Evaluate the indefinite integral. ?

Question

integral { (x + 22) sqrt(44 x + x^2) }

Please explain.

Answer 1

∫(x+22) (44x+x^2)^.5 dx

let u = 44x + x^2

du = (44 + 2x) dx

du = 2 (22+x) dx

(22+x)dx = (1/2) du

substititute:

∫(1/2) u^.5 du

(1/2) (2/3) u^(3/2) + C

(1/3) (44x+x^2)^(3/2) + C