Question

antiderivative of (x^2+4x)^1/3 ?

Answer 1

\[\sqrt[3]{x^2+4x}\]

Answer 2

i know that u = x^2+4x
so du = (2x+4)dx
where do i go from there?

Answer 3

@agent0smith @Dido525

Answer 4

well u multipl that by 1/3 too

Answer 5

1/3 dx (x^2 + 4x) = 1/3* (2x + 4)..I think so

Answer 6

how did you get that? can u explain?

Answer 7

cuz du = (2x+4)dx = (2(x+2))dx
so 1/2du = (x+2)dx
then...?

Answer 8

actually, the value of power multplies..hmm

du = 1/3*(2x + 4)dx => 3*du = (2x + 4)dx

Answer 9

I'm pretty sure you need to either do a Trig-Sub, or Integration-By-Parts might also be possible.

No U-Sub available though :(

Have you learned either of those methods yet?

Answer 10

yeah the substitution method.

Answer 11

Trig subs? :D

Answer 12

i think so? remind me what that is?

Answer 13

I think you might want to add and subtract +4 and -4 under the cube root so that you can factor.

Answer 14

google the concept behind it :)

Answer 15

idk how to do this, I'm just posting so that I get notified when someone answers it.

Answer 16

I could reduce it down so that it becomes \[2^{3/5}\int\limits_{}^{}\tan^{3/5} \theta \sec \theta d \theta\] after making the substitution:
\[(x+2)=2\sec \theta\]

Answer 17

the fraction should be 5/3 not 3/5 on the 2 and tan(theta)

Answer 18

this link will help you :)
http://www.the-mathroom.ca/freebs/cali3/cali3.htm

Answer 19

I can't seem to crack it. You're in calculus 1 or 2?

Answer 20

1

Answer 21

where did the tangent, secant stiff come from?

Answer 22

Ah sorry I was busy :C Kanoo been helping you? c:

Answer 23

I was doing trigonometric substitution, but you don't learn that until cal 2. If there's an easier way with just using u-sub then I would be surprised! Good luck zeppy! =P

Answer 24

Ya I dunno sorry Jenny :c
This doesn't seem like a problem you should be doing yet, hmm.

Answer 25

Check this out: http://www.wolframalpha.com/input/?i=(x%5E2%2B4x)%5E1%2F3dx&t=crmtb01

I've never even heard of that stuff. Hypergeometric function? lol

Answer 26

Woah that looks fun :O

Answer 27

oy.....!
-_-