Need help with anti-derivatives. 10 points for help.

Find the following
S 5x(x^2 - 8) dx
The answer is 5x^4/4 - 20x^2 + c. How did they get that?

multiply 5x(x^2-8) = 5x^3-40x

integral of 5x^3= 5x^4/4

integral of -40x = -40x^2/2 = -20x^2

Answer = 5x^4/4 -20x^2 + C

First distribute the multiplication to get 5x^3 - 40 x

Then use the basic power rule of integration integral ax^n dx = (ax^(n+1)) / (n+1) and voila....