Evaluate the indefinite integral of y=x^2(x^3+1)^4.

To evaluate the integral, we'll change the
variable:

1 + x^3 = t

We'll
differentiate both sides:

3x^2dx =
dt

x^2dx = dt/3

We'll re-write
the integral in t:

Int x^2(x^3+1)^4 dx = Int t^4
dt/3

 Int t^4 dt/3 = (1/3)Int  t^4
dt

(1/3)Int  t^4 dt = (1/3)*(t^5/5)
+C

(1/3)Int  t^4 dt = t^5/15 +
C

Int x^2(x^3+1)^4 dx = (x^3+1)^5/15 +
C