Optimal. Leaf size=17 \[ \frac {1}{6} \sin (3 x)-\frac {1}{18} \sin (9 x) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {4282} \[ \frac {1}{6} \sin (3 x)-\frac {1}{18} \sin (9 x) \]
Antiderivative was successfully verified.
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Rule 4282
Rubi steps
\begin {align*} \int \sin (3 x) \sin (6 x) \, dx &=\frac {1}{6} \sin (3 x)-\frac {1}{18} \sin (9 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ \frac {1}{6} \sin (3 x)-\frac {1}{18} \sin (9 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 14, normalized size = 0.82 \[ -\frac {2}{9} \, {\left (\cos \left (3 \, x\right )^{2} - 1\right )} \sin \left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 13, normalized size = 0.76 \[ -\frac {1}{18} \, \sin \left (9 \, x\right ) + \frac {1}{6} \, \sin \left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 9, normalized size = 0.53 \[ \frac {2 \left (\sin ^{3}\left (3 x \right )\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 13, normalized size = 0.76 \[ -\frac {1}{18} \, \sin \left (9 \, x\right ) + \frac {1}{6} \, \sin \left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 13, normalized size = 0.76 \[ \frac {\sin \left (3\,x\right )}{6}-\frac {\sin \left (9\,x\right )}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.61, size = 24, normalized size = 1.41 \[ - \frac {2 \sin {\left (3 x \right )} \cos {\left (6 x \right )}}{9} + \frac {\sin {\left (6 x \right )} \cos {\left (3 x \right )}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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