Evaluate the integral ? # int pi (cos (2pix))/(sin(2pix)) dx# Calculus Introduction to Integration Definite and indefinite integrals 1 Answer Steve M Oct 2, 2017 # int \ pi (cos (2pix))/(sin(2pix)) \ dx = 1/2 ln |sin2pix| + C # Explanation: # int \ pi (cos (2pix))/(sin(2pix)) \ dx = pi \ int \ cot (2pix) \ dx # # " " = pi \ (ln |sin2pix|)/(2pi) + C # # " " = 1/2 ln |sin2pix| + C # Answer link Related questions What is the difference between definite and indefinite integrals? What is the integral of #ln(7x)#? Is f(x)=x^3 the only possible antiderivative of f(x)=3x^2? If not, why not? How do you find the integral of #x^2-6x+5# from the interval [0,3]? What is a double integral? What is an iterated integral? How do you evaluate the integral #1/(sqrt(49-x^2))# from 0 to #7sqrt(3/2)#? How do you integrate #f(x)=intsin(e^t)dt# between 4 to #x^2#? How do you determine the indefinite integrals? How do you integrate #x^2sqrt(x^(4)+5)#? See all questions in Definite and indefinite integrals Impact of this question 2628 views around the world You can reuse this answer Creative Commons License