1. 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

2. 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

3. 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?

4. 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

5. That's a possibility. I'll ask my professor to confirm that on Monday.

6. 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

7. 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.

8. QuickMaths says: