`int (cos(3theta)-1)d theta=`
Use additivity of integral: `int (f(x)+g(x))dx=int f(x)dx+int g(x)dx.` `int cos(3theta)d theta-int d theta=`
Since the second integral is easy `int d theta=theta+C` we will concentrate on the first integral. To solve the first integral we will make substitution `u=3theta,` `du=3d theta=>d theta=(du)/3`
`int cos(3theta)d theta=1/3int cos u du=1/3sin u +C=`
Return the substitution.
`1/3sin(3theta)+C`
Therefore, the final solution is
`1/3sin(3theta)-theta+C`
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