Optimal. Leaf size=18 \[ \frac {x}{2}-\frac {1}{6} \sin (3 x) \cos (3 x) \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, 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 8
Rule 2635
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*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 0.78 \[ \frac {x}{2}-\frac {1}{12} \sin (6 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 14, normalized size = 0.78 \[ -\frac {1}{6} \, \cos \left (3 \, x\right ) \sin \left (3 \, x\right ) + \frac {1}{2} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.84, size = 10, normalized size = 0.56 \[ \frac {1}{2} \, x - \frac {1}{12} \, \sin \left (6 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 15, normalized size = 0.83 \[ -\frac {\cos \left (3 x \right ) \sin \left (3 x \right )}{6}+\frac {x}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 10, normalized size = 0.56 \[ \frac {1}{2} \, x - \frac {1}{12} \, \sin \left (6 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 10, normalized size = 0.56 \[ \frac {x}{2}-\frac {\sin \left (6\,x\right )}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 14, normalized size = 0.78 \[ \frac {x}{2} - \frac {\sin {\left (3 x \right )} \cos {\left (3 x \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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