What is the integral of $int (sin(2x)*sin(5x)dx)$ ?

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Answer 1 · 2017-02-27T07:46:25

The answer is $==1/6sin3x-1/14sin7x+C$

We use,

$cos(a-b)=cosacosb+sinasinb$

$cos(a+b)=cosacosb-sina sinb$

$cos(a-b)-cos(a+b)=2sinasinb$

Here we have,

$a=5x$

$b=2x$

$2sin5xsin2x=cos3x-cos7x$

Therefore,

$intsin5xsin2xdx=1/2intcos3dx-1/2intcos7xdx$

$=1/2(sin3x)/3-1/2(sin7x)/7+C$

$=1/6sin3x-1/14sin7x+C$

What is the integral of int (sin(2x)*sin(5x)dx)int (sin(2x)*sin(5x)dx)?