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Math Help - Evaluate the Indefinite Integral

  1. #1
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    Evaluate the Indefinite Integral

    \int{\frac{\sqrt{x}-x^2+4}{x}}dx

    Lost on what to do.
    Thanks for the help!
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  2. #2
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    Quote Originally Posted by Jim Marnell View Post
    \int{\frac{\sqrt{x}-x^2+4}{x}}dx

    Lost on what to do.
    Thanks for the help!

    SImplify it first.

    \int (\frac{1}{\sqrt{x}} - x + \frac{4}{x}) dx

    Then integrate term by term. Can you try it from here?
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  3. #3
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    thanks! ill try it from here and post what i get.
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  4. #4
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    \int{\frac{\sqrt{x}-x^2+4}{x}}dx
    \int (\frac{1}{\sqrt{x}} - x + \frac{4}{x}) dx
    \int (-x^{1/2}-x+\frac{4}{x}) dx

    Would that be the correct step, i'm lost after that. Not sure how to get the antiderivatives to evaluate
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  5. #5
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    Quote Originally Posted by Jim Marnell View Post
    \int{\frac{\sqrt{x}-x^2+4}{x}}dx
    \int (\frac{1}{\sqrt{x}} - x + \frac{4}{x}) dx
    \int (-x^{1/2}-x+\frac{4}{x}) dx Mr F says: No. You have to use your basic index laws. It's {\color{red}\int \! x^{-1/2} - x + 4 x^{-1} \, dx}.

    Would that be the correct step, i'm lost after that. Not sure how to get the antiderivatives to evaluate
    You're expected to know that \int \! a x^{n} \, dx = \frac{a}{n+1} x^{n+1} + C, provided n \neq -1.
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  6. #6
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    so would this be the next step:
    \int (\frac{-x^{3/2}}{3/2}-\frac{x^2}{2}+\frac{4}{x})dx

    not sure how to find the antiderivative of 4/x
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  7. #7
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    Quote Originally Posted by Jim Marnell View Post
    so would this be the next step:
    \int (\frac{-x^{3/2}}{3/2}-\frac{x^2}{2}+\frac{4}{x})dx

    not sure how to find the antiderivative of 4/x
    Since this answer means you have done the integral, the integration operator should not be included. So you have

    \frac{-x^{3/2}}{3/2} - \frac{x^2}{2} + \int \! \frac{4}{x} \, dx.

    The last integral is equal to 4 \ln |x | (again, you're expected to know this.)

    Your final answer needs to include a "+ C" (and again, this is something you're meant to know).
    Last edited by mr fantastic; April 14th 2009 at 07:21 AM. Reason: Fixed a spelling error and removed a superfluous |.
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  8. #8
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    what is the final answer to this?
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  9. #9
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    Quote Originally Posted by foodmmm View Post
    what is the final answer to this?
    The final answer is already given, read post #7.

    Note: \frac{- x^{3/2}}{3/2} = - \frac{2}{3} x^{2/3}.
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