How does one integrate a quotient?

[James2]

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

Thanks for the help!

 

[Mark44]

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

Is this homework?

 

[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.

 

[Mark44]

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."

 

[JJacquelin]

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