How do you evaluate \int 6x e ^ { 5x } d x ?

1 Answer
Dec 19, 2017

(6xe^(5x))/5-6/25e^(5x)+c

Explanation:

Take the integral

int6xe^(5x)dx

Factor out constants

6intxe^(5x)dx

For the integrand xe^(5x) integrate by parts,

u=x
du=dx

dv=e^(5x)dx
v=e^(5x)/5

6intxe^(5x)dx=6((xe^(5x))/5-inte^(5x)/5dx)

inte^(5x)/5dx=e^(5x)/25

6intxe^(5x)dx=6((xe^(5x))/5-e^(5x)/25)+c

6intxe^(5x)dx=(6xe^(5x))/5-6/25e^(5x)+c