`int x^2 e^(x^3) dx` Evaluate the indefinite integral.

You need to evaluate the indefinite integral by performing the substitution `x^3 = t` , such that:

`x^3 = t => 3x^2dx = dt => x^2dx = (dt)/3`

`int x^2*e^(x^3) dx= (1/3)int e^t dt`

`(1/3)int e^t dt = (1/3)(e^t) + c`

Replacing back `x^3` for t yields:

`int x^2*e^(x^3) dx=  (1/3)(e^(x^3)) + c`

Hence, evaluating the indefinite integral yields `int x^2*e^(x^3) dx=  (1/3)(e^(x^3)) + c.`