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=(1)/(a)\cdot e^(ax) \\ du=nx^(n-1) \end{gathered}`

Applying the formula

`\begin{gathered} uv-\int vdu \\ x^n\cdot(1)/(a)\cdot e^(ax)-\int (1)/(a)\cdot e^(ax)\cdot nx^(n-1) \end{gathered}`

Answer:

`(x^n\cdot(1)/(a)\cdot e^(ax))-\int ((1)/(a)\cdot e^(ax)\cdot nx^(n-1))`