Evaluate $\int x e ^ { x / 5 } d x$
A) $5 x e ^ { x / 5 } + 25 e ^ { x / 5 } + C$
B) $\frac { x e ^ { x / 5 } } { 5 } + \frac { e ^ { x / 5 } } { 25 } + C$
C) $\frac { x e ^ { x / 5 } } { 5 } - \frac { e ^ { x / 5 } } { 25 } + C$
D) $5 x e ^ { x / 5 } - 25 e ^ { x / 5 } + C$

Question

Quizplus · Accepted Answer

The integral can be solved using integration by parts. Let $ u = x $ and $ dv = e^{x/5} dx $. Then $ du = dx $ and $ v = 5e^{x/5} $. Applying integration by parts, $\int u \, dv = uv - \int v \, du$, we get $5x e^{x/5} - \int 5 e^{x/5} dx = 5x e^{x/5} - 25 e^{x/5} + C$.

Evaluate ∫xex/5dx\int x e ^ { x / 5 } d x∫xex/5dx

Evaluate $\int x e ^ { x / 5 } d x$