How do I find the indefinite integral of $sin(3x)cos(3x)$ ?

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Answer 1 · 2018-08-05T12:35:13

The answer is $=-1/12cos(6x)+C$

We know that

$sin2x=2sinxcosx$

Therefore,

$sin(3x)cos(3x)=1/2sin(6x)$

So,

The integral is

$I=intsin(3x)cos(3x)dx=1/2intsin(6x)dx$

$=-1/12cos(6x)+C$

How do I find the indefinite integral of sin(3x)cos(3x)sin(3x)cos(3x)?