Trigonometric integral by sustitution



Dear All,

changevar(integrate(a*b/(a^2*(cos(theta))^2+b^2*(sin(theta))^2),theta,0,2*%pi),t-tan(theta/2),t,theta)
;

gives the answer zero.  I'm fairly sure the answer should be 2*%pi
(absolutely sure in the special case a = b).  Any ideas, please?

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Thanks,

Dan