Optimal. Leaf size=15 \[ \frac{\sin (x)}{2}-\frac{1}{6} \sin (3 x) \]
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Rubi [A] time = 0.0088231, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {4282} \[ \frac{\sin (x)}{2}-\frac{1}{6} \sin (3 x) \]
Antiderivative was successfully verified.
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Rule 4282
Rubi steps
\begin{align*} \int \sin (x) \sin (2 x) \, dx &=\frac{\sin (x)}{2}-\frac{1}{6} \sin (3 x)\\ \end{align*}
Mathematica [A] time = 0.0052901, size = 15, normalized size = 1. \[ \frac{\sin (x)}{2}-\frac{1}{6} \sin (3 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 7, normalized size = 0.5 \begin{align*}{\frac{2\, \left ( \sin \left ( x \right ) \right ) ^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960009, size = 15, normalized size = 1. \begin{align*} -\frac{1}{6} \, \sin \left (3 \, x\right ) + \frac{1}{2} \, \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.30363, size = 38, normalized size = 2.53 \begin{align*} -\frac{2}{3} \,{\left (\cos \left (x\right )^{2} - 1\right )} \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.549111, size = 20, normalized size = 1.33 \begin{align*} - \frac{2 \sin{\left (x \right )} \cos{\left (2 x \right )}}{3} + \frac{\sin{\left (2 x \right )} \cos{\left (x \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12975, size = 15, normalized size = 1. \begin{align*} -\frac{1}{6} \, \sin \left (3 \, x\right ) + \frac{1}{2} \, \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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