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Math Help - Anti-Derivative

  1. #1
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    Question Anti-Derivative



    Can anyone explain to me how to get to the second step?
    I don't understand how the X^(5/2) - 7(square X) + X^(-1/2) came from.
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  2. #2
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    Quote Originally Posted by Brazuca View Post


    Can anyone explain to me how to get to the second step?
    I don't understand how the X^(5/2) - 7(square X) + X^(-1/2) came from.
    remember \sqrt{x} = x^{\frac{1}{2}}

    \frac{x^3-7x+1}{x^{\frac{1}{2}}} =

    \frac{x^3}{x^{\frac{1}{2}}} - \frac{7x}{x^{\frac{1}{2}}} + \frac{1}{x^{\frac{1}{2}}}

    subtract exponents when dividing ... right?
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  3. #3
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    We can first split the fraction up to:

    (Nevermind, can't get the LaTeX right, just refer above)

    Note: \sqrt{x} = x^{1/2}

    Now, when we divide by x's of different powers, we can subtract the exponents.

     3 - \frac{1}{2} = \frac{5}{2}

    So that's where the x^5/2 came from...

    You should be able to finish it from here, just keep subtracting the powers.
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  4. #4
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    I forgot that the bottom part effects each thing on top induvidualy...
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