Question

evaluate the integral using integration by parts with the indicated choices of u and dv. (use c for the constant of integration.) xe5x dx; u

Answer 1

`\displaystyle \int {xe^(5x)} \, dx=(1)/(5)xe^(5x)-(1)/(25)e^(5x)+C`

Explanation:

Given Problem

`\displaystyle \int {xe^(5x)} \, dx`

Make substitutions for IBP

Let
`u=x,\,du=dx` and
`v=(1)/(5)e^(5x),\,dv=e^(5x)dx`

Perform IBP

`\displaystyle \int {u} \,dv=uv-\int {v} \, du\\\\\int {xe^(5x)} \, dx=(1)/(5)xe^(5x) -\int {(1)/(5)e^(5x)} \, dx\\\\\displaystyle \int {xe^(5x)} \, dx=(1)/(5)xe^(5x)-(1)/(25)e^(5x)+C`