I want to integrate(cos(3theta)/(5-4cos(theta)),(theta,0,2pi)) this expression whose
answer is pi/12. But sympy does not execute the integral correctly.
So, I replaced cos(3theta) with
4cos(theta)*3-3cos(theta). Then I am obtained -21pi/8. Also, when I replaced cos(3theta) with
cos(theta) sympy executed the integral and gave -pi/2. Can anyone please elaborate why sympy is not giving the correct integral? What would be the right code to obtain the correct answer?
from sympy import integrate, cos, pi, symbols
theta = symbols('theta')
sol = integrate(cos(3 * theta) / (5 - 4 * cos(theta)), (theta, 0, 2 * pi))
print(sol)
Output: 67*pi/24
Correct output would be pi/12