Thread: 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

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?

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)

Have you tried this already?

WRT x

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

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.

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.

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