- #1
PFStudent
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Homework Statement
[tex]
{\int_{}^{}}{ \frac{ds}{{({s}^{2}+{d}^{2})}^{\frac{3}{2}}}}
[/tex]
[itex]s[/itex] [itex]\equiv[/itex] variable
[itex]d[/itex] [itex]\equiv[/itex] constant
Homework Equations
u-substitution techniques for integration.
The Attempt at a Solution
This integral is particularly tricky as I have already made several attempts using conventional u-substitution, however this integral is not coming out right.
Below is my best attempt,
If I split the denominator and multiply the top and bottom by [itex]s[/itex],
[tex]
{\frac{sds}{{s{({s}^{2}+{d}^{2})}^{\frac{1}{2}}}{{({s}^{2}+{d}^{2})}^{1}}}}
[/tex]
And let,
[tex]
u = {s}^{2}+{d}^{2}
[/tex]
[tex]
du = 2sds
[/tex]
With the substitution yields,
[tex]
{\frac{1}{2}}{\int_{}^{}}{\frac{du}{{{u}^{\frac{3}{2}}}{\sqrt{{u}-{d}^{2}}}}}
[/tex]
However, this seems to get me no where.
Any help is appreciated.
Thanks,
-PFStudent
P.S.: I do realize I can look this up in the integraion tables, however I would like to know how to do this on my own without using a table.
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