# Math Help - integration method

1. ## integration method

what method would you use to integrate:

y^4*((x+1)/((x-2)(x^2+5)))

Thought it would be partial fractions and by parts but doesn't seem to work, thanks

2. Originally Posted by jpquinn91
what method would you use to integrate:

y^4*((x+1)/((x-2)(x^2+5)))

Thought it would be partial fractions and by parts but doesn't seem to work, thanks
Which variable are you integrating with respect to?

3. I'm assuming you're integrating with respect to x which means y is a constant and can be placed outside the integral.

Which leaves you with:
(x+1)/((x-2)(x^2+5)) = A / (x-2) + (Bx + C) / (x^2 + 5)

4. WRT x

OK, I got A=1/3 , B=-1/3 & C=1/3 but I dont know how to integrate those fractions

5. Originally Posted by jpquinn91
WRT x

OK, I got A=1/3 , B=-1/3 & C=1/3 but I dont know how to integrate those fractions
So you have (1/3) / (x-2), the derivative of ln(u) is du/u.

All you do is take the 1/3 and put it in front to get: 1/3ln(x-2). Hope that made sense, let me know if you can't get the next one.

6. OK that makes sense but I'm not sure about the 2nd 1.

I got -1/6(ln(x^2+5) as I took the 1/3 out and then -1/2 out so the top would be -2x (derivative of denominator) but not sure if you're allowed to do all that.

7. I didn't realize this at first, but I think you need to use complex numbers to solve this. I've never had to do this with partial fractions, but I did find this link Integration by Partial Fractions Check out the example about 1/4 down, that should help. As far as I can tell, partial fractions should still work