∫ x^3 √(x^2+9) dx

Question

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.

Answer 1

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.