What is the integral of #int tan (5x)dx#? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer Cesareo R. Jul 10, 2016 #-1/5log_e(cos(5x))# Explanation: #tan(5x) = sin(5x)/(cos(5x)) =( -1/5(dcos(5x))/(dx))/cos(5x)# then #int tan(5x)dx = int ( -1/5(dcos(5x))/(dx))/cos(5x)dx = -1/5log_e(cos(5x))# 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 9107 views around the world You can reuse this answer Creative Commons License