# Math Help - Help needed in solving Integration and Convergence Test

1. ## 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...

2. $
\begin{gathered}
u = \sqrt {x^2 + 6} \hfill \\
du = \frac{x}
{{\sqrt {x^2 + 6} }}dx \hfill \\
\end{gathered}$

$
\int {\frac{{u^2 }}
{{u^2 - 6}}du} = \int {1 + \frac{6}
{{\left( {u + 6} \right)\left( {u - 6} \right)}}du = u + \frac{1}
{2}\int {\frac{1}
{{u - 6}} - \frac{1}
{{u + 6}}} } du
$

$
= u + \frac{1}
{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}}
{{\sqrt {x^2 + 6} + 6}}}

$

to determine the convergence use can use the ratio test

3. Thank you very much...