∫ x^3 √(x^2+9) dx
If you work it can you write the steps? I really don't like the way my teacher teaches it. Someone else doing it might help.
since sec^2 = tan^2+1,
let x = 3tanθ
dx = 3sec^2 θ dθ
x^2+9 = 9+9tan^2θ = 9sec^2θ
Now the integrand is
(3tanθ)^3 secθ (3sec^2θ) dθ
= 81 tan^3(θ) sec^3(θ) dθ
See what you can do with that.