How do you evaluate the integral #int costheta/(1+sintheta)#? Calculus Introduction to Integration Integrals of Rational Functions 1 Answer Monzur R. Mar 3, 2017 #"F"(x) = ln|sintheta +1|+"C"# Explanation: This is a standard integral #int (f'(theta))/(f(theta)) = ln|f(theta)| + "C"#. So #"F"(x) = ln|1+sintheta| + " C"# Answer link Related questions How do you integrate #(x+1)/(x^2+2x+1)#? How do you integrate #x/(1+x^4)#? How do you integrate #dx / (2sqrt(x) + 2x#? What is the integration of #1/x#? How do you integrate #(1+x)/(1-x)#? How do you integrate #(2x^3-3x^2+x+1)/(-2x+1)#? How do you find integral of #((secxtanx)/(secx-1))dx#? How do you integrate #(6x^5 -2x^4 + 3x^3 + x^2 - x-2)/x^3#? How do you integrate #((4x^2-1)^2)/x^3dx #? How do you integrate #(x+3) / sqrt(x) dx#? See all questions in Integrals of Rational Functions Impact of this question 2150 views around the world You can reuse this answer Creative Commons License