What is the antiderivative of #1/cosx(2+sinx)#? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer Anjali G Mar 5, 2017 #int frac{sinx+2}{cosx}dx# #=ln|secx|+2ln|secx+tanx|+C# Explanation: #int frac{sinx+2}{cosx}dx# #int frac{sinx}{cosx}+frac{2}{cosx}dx# #=int (tanx)dx + 2int(secx)dx# #=ln|secx|+2ln|secx+tanx|+C# Use logarithm rules: #=ln|secx|+ln(secx+tanx)^2+C# #=ln|(secx)(secx + tanx)^2|+C# Answer link Related questions How do I evaluate the indefinite integral #intsin^3(x)*cos^2(x)dx# ? How do I evaluate the indefinite integral #intsin^6(x)*cos^3(x)dx# ? How do I evaluate the indefinite integral #intcos^5(x)dx# ? How do I evaluate the indefinite integral #intsin^2(2t)dt# ? How do I evaluate the indefinite integral #int(1+cos(x))^2dx# ? How do I evaluate the indefinite integral #intsec^2(x)*tan(x)dx# ? How do I evaluate the indefinite integral #intcot^5(x)*sin^4(x)dx# ? How do I evaluate the indefinite integral #inttan^2(x)dx# ? How do I evaluate the indefinite integral #int(tan^2(x)+tan^4(x))^2dx# ? How do I evaluate the indefinite integral #intx*sin(x)*tan(x)dx# ? See all questions in Integrals of Trigonometric Functions Impact of this question 3702 views around the world You can reuse this answer Creative Commons License