Question

Make substitutions in the integration by parts formula and simplify.

Answer 1

For integral by parts

Your exercise inform:

Therefore

$\begin{gathered} u=x^n \\ v=\frac{1}{a}\cdot e^{ax} \\ du=nx^{n-1} \end{gathered}$

Applying the formula

$\begin{gathered} uv-\int vdu \\ x^n\cdot\frac{1}{a}\cdot e^{ax}-\int \frac{1}{a}\cdot e^{ax}\cdot nx^{n-1} \end{gathered}$

Answer:

$(x^n\cdot\frac{1}{a}\cdot e^{ax})-\int (\frac{1}{a}\cdot e^{ax}\cdot nx^{n-1})$