How do I integrate (x^2+a^2)^(-3/2)?

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SUMMARY

The integral of the function (x^2 + a^2)^(-3/2) can be solved using specific substitutions. The recommended substitutions are x = a sinh(t) and x = a tan(θ). Both methods simplify the integral, allowing for straightforward evaluation without the need for integral tables.

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I haven't done basic integrals for awhile...but just wondering how you would integrate the following functions without looking it up in the integral table.

(x^2+a^2)^(-3/2) where a is a constant.

Thanks!
 
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Make the substitution [itex]x=a\sinh t[/itex] and then see what you get.
 
The substitution [itex]x= atan(\theta)[/itex] will also work.
 

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