Optimal. Leaf size=17 \[ \frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x) \]
[Out]
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Rubi [A] time = 0.0163079, 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 \[ \frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]*Cos[4*x],x]
[Out]
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Rubi in Sympy [A] time = 0.965101, size = 12, normalized size = 0.71 \[ \frac{\sin{\left (3 x \right )}}{6} + \frac{\sin{\left (5 x \right )}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)*cos(4*x),x)
[Out]
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Mathematica [A] time = 0.00964717, size = 17, normalized size = 1. \[ \frac{1}{6} \sin (3 x)+\frac{1}{10} \sin (5 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]*Cos[4*x],x]
[Out]
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Maple [A] time = 0.066, size = 14, normalized size = 0.8 \[{\frac{\sin \left ( 3\,x \right ) }{6}}+{\frac{\sin \left ( 5\,x \right ) }{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)*cos(4*x),x)
[Out]
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Maxima [A] time = 1.37692, size = 18, normalized size = 1.06 \[ \frac{1}{10} \, \sin \left (5 \, x\right ) + \frac{1}{6} \, \sin \left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(4*x)*cos(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231394, size = 24, normalized size = 1.41 \[ \frac{1}{15} \,{\left (24 \, \cos \left (x\right )^{4} - 8 \, \cos \left (x\right )^{2} - 1\right )} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(4*x)*cos(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.723057, size = 20, normalized size = 1.18 \[ - \frac{\sin{\left (x \right )} \cos{\left (4 x \right )}}{15} + \frac{4 \sin{\left (4 x \right )} \cos{\left (x \right )}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*cos(4*x),x)
[Out]
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GIAC/XCAS [A] time = 0.198041, size = 18, normalized size = 1.06 \[ \frac{1}{10} \, \sin \left (5 \, x\right ) + \frac{1}{6} \, \sin \left (3 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(4*x)*cos(x),x, algorithm="giac")
[Out]