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Math Help - Antiderivative

  1. #1
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    Antiderivative

    What is the algorithm for antiderivatives???
    I know x^n dy/dx  = n * x^ {n-1} is the way you do the derivative, but how to you get the antiderivative...
    I just need the method... It's just bothering me.... lol
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Muhammed Ali View Post
    What is the algorithm for antiderivatives???
    I know x^n dy/dx  = n * x^ {n-1} is the way you do the derivative, but how to you get the antiderivative...
    I just need the method... It's just bothering me.... lol
    Let's take your example:
    \int x^n~dx = \frac{1}{n + 1} \cdot x^{n + 1} + C
    because
    \frac{d}{dx} \left ( \frac{1}{n + 1} \cdot x^{n + 1} + C  \right ) = x^n

    Basically what rules there are for antiderivatives come from the derivative shortcut formulas. However they aren't always as easy as the derivative rules. You will eventually get to integration by parts, which is the reverse of the product rule for derivatives. It isn't all that hard a method, but it is much more difficult that the product rule.

    -Dan
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    Grand Panjandrum
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    Quote Originally Posted by Muhammed Ali View Post
    What is the algorithm for antiderivatives???
    I know x^n dy/dx  = n * x^ {n-1} is the way you do the derivative, but how to you get the antiderivative...
    I just need the method... It's just bothering me.... lol
    If I were you I would go back and relearn what I think I know, before seeking new knowlege.

    <br />
\frac{d}{dx}\left[x^n\right]=n~x^{n-1}<br />

    RonL
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  4. #4
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    You can calm down, because the form I posted is something I came up with on my own... I was just making assumptions based on what I had been taught.
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  5. #5
    GAMMA Mathematics
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    Quote Originally Posted by Muhammed Ali View Post
    What is the algorithm for antiderivatives???
    I know x^n dy/dx  = n * x^ {n-1} is the way you do the derivative, but how to you get the antiderivative...
    I just need the method... It's just bothering me.... lol
    The power rule for integrals is simply the reverse. Add one to the exponent and divide by that new power:

    \int x^n dx = \frac{x^{n+1}}{n+1}
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