# Anti-Derivatives

• Apr 14th 2007, 08:14 PM
zachb
Anti-Derivatives
I need help finding the anti-derivative of this function:

f(x) = the cubed root of x + 5/x^6

When I try to do the problem it comes out wrong:

f(x) = x^1/3 + 5(x^-6)
f(x) = x^(1 + 1/3)/1 + 1/3 + 5([x^(1 - 6)]/1 - 6)
f(x) = x^4/3/4/3 + 5([X^-5]/-5)
f(x) (4/3)x^4/3 - x^-5

• Apr 14th 2007, 08:47 PM
ThePerfectHacker
Quote:

Originally Posted by zachb
I need help finding the anti-derivative of this function:

f(x) = the cubed root of x + 5/x^6

When I try to do the problem it comes out wrong:

f(x) = x^1/3 + 5(x^-6)
f(x) = x^(1 + 1/3)/1 + 1/3 + 5([x^(1 - 6)]/1 - 6)
f(x) = x^4/3/4/3 + 5([X^-5]/-5)
f(x) (4/3)x^4/3 - x^-5

Because,

1/(4/3) is not 4/3

You flip the fraction,

3/4
• Apr 14th 2007, 09:11 PM
zachb
Okay, but my book says the full answer is 3/4 x^3/4 - x^-5

So, how do you explain x being raised to the 3/4 power instead of the 4/3 power?
• Apr 14th 2007, 09:15 PM
Jhevon
Quote:

Originally Posted by zachb
Okay, but my book says the full answer is 3/4 x^3/4 - x^-5

So, how do you explain x being raised to the 3/4 power instead of the 4/3 power?

the book made an error apparently
• Apr 14th 2007, 09:28 PM
zachb
That's a possibility. I'll ask my professor to confirm that on Monday. :)
• Apr 14th 2007, 09:35 PM
Jhevon
Quote:

Originally Posted by zachb
That's a possibility. I'll ask my professor to confirm that on Monday. :)

there should be no need to confirm. if the question is in fact exactly how you worded it, the book is wrong. double check. you have no idea how many times i've solved problems and got a different answer than the book, and after many trials and hours, i realized i actually read the question wrong
• Apr 14th 2007, 09:47 PM
zachb
It's a basic "find the antiderivative" question so I didn't read the question wrong. Anyway, if you differentiate 3/4 x ^4/3 - x^-5 you get x^1/3 + 5x/6 , so I guess the book is wrong. I'll tell my professor about the mistake on Monday as I believe one of his colleagues is one of the co-authors of the book we're using.
• Apr 15th 2007, 12:18 AM
CaptainBlack
QuickMaths says: