Can i please get help on this integral, i will write it out

Question

anonymous · Answer

$$\int\limits_{}^{}  x^4\sqrt[3]{2x^5+6}$$


I get to this point: 

$$1/10 \int\limits_{}^{} \sqrt[3]{u}                 $$

anonymous · Answer

what do i do next?

dumbcow · Answer

looks good so far
now rewrite using rational exponent then integrate using power rule
$$1/10\int\limits_{}^{}\sqrt[3]{u} =1/10\int\limits_{}^{}u^{1/3}$$

anonymous · Answer

okay, that would then be:

(1/10)(3/4)(u^4/3)

anonymous · Answer

right?

dumbcow · Answer

yes good
now replace u with expression of x

anonymous · Answer

then it would become: (3(2x^5+6)^4/3)/40 ?

dumbcow · Answer

yep

anonymous · Answer

and thats it?

dumbcow · Answer

yeah well add the constant "+C" i guess

anonymous · Answer

why does my book say: it should be before replacing: (3u(u)^1/3)/(40)

dumbcow · Answer

oh because u^4/3 = u*u^1/3

dumbcow · Answer

just a different way of writing it

anonymous · Answer

why would they write it like that? as u*u^1/3

dumbcow · Answer

textbooks dont like improper fraction exponents

anonymous · Answer

that could really confuse a student

dumbcow · Answer

tell me about it...past memories :)

anonymous · Answer

thanks for your help dumbcow, i really appreciate it

anonymous · Answer

and your right lagrangeson, that is confusing :)

dumbcow · Answer

your teacher prob won't care, so it just annoying when you check your answers

anonymous · Answer

thanks again

anonymous · Answer

that's an ugly looking integral but easily solved