How do you integrate int xe^(x/2) dx?

1 Answer
Aug 23, 2015

Use integration by parts with u = x and dv = e^(x/2)dx.

Explanation:

int xe^(x/2) dx

Let u = x " "and " " dv = e^(x/2)dx

So du = dx " " and " " v = 2e^(x/2) " "(use substitution w = x/2)

int xe^(x/2) dx = (x)(2e^(x/2)) - int 2e^(x/2) dx

= 2xe^(x/2) - 2 int e^(x/2) dx " "(again use substitution w = x/2)

= 2xe^(x/2) - 4e^(x/2) +C