Hey, i was wondering if anyone could help me with this question:
integrate: 4x^3 exp(2x^4)
i know what the answer is but i really dont understand how to do the question as apparently, it doesnt involve any integration at all!!!
Thanks
Hey, i was wondering if anyone could help me with this question:
integrate: 4x^3 exp(2x^4)
i know what the answer is but i really dont understand how to do the question as apparently, it doesnt involve any integration at all!!!
Thanks
fine, we will spoil you this time
$\displaystyle \int 4x^3 e^{2x^4}$
Let $\displaystyle u = 2x^4$
$\displaystyle \Rightarrow du = 8x^3 ~dx$
$\displaystyle \Rightarrow \frac {du}2 = 4x^3 ~dx$
So our integral becomes:
$\displaystyle \frac 12 \int e^u~du = \frac 12 e^u + C$
$\displaystyle = \frac 12 e^{2x^4} + C$
TD!'s underbraces make the substitution more explicit