Optimal. Leaf size=17 \[ \frac{1}{6} \sin (3 x)-\frac{1}{14} \sin (7 x) \]
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Rubi [A] time = 0.0084189, 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} \[ \frac{1}{6} \sin (3 x)-\frac{1}{14} \sin (7 x) \]
Antiderivative was successfully verified.
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Rule 4282
Rubi steps
\begin{align*} \int \sin (2 x) \sin (5 x) \, dx &=\frac{1}{6} \sin (3 x)-\frac{1}{14} \sin (7 x)\\ \end{align*}
Mathematica [A] time = 0.0065277, size = 17, normalized size = 1. \[ \frac{1}{6} \sin (3 x)-\frac{1}{14} \sin (7 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 14, normalized size = 0.8 \begin{align*}{\frac{\sin \left ( 3\,x \right ) }{6}}-{\frac{\sin \left ( 7\,x \right ) }{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.933001, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{14} \, \sin \left (7 \, 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 = 2.08164, size = 81, normalized size = 4.76 \begin{align*} -\frac{2}{21} \,{\left (48 \, \cos \left (x\right )^{6} - 60 \, \cos \left (x\right )^{4} + 11 \, \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 [B] time = 0.503333, size = 26, normalized size = 1.53 \begin{align*} - \frac{5 \sin{\left (2 x \right )} \cos{\left (5 x \right )}}{21} + \frac{2 \sin{\left (5 x \right )} \cos{\left (2 x \right )}}{21} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04559, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{14} \, \sin \left (7 \, 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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