(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[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

2. Relevant equations

u-substitution techniques for integration.

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Tricky Integral (need help with substitution)

**Physics Forums | Science Articles, Homework Help, Discussion**