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Math Help - Finding The Most General Antiderivative

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    Finding The Most General Antiderivative

    I am having a severe amount of trouble with the following question. I am unsure where to start or how to even tackle it. Thanks for any help

    Find the most general antiderivative for the following function:

    g(x) = (3-x+(the square root of x) all over x to the power of 4.

    I hope you could understand that, feel free to ask questions otherwise. Thanks again.
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    Quote Originally Posted by GreenDay14 View Post
    I am having a severe amount of trouble with the following question. I am unsure where to start or how to even tackle it. Thanks for any help

    Find the most general antiderivative for the following function:

    g(x) = (3-x+(the square root of x) all over x to the power of 4.

    I hope you could understand that, feel free to ask questions otherwise. Thanks again.
    \int \frac{3 - x^2 + \sqrt{x}}{x^4} \, dx = \int \frac{3}{x^4} - \frac{x^2}{x^4} + \frac{x^{1/2}}{x^4}\, dx.

    Simplify each term using the usual index laws and integrate in the usual way.
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    Sorry for the double post I thought I may have posted in the wrong section at first. As for your response to my question that does not really help me much I could have gotten that far but I am unsure how to get much farther.
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    Quote Originally Posted by GreenDay14 View Post
    Sorry for the double post I thought I may have posted in the wrong section at first. As for your response to my question that does not really help me much I could have gotten that far but I am unsure how to get much farther.
    \frac{3}{x^4} = 3 x^{-4}.

    \frac{x^2}{x^4} = x^2.

    \frac{x^{1/2}}{x^4} = x^{-7/2}.

    It's expected that you can simplify expressions such as these using index laws. It's expected that you can integrate each of these things.
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    If it is not to much to ask, could you possibly link me to a site explaining the index laws or something? Because i have no idea what you are referring to. Thanks for the help tho.
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    Quote Originally Posted by GreenDay14 View Post
    If it is not to much to ask, could you possibly link me to a site explaining the index laws or something? Because i have no idea what you are referring to. Thanks for the help tho.
    \frac{x^a}{x^b} = x^{a - b}
    and
    \int x^n~dx = \frac{1}{n + 1}x^{n + 1} + C

    -Dan
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    also how does x squared over x to the power of 4 = x squared ?
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    Quote Originally Posted by GreenDay14 View Post
    also how does x squared over x to the power of 4 = x squared ?
    It was a typo.
    \frac{x^2}{x^4} = x^{-2}

    -Dan
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    Quote Originally Posted by GreenDay14 View Post
    If it is not to much to ask, could you possibly link me to a site explaining the index laws or something? Because i have no idea what you are referring to. Thanks for the help tho.
    I'm referring to rules like a^m a^n = a^{m+n}, \frac{a^m}{a^n} = a^{m-n}, \frac{1}{a^m} = a^{-m}, \sqrt{x} = x^{1/2}.

    You might know them by a different name.

    They are pre-calculus things that you're certainly expected to know and use when studying calculus.
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    Thanks for all the help guys.
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