Question

Find the indefinite integral.
x^2(5 x^3 + 9)^3 dx

Answer 1

I observed that the derivative of the inside of the bracket sits out front as a multiple of that.
If that is the case, I just reverse by "thinking"

if dy/dx = x^2(5x^3 + 9)^3

y = (x^2/(15x^2)) (5x^3 +9)^4 * (1/4)+ c
= (1/60) (5x^3 + 9)^4 + c

Answer 2

Thanks Reiny for all your help, I really appreciate it.