What type of integration to use?

1. Feb 22, 2014

jdawg

1. The problem statement, all variables and given/known data
∫(x2+9x)/(4x2) dx

2. Relevant equations

3. The attempt at a solution
I started by using trigonometric substitution:
x2=9tan2θ
x=3tanθ
dx=3sec2θ dθ

∫9(sec2θ)/4(9tan2)*3sec2θ dθ

(3/4)∫(sec4θ)/(tan2θ) dθ

I'm not really sure what to do next, or if I even used the best method of integration. Could I maybe use u substitution and let tanθ=u? Or maybe rewrite the integral as (1/cos4θ)/(sin2θ/cos2θ)
Please help! Also if you have any tips on how to spot which integration techniques to use that would be great!

2. Feb 22, 2014

Pythagorean

you might try some algebraic manipulation before you even try a trig sub...

3. Feb 22, 2014

jdawg

Ohhh! I can't believe I overlooked that, thanks!

4. Feb 22, 2014

pasmith

The sum is in the numerator, not the denominator, so the correct approach is to simplify.

5. Feb 22, 2014

jdawg

So now I have (1/4)∫(x+9)/(x) dx

u substitution doesn't work, I don't know what to do next.

6. Feb 22, 2014

Pythagorean

You still haven't quite taken mine and pasmith's advice yet. It turns out no substitution is necessary.

7. Feb 22, 2014

jdawg

Oh, maybe I didn't understand what you meant then. I thought you just meant to cancel out the x's?

8. Feb 22, 2014

D H

Staff Emeritus
Write it as a sum of two integrals.

9. Feb 22, 2014

jdawg

Oh! Thanks so much, I forgot you could split up the numerator!