What is the integral of #int cos^2(x) tan^3(x) dx#? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer Lucy · Sahar Mulla ❤ Apr 4, 2018 #((tanx)^2/2)+c# Explanation: #int(cosx)^2(tanx)^3(dx)# =#int(cosx)^2times(sinx)^3/(cosx)^3times(dx)# =#int(sinx)^3/(cosx)(dx)# =#int(tanx)(secx)^2(dx)# Let #tanx = t# #:.sec^2x dx = dt# Replacing, =#inttdt# =#t^2/2+c# Replacing back, =#((tanx)^2/2)+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 1220 views around the world You can reuse this answer Creative Commons License