How does one integrate a quotient?

James2 · Oct 21, 2012

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

Thanks for the help!

Mark44 · Oct 21, 2012

James2 said:

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

Is this homework?

James2 · Oct 21, 2012

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 · Oct 21, 2012

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 · Oct 22, 2012

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

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