Evaluate the integral.
-$$\int ( 3 x + 7 ) e ^ { - 5 x } d x$$
A) $- \frac { 3 } { 5 } x e ^ { - 5 x } - \frac { 38 } { 25 } e ^ { - 5 x } + C$
B) $- 15 x e ^ { - 5 x } - 110 e ^ { - 5 x } + C$
C) $\frac { 3 } { 5 } x e ^ { - 5 x } + \frac { 38 } { 25 } e ^ { - 5 x } + C$
D) $- \frac { 3 } { 5 } x e ^ { - 5 x } - e ^ { - 5 x } + C$

Question

Quizplus · Accepted Answer

This integral can be solved using integration by parts, where $u = 3x + 7$ and $dv = e^{-5x}dx$. The derivative of $u$ is $du = 3dx$, and the integral of $dv$ is $v = -\frac{1}{5}e^{-5x}$. Applying the integration by parts formula, $\int u dv = uv - \int v du$, and simplifying, we obtain $- \frac { 3 } { 5 } x e ^ { - 5 x } - \frac { 38 } { 25 } e ^ { - 5 x } + C$, which matches choice A.

Evaluate the Integral ∫(3x+7)e−5xdx\int ( 3 x + 7 ) e ^ { - 5 x } d x∫(3x+7)e−5xdx

Evaluate the Integral $\int ( 3 x + 7 ) e ^ { - 5 x } d x$