# Calc 121

posted by
**Me**
.

How do you integrate using substitution: the integral from 1 to 3 of: ((3x^2)+(2))/((x^3)+(2x))

There is a trick to this one that grealy simplifies the integral.

Let u = x^3 + 2x. Then

du = (3x^2 + 2)dx

The integral then bemoces just the integral of du/u, which is

ln u = ln (x^3 + 2x)

The limits of integration are from 1 to 3, so the answer is

ln (27 + 6) - ln (1+2) = ln 33/3 = ln 11

THANK YOU SOOOOOOOOOOOO MUCH!!! I actually understand that. Thanks!