Question

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

Answer 1

\[\int\limits_{}^{} x^4\sqrt[3]{2x^5+6}\]


I get to this point:

\[1/10 \int\limits_{}^{} \sqrt[3]{u} \]

Answer 2

what do i do next?

Answer 3

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

Answer 4

okay, that would then be:

(1/10)(3/4)(u^4/3)

Answer 5

right?

Answer 6

yes good
now replace u with expression of x

Answer 7

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

Answer 8

yep

Answer 9

and thats it?

Answer 10

yeah well add the constant "+C" i guess

Answer 11

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

Answer 12

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

Answer 13

just a different way of writing it

Answer 14

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

Answer 15

textbooks dont like improper fraction exponents

Answer 16

that could really confuse a student

Answer 17

tell me about it...past memories :)

Answer 18

thanks for your help dumbcow, i really appreciate it

Answer 19

and your right lagrangeson, that is confusing :)

Answer 20

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

Answer 21

thanks again

Answer 22

that's an ugly looking integral but easily solved