Evaluate Integral of (x^3+2x)/(sqrt(x^2-2))dx

Question

Use u-sub or Trig substitution, I think

Answer 1

Split into two parts

A x^3 / sqrt (x^2-2)

Trig sub : x = sqrt (2) sec (u)

Reduces to (sqrt 2)^3 integral of sec(u)^4 du

sec(u)^ 4 = sec (u)^2 (1 + tan^2 (u)) = sec(u)^2 + sec(u)^2 tan(u)^2

First integrates to tan (u)

For second sub v = tan(u)

B 2x / sqrt (x^2-2)

u sub - u = x^2-2