Optimal. Leaf size=17 \[ \frac{1}{4} \sin (2 x)-\frac{1}{8} \sin (4 x) \]
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Rubi [A] time = 0.0082572, antiderivative size = 17, 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} \[ \frac{1}{4} \sin (2 x)-\frac{1}{8} \sin (4 x) \]
Antiderivative was successfully verified.
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Rule 4282
Rubi steps
\begin{align*} \int \sin (x) \sin (3 x) \, dx &=\frac{1}{4} \sin (2 x)-\frac{1}{8} \sin (4 x)\\ \end{align*}
Mathematica [A] time = 0.0065166, size = 17, normalized size = 1. \[ \frac{1}{4} \sin (2 x)-\frac{1}{8} \sin (4 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.026, size = 14, normalized size = 0.8 \begin{align*}{\frac{\sin \left ( 2\,x \right ) }{4}}-{\frac{\sin \left ( 4\,x \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.970992, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{8} \, \sin \left (4 \, 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 = 2.32462, size = 39, normalized size = 2.29 \begin{align*} -{\left (\cos \left (x\right )^{3} - \cos \left (x\right )\right )} \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.774595, size = 20, normalized size = 1.18 \begin{align*} - \frac{3 \sin{\left (x \right )} \cos{\left (3 x \right )}}{8} + \frac{\sin{\left (3 x \right )} \cos{\left (x \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10946, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{8} \, \sin \left (4 \, 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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