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Math Help - antiderivative help

  1. #1
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    antiderivative help

    a little confused on this one. more advanced than the ones we've done in class. any step by step help is appreciated.

    NOTE: i'm not too sure why it's not letting me enter x to the 10th power or 2x to the -1 power. thats why it looks weird but it's supposed to be x^10 and 2x^-1

    find the anti-derivative:

    f(x) = x^10 + \sqrt{x^3} + \frac{1}{\sqrt[7]{x}} +2x^-1
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  2. #2
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    Put the exponent in curly braces, like x^{10}.

    Write it as x^{10}+x^{3/2}+x^{-1/7}+2x^{-1} and use the rules \int x^\alpha = \frac1{\alpha+1}x^{\alpha+1} for \alpha\neq-1 and \int\frac1x = \log|x| otherwise.
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  3. #3
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    Quote Originally Posted by JGaraffa View Post
    a little confused on this one. more advanced than the ones we've done in class. any step by step help is appreciated.

    NOTE: i'm not too sure why it's not letting me enter x to the 10th power or 2x to the -1 power. thats why it looks weird but it's supposed to be x^10 and 2x^-1

    find the anti-derivative:

    f(x) = x^10 + \sqrt{x^3} + \frac{1}{\sqrt[7]{x}} +2x^-1
    Remember  \sqrt(x) = x^{1/2}  and  \sqrt[7]{x} = x^{1/7} and  \int{\frac{2}{x}}  = 2\int{\frac{1}{x}}

    Using you're basic Anti-derivatives rules.

    Answer
    <br />
\frac{x^{11}}{11} + \frac{2x^{5/2}}{5} + \frac{7x^{6/7}}{6} +2\ln{x}<br />
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