Use integration by parts to find the integral.
-$\int 3 x e^{x} d x$
A) $3 x e^{x}-3 e^{x}+C$
B) $3 e^{x}-e^{x}+C$
C) $3 e^{x}-3 x e^{x}+C$
D) $x e^{x}-3 e^{x}+C$

Question

Quizplus · Accepted Answer

Integration by parts formula is $\int u \, dv = uv - \int v \, du$. Let $u = 3x$ and $dv = e^x \, dx$. Then $du = 3 \, dx$ and $v = e^x$. Applying the formula gives $\int 3x e^x \, dx = 3x e^x - \int 3 e^x \, dx = 3x e^x - 3 e^x + C$.

Use Integration by Parts to Find the Integral ∫3xexdx\int 3 x e^{x} d x∫3xexdx

Use Integration by Parts to Find the Integral $\int 3 x e^{x} d x$