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Math Help - Integrating with fractions

  1. #1
    Senior Member Mukilab's Avatar
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    Integrating with fractions

    Hi

    I'm trying to integrate the following and I just can't get it. Any help please?

    Integrate \frac{2}{3*x^{\frac{2}{3}}}

    ^Can't see what is wrong with my latex, can anyone please correct it?

    I get \frac{2}{3}*x^{\frac{-2}{3}} which I then integrate to x^{\frac{1}{3}}*\frac{3}{1}=3x^{\frac{1}{3}} Which isn't right. Where am I going wrong?


    Similarly with \frac{-x^{\frac{-3}{4}}}{4}

    I end up getting \frac{-1}{4}*x^{\frac{3}{4}}*\frac{4}{3}=\frac{-x^{\frac{3}{4}}}{3}

    Help would be greatly appreciated, thank you.
    Last edited by Mukilab; September 9th 2012 at 01:12 AM.
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Integrating with fractions

    ans 1 :: 2 x^{1/3}

    ans 2 :: x^{1/4}
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  3. #3
    Senior Member Mukilab's Avatar
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    Re: Integrating with fractions

    Quote Originally Posted by MaxJasper View Post
    ans 1 :: 2 x^{1/3}

    ans 2 :: x^{1/4}
    Can you tell me how you got those please? I can only continue answering those questions if I know the method.
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  4. #4
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    Re: Integrating with fractions

    Integrate [tex]\frac{2}{3\cdot x^{\frac{2}{3}}}[/tex] gives \frac{2}{3\cdot x^{\frac{2}{3}}}

    Note you were missing a final }
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  5. #5
    Senior Member MaxJasper's Avatar
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    Re: Integrating with fractions

    First remove the constant factors then integrate then include the constants.
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  6. #6
    Senior Member Mukilab's Avatar
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    Re: Integrating with fractions

    Quote Originally Posted by MaxJasper View Post
    ans 1 :: 2 x^{1/3}

    ans 2 :: x^{1/4}
    Wouldn't answer 2 be (-)x^1/4 rather than just x^1/4? Since you started off with a -x.
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