# How does one integrate a quotient?

1. Oct 21, 2012

### James2

How do you integrate quotients? Let's practice with one like... $$\int\frac{3x + x^{2}}{5x - 1} dx$$

Thanks for the help!

Last edited by a moderator: Oct 21, 2012
2. Oct 21, 2012

### Staff: Mentor

Is this homework?

3. Oct 21, 2012

### James2

No, I just pulled that one out of thin air. This will help me with homework in the future, but right now, that is just an example.

4. Oct 21, 2012

### Staff: Mentor

I would use polynomial long division to write the integrand as a polynomial plus a remainder term that is a proper rational expression. If you don't know this technique, do a search on wikipedia for "polynomial long division."

5. Oct 22, 2012

### JJacquelin

Another method : change of variable
t=5x-1
Rewrite the integral with t and dt (witout x nor dx in it)