Evaluate the indefinite integral. (Use C for the constant of integration.)

Question

x rad 8-x^2 dx

Answer 1

Re-write as ∫x(8 - x²)^1/2 dx

Let u = 8 - x² so du/dx = -2x or du = -2x dx or (-1/2)du = x dx so substituting these we get:

∫(-1/2)(u)^1/2 du = (-1/2)∫u^1/2 du = (-1/2)(2/3)u^3/2 + C = -1/3u^3/2 + C then back-substituting we get -1/3(8 - x²)^3/2 + C