I believe what's being shown is a method of finding an integral called "u substitution". So I understand that $\displaystyle u=x^4+2$. Also I understand that $\displaystyle du=4x^3dx$ although I wonder at this point why is a derivative being taken? I thought we were finding the anti derivative? Following further I understand that [tex](x^4+2)^5=u^5. Then there is $\displaystyle x^3dx=\frac{1}{4}du$ which I don't understand at all. I am just left wondering where the $\displaystyle \frac{1}{4}$ came from.

At this point in my online course they are talking about the anti derivative and we have yet only talked about the indefinite integral.

Thanks for any responses...