- #1

jdawg

- 367

- 2

## Homework Statement

∫(x

^{2}+9x)/(4x

^{2}) dx

## Homework Equations

## The Attempt at a Solution

I started by using trigonometric substitution:

x

^{2}=9tan

^{2}θ

x=3tanθ

dx=3sec

^{2}θ dθ

∫9(sec

^{2}θ)/4(9tan

^{2})*3sec

^{2}θ dθ

(3/4)∫(sec

^{4}θ)/(tan

^{2}θ) 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/cos

^{4}θ)/(sin

^{2}θ/cos

^{2}θ)

Please help! Also if you have any tips on how to spot which integration techniques to use that would be great!