# 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!