How do you find the antiderivative of #f(x) = 1 / (5cos^2(5x))#? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer Salvatore I. · Noah G Nov 7, 2016 #tan(5x)/25 + C# Explanation: As the derivative of #tan(x)# is #1/cos^2(x)#, we can deduce that #int1/(5cos^2(5x))=tan(5x)/25+ "Constant"# 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 1779 views around the world You can reuse this answer Creative Commons License