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Math Help - cannot simplify this antiderative

  1. #1
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    cannot simplify this antiderative

    f(x) = 17/2 * (squareroot of x)^15 when C=0

    I used the rule given by my teacher X^n = 1/(n+1^x) * x^n+1 +C

    and end up with:

    1/(15/2 + 1^17/2) * x^(15/2 + 1)

    I tried simplifying this to: (x^17/2) / (17/2)
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  2. #2
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    Quote Originally Posted by solidstatemath View Post
    f(x) = 17/2 * (squareroot of x)^15 when C=0

    I used the rule given by my teacher X^n = 1/(n+1^x) * x^n+1 +C

    and end up with:

    1/(15/2 + 1^17/2) * x^(15/2 + 1)

    I tried simplifying this to: (x^17/2) / (17/2)
    is this the function you are attempting to integrate ...

    \displaystyle f(x) = \frac{17}{2} (\sqrt{x})^{15}

    ???
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  3. #3
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    Yes.

    How did you write it like that?
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  4. #4
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    \displaystyle \int \frac{17}{2} (\sqrt{x})^{15} \, dx = \int \frac{17}{2} x^{\frac{15}{2}} \, dx = x^{\frac{17}{2}} + C

    the math text is created by Latex ... there is an entire forum on this site dedicated to it.
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  5. #5
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    Quote Originally Posted by solidstatemath View Post
    Yes.

    How did you write it like that?
    Click on the appropriate link in my signature.
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  6. #6
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    Quote Originally Posted by solidstatemath View Post
    f(x) = 17/2 * (squareroot of x)^15 when C=0

    I used the rule given by my teacher X^n = 1/(n+1^x) * x^n+1 +C
    You have misquoted your teacher in two ways:
    1) that is NOT equal to x^n so you should not write "x^n= ".
    2) there is no "^x" in the first denominator.

    The anti-derivative of x^n is [1/(n+1)]x^(n+1)+ C.
    In Latex, that is
    \frac{x^{n+1}}{n+1}+ C
    Click on that formula to see the code for it.

    and end up with:

    1/(15/2 + 1^17/2) * x^(15/2 + 1)

    I tried simplifying this to: (x^17/2) / (17/2)
    Of course, you can check if an anti-derivative is correct by differentiating it.
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