Can someone help me check what I'm getting as the anti-derivative of "1/(3(x^(1/3)))"?
Any and all help is greatly appreciated! :)

Question

Can someone help me check what I'm getting as the anti-derivative of "1/(3(x^(1/3)))"?
Any and all help is greatly appreciated! :)

anonymous · Answer

that is really hard to read, but the idea is to write it in exponential form

amonoconnor · Answer

Yes, I apologize for the nasty way I had to type it! :/

amonoconnor · Answer

I got "(x^(4/3))/4" as the anti., but the answer key does NOT have that... Did I goof? I've checked my work like, literally 8 times!

anonymous · Answer

http://openstudy.com/study#/updates/5306c8f6e4b00fb1e2375e82

amonoconnor · Answer

So... Here's my work, as I was taught to do theses :)
1/(3(x^(1/3))) = (1/3)(x^(1/3))
                     = (1/3)(x^((1/3) + 1)))
                     = (1/3)(x^(4/3))
                     = [(1/3)/(4/3)]x^(4/3)
                     = [(1/3)((3/4)]x^(4/3)
                     = (3/12)x^(4/3)
                     = (1/4)x^(4/3)
                     = (x^(4/3))/4 + C

anonymous · Answer

It's x^(-1/3) not x^(1/3).

anonymous · Answer

The x is in the denominator.

amonoconnor · Answer

*rage* okay... Stupid me... I see how even though the 1/3 is factored, it's 1/(x^(1/3)) or x^(1/3), but... Yeah, just yeah. God I'm dumb. Thank you, oh amazing one. ;)

amonoconnor · Answer

Lols, I even forgot the negative there too. ;)