What is the Integral of (tan x)^6? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer bp May 13, 2016 1/5 tan^5 x- 1/3 tan^3 x +tan x -x +C Explanation: Use trignometric identity tan^2 x= sec^2x -1 to convert the integral into integrable form. 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 11195 views around the world You can reuse this answer Creative Commons License