 x }$ $\left( \frac { 1 } { 3 } x - \frac { 1 } { 9 } \right)$ + C
C) $e ^ { 3 x }$ $\left( \frac { 1 } { 3 } x - 1 \right)$ + C
D) $\frac { 1 } { 3 }$ $e ^ { 3 x }$ + C

Question

Quizplus · Accepted Answer

Integration by parts formula is $\int u dv = uv - \int v du$. Let $u = x$ and $dv = e^{3x}dx$, then $du = dx$ and $v = \frac{1}{3}e^{3x}$. Applying the formula, we get $uv - \int v du = x(\frac{1}{3}e^{3x}) - \int \frac{1}{3}e^{3x} dx = \frac{1}{3}xe^{3x} - \frac{1}{9}e^{3x} + C$.

Evaluate the Integral Using Integration by Parts ∫xe3xdx\int x e ^ { 3 x } d x∫xe3xdx

Evaluate the Integral Using Integration by Parts $\int x e ^ { 3 x } d x$