Optimal. Leaf size=15 \[ \frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x) \]
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Rubi [A] time = 0.0082189, antiderivative size = 15, 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 = {4283} \[ \frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x) \]
Antiderivative was successfully verified.
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Rule 4283
Rubi steps
\begin{align*} \int \cos (3 x) \cos (4 x) \, dx &=\frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x)\\ \end{align*}
Mathematica [A] time = 0.0060621, size = 15, normalized size = 1. \[ \frac{\sin (x)}{2}+\frac{1}{14} \sin (7 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 12, normalized size = 0.8 \begin{align*}{\frac{\sin \left ( x \right ) }{2}}+{\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 = 0.939458, size = 15, normalized size = 1. \begin{align*} \frac{1}{14} \, \sin \left (7 \, 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 [B] time = 2.12828, size = 78, normalized size = 5.2 \begin{align*} \frac{1}{7} \,{\left (32 \, \cos \left (x\right )^{6} - 40 \, \cos \left (x\right )^{4} + 12 \, \cos \left (x\right )^{2} + 3\right )} \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.52267, size = 26, normalized size = 1.73 \begin{align*} - \frac{3 \sin{\left (3 x \right )} \cos{\left (4 x \right )}}{7} + \frac{4 \sin{\left (4 x \right )} \cos{\left (3 x \right )}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06341, size = 15, normalized size = 1. \begin{align*} \frac{1}{14} \, \sin \left (7 \, 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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