kill(all)$

van=facebook.com/LearningCalculus$

     Jawad Hamidi asks to prove:

%i*integrate(%e^(3*%i*theta)/(e^(%i*theta)-3),theta,0,2*%pi) = 0;

f(theta) := (%e^(3*%i*theta));
g(theta) := (e^(%i*theta)-3);
h(theta) := f(theta)/g(theta)$ h(theta);
k(theta) := g(theta)+6$ k(theta);
l(theta) := (f(theta)*k(theta))/(g(theta)*k(theta))$ l(theta);

rectform(f(theta));

fullratsimp(f(theta));

integrate(h(theta),theta,0,2*%pi);

changevar(%,u=%e^(%i*theta),u,theta);