How do you find the integral of #int cos^3(x) sin^4(x) dx#? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer Sasha P. Sep 18, 2015 #(sin^5 x)/5 + (sin^7 x)/7 +C# Explanation: #intcos^3 xsin^4 xdx=intcosxcos^2 xsin^4 xdx=# #intcosx(1-sin^2 x)sin^4 xdx=I# #sinx=t => cosxdx=dt# #I=int(1-t^2)t^4dt=t^5/5-t^7/7+C=# #I=(sin^5 x)/5 + (sin^7 x)/7 +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 3286 views around the world You can reuse this answer Creative Commons License