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Math Help - Anti-Derivatives

  1. #1
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    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

    Someone please help.
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  2. #2
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    Quote Originally Posted by zachb View Post
    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

    Someone please help.

    Because,

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

    You flip the fraction,

    3/4
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  3. #3
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    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?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zachb View Post
    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
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  5. #5
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    That's a possibility. I'll ask my professor to confirm that on Monday.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zachb View Post
    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
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  7. #7
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    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.
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  8. #8
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    QuickMaths says:
    Attached Thumbnails Attached Thumbnails Anti-Derivatives-gash.jpg  
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