$\frac{d}{dx}\left(\frac{1}{9}\sin\left(3x\right)-\frac{1}{3}x\cos\left(3x\right)\right)=\frac{1}{3}\cos\left(3x\right)-\frac{1}{3}\left(\cos\left(3x\right)-3x\sin\left(3x\right)\right)$
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Integral
$\int\left(\frac{1}{9}\sin\left(3x\right)-\frac{1}{3}x\cos\left(3x\right)\right)dx=-\frac{2}{27}\cos\left(3x\right)-\frac{1}{9}x\sin\left(3x\right)+C_0$
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