I need some assistance with integrals...?

Question

Evaluate the indefinite integral.

∫(x+40)√(80x+x² )dx

I'm having difficulty understanding the steps to process the derivative.

Answer 1

I = ∫ (x + 40) (80x + x²)^(1/2) dx

Let u = x² + 80 x

du = (2x + 80) dx

du/2 = (x + 40) dx

I = (1/2) ∫ u^(1/2) du

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

I = (1/3) (x² + 80 x)^(3/2) + C

Answer 2

u = 80x + x^2

du = 2x + 80

(1/2)du = x + 40

∫(1/2)du√u

= (1/3)(80x + x^2)^(3/2)