How do you find the integral of #(sin^3(x/2))(cos(x/2))#? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer sruthi bhamidipati · Monzur R. Jan 22, 2018 #intsin^3(x/2)cos(x/2)dx=sin^4(x/2)/2# Explanation: Let #sin(x/2)=t# Then #1/2cos(x/2)dx=dt# And #2*int t^3 dt=t^ 4 * 2/4=sin^4( x/2)/2# 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 7716 views around the world You can reuse this answer Creative Commons License