Use integration by parts to establish a reduction formula for the integral.
-$\int x ^ { n } e ^ { x } d x$
A) $\int x ^ { n } e ^ { x } d x = x ^ { n } e ^ { x } + n \int x ^ { n - 1 } e ^ { x } d x$
B) $\int x ^ { n } e ^ { x } d x = x ^ { n } e ^ { x } - n \int x ^ { n - 1 } e ^ { x } d x$
C) $\int x ^ { n } e ^ { x } d x = x ^ { n } e ^ { x } - \frac { 1 } { n + 1 } \int x ^ { n - 1 } e ^ { x } d x$
D) $\int x ^ { n } e ^ { x } d x = x ^ { n } e ^ { x } - n \int x ^ { n + 1 } e ^ { x } d x$

Question

Quizplus · Accepted Answer

Integration by parts formula is $\int u \, dv = uv - \int v \, du$. Let $u = x^n$ and $dv = e^x \, dx$. Then $du = n x^{n-1} \, dx$ and $v = e^x$. Applying the formula gives $\int x^n e^x \, dx = x^n e^x - n \int x^{n-1} e^x \, dx$.

Use Integration by Parts to Establish a Reduction Formula for the Integral