How do you find the integral of ##sin^2(3x)dx##?
February 20th, 2023
##=1/2x – 1/12sin6x + C##
##int sin^2 (3x) dx##
small book keeping gesture is to make the sub ##u = 3x, du = 3 dx##
##1/3int sin^2 (u) du##
then we use the cosine double angle formulae
##cos 2A = 1 – 2 sin^2 A##
so ## sin^2 A = (1 – cos 2A)/2##
##=1/6int 1 – cos 2u du##
##=1/6( u – 1/2sin 2u ) + C##
##=1/6( 3x – 1/2sin( 2*3x) ) + C##
##=1/2x – 1/12sin6x + C##
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How do you find the integral of ##sin^2(3x)dx##?
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