Question

Evaluate the integral

Answer 1

`\text{Let u = } x^(4)`

`(du)/(dx) = 4x^(3)`

`(1)/(2)(du)/(dx) = 2x^(3)`

`(1)/(2)du = (2x^(3))dx`

Substituting this back into the original integral:

`\int 2x^(3)e^{x^(4)}\, dx = (1)/(2)\int e^(u)\, du`

`= (1)/(2)e^(u) + C`


`= \frac{e^{x^(4)}}{2} + C`