Optimal. Leaf size=18 \[ \frac{x}{2}-\frac{1}{6} \sin (3 x) \cos (3 x) \]
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Rubi [A] time = 0.0060824, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {2635, 8} \[ \frac{x}{2}-\frac{1}{6} \sin (3 x) \cos (3 x) \]
Antiderivative was successfully verified.
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Rule 2635
Rule 8
Rubi steps
\begin{align*} \int \sin ^2(3 x) \, dx &=-\frac{1}{6} \cos (3 x) \sin (3 x)+\frac{\int 1 \, dx}{2}\\ &=\frac{x}{2}-\frac{1}{6} \cos (3 x) \sin (3 x)\\ \end{align*}
Mathematica [A] time = 0.0062876, size = 14, normalized size = 0.78 \[ \frac{x}{2}-\frac{1}{12} \sin (6 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 15, normalized size = 0.8 \begin{align*}{\frac{x}{2}}-{\frac{\cos \left ( 3\,x \right ) \sin \left ( 3\,x \right ) }{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936092, size = 14, normalized size = 0.78 \begin{align*} \frac{1}{2} \, x - \frac{1}{12} \, \sin \left (6 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.58258, size = 43, normalized size = 2.39 \begin{align*} -\frac{1}{6} \, \cos \left (3 \, x\right ) \sin \left (3 \, x\right ) + \frac{1}{2} \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.060721, size = 14, normalized size = 0.78 \begin{align*} \frac{x}{2} - \frac{\sin{\left (3 x \right )} \cos{\left (3 x \right )}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07291, size = 14, normalized size = 0.78 \begin{align*} \frac{1}{2} \, x - \frac{1}{12} \, \sin \left (6 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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