Optimal. Leaf size=17 \[ \frac{1}{6} \sin (3 x)-\frac{1}{18} \sin (9 x) \]
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Rubi [A] time = 0.0082184, antiderivative size = 17, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0064867, size = 17, normalized size = 1. \[ \frac{1}{6} \sin (3 x)-\frac{1}{18} \sin (9 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 9, normalized size = 0.5 \begin{align*}{\frac{2\, \left ( \sin \left ( 3\,x \right ) \right ) ^{3}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.938837, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{18} \, \sin \left (9 \, x\right ) + \frac{1}{6} \, \sin \left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.10254, size = 43, normalized size = 2.53 \begin{align*} -\frac{2}{9} \,{\left (\cos \left (3 \, x\right )^{2} - 1\right )} \sin \left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.53335, size = 24, normalized size = 1.41 \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05213, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{18} \, \sin \left (9 \, x\right ) + \frac{1}{6} \, \sin \left (3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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