What is the integral `int x^2*e^(x^3) dx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The integral `int x^2*e^(x^3) dx` has to be determined.

Substitute `x^3 = y`

`dy/dx = 3*x^2`

`=> (dy)/3 = x^2*dx`

Substituting this in the original integral gives:

`int x^2*e^(x^3) dx`

`= int e^y/3 dy`

`= e^y/3`

Writing y in terms of x gives:


The integral `int x^2*e^(x^3) dx = (e^(x^3))/3`