integrate by parts

Question

(2x^2 + x) / (x^2 + x - 2) dx Integrate by parts

Answer 1

Definitely use fractional decomposition, I can see that the denominator can be broken down into simpler parts and that once you do, you should be able to integrate this. I don't really recommend integration by parts all that often when it comes to fractional functions like these.

Answer 2

Dear Karl,

 

I don't do other people's homework, but I will give you some hints to help you along.

 

[(2x^2 + x)/(x^2 + x - 2)]dx can be written as   [x][(2x + 1)/(x^2 + x - 2)]dx

 

Take U = x   and  dV = [(2x + 1)/(x^2 + x - 2)]dx

 

Then UdV = UV - VdU

 

To do the integral VdU you will need the property of logarithm: ln(ab) = ln(a) + ln(b)

and integral ln(x)dx = xln(x) - x.

 

Good luck.

 

If you need a tutor, I do tutor online and you can contact me through Wyzant.

 

PG Tran