Optimal. Leaf size=17 \[ \frac{1}{4} \sin (2 x)-\frac{1}{12} \sin (6 x) \]
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Rubi [A] time = 0.0080002, 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} \[ \frac{1}{4} \sin (2 x)-\frac{1}{12} \sin (6 x) \]
Antiderivative was successfully verified.
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Rule 4282
Rubi steps
\begin{align*} \int \sin (2 x) \sin (4 x) \, dx &=\frac{1}{4} \sin (2 x)-\frac{1}{12} \sin (6 x)\\ \end{align*}
Mathematica [A] time = 0.0061412, size = 17, normalized size = 1. \[ \frac{1}{4} \sin (2 x)-\frac{1}{12} \sin (6 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 9, normalized size = 0.5 \begin{align*}{\frac{ \left ( \sin \left ( 2\,x \right ) \right ) ^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.932666, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{12} \, \sin \left (6 \, x\right ) + \frac{1}{4} \, \sin \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.41495, size = 43, normalized size = 2.53 \begin{align*} -\frac{1}{3} \,{\left (\cos \left (2 \, x\right )^{2} - 1\right )} \sin \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.558186, size = 22, normalized size = 1.29 \begin{align*} - \frac{\sin{\left (2 x \right )} \cos{\left (4 x \right )}}{3} + \frac{\sin{\left (4 x \right )} \cos{\left (2 x \right )}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10083, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{12} \, \sin \left (6 \, x\right ) + \frac{1}{4} \, \sin \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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