Integrate (x^2)(sqrt(x^2-a^2))^(-1)

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  • #1
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Anyone know how to integrate this?

Thanks
 

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  • #2
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Yes. Start by factoring out 1/a, then make the trig substitution [tex]x = a \sec \theta[/tex]. After simplification, you will obtain an integral in terms of secant cubed, for which there is an entire http://en.wikipedia.org/wiki/Integral_of_secant_cubed" [Broken] devoted to explaining how to integrate that. Do so, back-substitute, and simplify. Or alternatively, simply look this up in your handy table of integrals, and find that the solution is:

<< complete solution deleted by berkeman >>
 
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  • #3
Fredrik
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[itex]y=\sqrt{x^2-a^2}[/itex] simplifies it a bit.
 

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