hmmm, graph that first function.
sin a cos b = (1/2)sin(a+b)+(1/2) sin(a-b)
(remember about beat frequencies :)
so
(1/2)[ sin(5x) dx - sin(x) dx ]
ok?
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let y = 3x
then dy = 3 dx or dx = (1/3) dy
so
(5/3) [ cos^2 y dy ]
integrate. (1):sin2xcos3x
(2):5(cos3x)^2
2 answers
5(cos3x)^2
but you need a siny to form the full derivative
cos^2 u = (1+cos 2u)/2
so, we have
5/2 (cos6x+1)
Now you have
5/2 (1/6 sin6x + x) + C
but you need a siny to form the full derivative
cos^2 u = (1+cos 2u)/2
so, we have
5/2 (cos6x+1)
Now you have
5/2 (1/6 sin6x + x) + C