Question #66116 Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer Monzur R. Apr 16, 2017 #"A"(x)=1/3sin3x-1/3sqrt3cos3x+"c"# Explanation: Recall that #intcos(ax)# #dx=1/asinx# and #intsin(ax)# #dx=-1/acosx#. #intcos3x+sqrt3sin3x# #dx=intcos3x# #dx+sqrt3intsin3x# #dx=# #1/3sin3x-1/3sqrt3cos3x+"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 1130 views around the world You can reuse this answer Creative Commons License