how do you integrate this...
would greatly appreciate any help. thanks
Easiest way to do this is to make the the substitution [itex]x=a \sinh u[/itex]. Note that [itex]\cosh^2 u-\sinh^2 u=1[/itex]. Try it out! If you're totally unfamiliar with hyperbolic functions use [itex]x=\tan u[/itex] instead.
would i be right in thinking that cosh(x)=cos(ix) and sinh(x)=-isin(ix) and therefore
Yes that's correct, although I don't see how this is relevant to your problem.
Since [itex]sin^2(u)+ cos^2(u)= 1[/itex] leads to [itex]tan^2(u)+ 1= sec^2(u)[/itex] (divide both sides by [itex]cos^2(u)[/itex]), you could also make the substitution ax= tan(u).
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