Optimal. Leaf size=15 \[ \frac{\sin (x)}{2}+\frac{1}{6} \sin (3 x) \]
[Out]
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Rubi [A] time = 0.0152933, antiderivative size = 15, 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 \[ \frac{\sin (x)}{2}+\frac{1}{6} \sin (3 x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]*Cos[2*x],x]
[Out]
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Rubi in Sympy [A] time = 0.947779, size = 10, normalized size = 0.67 \[ \frac{\sin{\left (x \right )}}{2} + \frac{\sin{\left (3 x \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)*cos(2*x),x)
[Out]
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Mathematica [A] time = 0.00680412, size = 15, normalized size = 1. \[ \frac{\sin (x)}{2}+\frac{1}{6} \sin (3 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]*Cos[2*x],x]
[Out]
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Maple [A] time = 0.015, size = 12, normalized size = 0.8 \[{\frac{\sin \left ( x \right ) }{2}}+{\frac{\sin \left ( 3\,x \right ) }{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)*cos(2*x),x)
[Out]
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Maxima [A] time = 1.39047, size = 15, normalized size = 1. \[ \frac{1}{6} \, \sin \left (3 \, x\right ) + \frac{1}{2} \, \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(2*x)*cos(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247074, size = 16, normalized size = 1.07 \[ \frac{1}{3} \,{\left (2 \, \cos \left (x\right )^{2} + 1\right )} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(2*x)*cos(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.748108, size = 20, normalized size = 1.33 \[ - \frac{\sin{\left (x \right )} \cos{\left (2 x \right )}}{3} + \frac{2 \sin{\left (2 x \right )} \cos{\left (x \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*cos(2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.198428, size = 15, normalized size = 1. \[ \frac{1}{6} \, \sin \left (3 \, x\right ) + \frac{1}{2} \, \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(2*x)*cos(x),x, algorithm="giac")
[Out]