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Math Help - Help needed in solving Integration and Convergence Test

  1. #1
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    Help needed in solving Integration and Convergence Test

    integrate: [sqrt(X^2 + 6)] / X

    Determine the convergence :
    [(-1)N!]/N^N

    Help me pls... thank u...
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  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
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    <br />
\begin{gathered}<br />
  u = \sqrt {x^2  + 6}  \hfill \\<br />
  du = \frac{x}<br />
{{\sqrt {x^2  + 6} }}dx \hfill \\ <br />
\end{gathered}

    <br />
\int {\frac{{u^2 }}<br />
{{u^2  - 6}}du}  = \int {1 + \frac{6}<br />
{{\left( {u + 6} \right)\left( {u - 6} \right)}}du = u + \frac{1}<br />
{2}\int {\frac{1}<br />
{{u - 6}} - \frac{1}<br />
{{u + 6}}} } du<br />

    <br />
 = u + \frac{1}<br />
{2}\left[ {\ln \left| {u - 6} \right| - \ln \left| {u + 6} \right|} \right] = \sqrt {x^2  + 6}  + \ln \sqrt {\frac{{\sqrt {x^2  + 6}  - 6}}<br />
{{\sqrt {x^2  + 6}  + 6}}} <br /> <br />

    to determine the convergence use can use the ratio test
    Last edited by Peritus; October 26th 2008 at 09:47 AM.
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  3. #3
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    Thank you very much...
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