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Math Help - indefinate integral

  1. #1
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    indefinate integral

    Hi I am a bit confused on how to differentiate a fraction like the problem:

    integral of 2 / (3 x^1/3) dx

    Im not sure where to start can you pull the 2/3 out front and just make it:

    1/ x^1/3? and take ln of x^1/3?

    Please help?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by craziebbygirl View Post
    Hi I am a bit confused on how to differentiate a fraction like the problem:

    integral of 2 / (3 x^1/3) dx

    Im not sure where to start can you pull the 2/3 out front and just make it:

    1/ x^1/3? and take ln of x^1/3?

    Please help?
    the natural log only comes into play if you have 1/x, which you do not have.

    note that \frac 2{3x^{1/3}} = \frac 23x^{-1/3}. now integrate that using the power rule for integrals \left( \int x^n~dx = \frac {x^{n + 1}}{n + 1} + C \text{ for } n \ne -1 \right)
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  3. #3
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    Thanks! so would the answer be 1/2 x^4/3 + c?
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  4. #4
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    also:
    I have the problem: find the integral of (5x - 6) / (square root of X) dx

    Can you separate it into 5x / X^1/2 - 6/x^1/2? even if I do that I still don't see how to solve it?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by craziebbygirl View Post
    Thanks! so would the answer be 1/2 x^4/3 + c?
    no. look at the rule again. note that you have a negative 1/3 power.

    Quote Originally Posted by craziebbygirl View Post
    also:
    I have the problem: find the integral of (5x - 6) / (square root of X) dx

    Can you separate it into 5x / X^1/2 - 6/x^1/2? even if I do that I still don't see how to solve it?
    please post one problem per thread.

    Hint: \frac {x^a}{x^b} = x^{a - b}
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