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!