...integral?

Question

what is the integral of x^3 * e^(2+x^4)?
i know to use the product rule, but i don't know the derivative of the e^(2+x^4)...integration by parts right? what do i use as the u?

Answer 1

These are u-substitution problems. In this case, let u=x+x⁴, then du = 4x³ dx, so we have:

1/4 ∫e^u du
1/4 e^u + C
1/4 e^(2+x⁴) + C

And we are done.