Finding the integral of an improper fraction

[howsockgothap]

Homework Statement

Use substitution to find the integral of (12x² + X -12)/(3x - 2)

Homework Equations

The Attempt at a Solution

I know I need to use long division to work it down to a proper fraction. That is where my real problem lies. Using long division I get that (12x²+x-12)/(3x-2) is equal to 4x-3 with a remainder of -6. I don't really understand what that means in terms of my question, especially with the remainder. Does this just mean that I have to find the integral of (4x-3) - 6/(3x-2)?

 

[gb7nash]

Does this just mean that I have to find the integral of (4x-3) - 6/(3x-2)?

Yes, assuming that your long division is correct. You should know how to take the integral of (4x-3) - 6/(3x-2).

 

[howsockgothap]

right on, thanks.