Optimal. Leaf size=30 \[ \frac{x}{4}+\frac{1}{8} \sin (2 x)+\frac{1}{16} \sin (4 x)+\frac{1}{24} \sin (6 x) \]
[Out]
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Rubi [A] time = 0.0482573, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{x}{4}+\frac{1}{8} \sin (2 x)+\frac{1}{16} \sin (4 x)+\frac{1}{24} \sin (6 x) \]
Antiderivative was successfully verified.
[In] Int[Cos[x]*Cos[2*x]*Cos[3*x],x]
[Out]
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Rubi in Sympy [A] time = 2.2711, size = 27, normalized size = 0.9 \[ \frac{x}{4} + \frac{\sin{\left (2 x \right )}}{4} + \frac{\sin{\left (3 x \right )} \cos{\left (3 x \right )}}{12} + \frac{\sin{\left (4 x \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)*cos(2*x)*cos(3*x),x)
[Out]
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Mathematica [A] time = 0.0137906, size = 30, normalized size = 1. \[ \frac{x}{4}+\frac{1}{8} \sin (2 x)+\frac{1}{16} \sin (4 x)+\frac{1}{24} \sin (6 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]*Cos[2*x]*Cos[3*x],x]
[Out]
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Maple [A] time = 0.003, size = 23, normalized size = 0.8 \[{\frac{x}{4}}+{\frac{\sin \left ( 2\,x \right ) }{8}}+{\frac{\sin \left ( 4\,x \right ) }{16}}+{\frac{\sin \left ( 6\,x \right ) }{24}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)*cos(2*x)*cos(3*x),x)
[Out]
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Maxima [A] time = 1.38854, size = 30, normalized size = 1. \[ \frac{1}{4} \, x + \frac{1}{24} \, \sin \left (6 \, x\right ) + \frac{1}{16} \, \sin \left (4 \, x\right ) + \frac{1}{8} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(3*x)*cos(2*x)*cos(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.25978, size = 34, normalized size = 1.13 \[ \frac{1}{12} \,{\left (16 \, \cos \left (x\right )^{5} - 10 \, \cos \left (x\right )^{3} + 3 \, \cos \left (x\right )\right )} \sin \left (x\right ) + \frac{1}{4} \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(3*x)*cos(2*x)*cos(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 22.0666, size = 114, normalized size = 3.8 \[ - \frac{x \sin{\left (x \right )} \sin{\left (2 x \right )} \cos{\left (3 x \right )}}{4} + \frac{x \sin{\left (x \right )} \sin{\left (3 x \right )} \cos{\left (2 x \right )}}{4} + \frac{x \sin{\left (2 x \right )} \sin{\left (3 x \right )} \cos{\left (x \right )}}{4} + \frac{x \cos{\left (x \right )} \cos{\left (2 x \right )} \cos{\left (3 x \right )}}{4} - \frac{\sin{\left (x \right )} \cos{\left (2 x \right )} \cos{\left (3 x \right )}}{24} - \frac{\sin{\left (2 x \right )} \cos{\left (x \right )} \cos{\left (3 x \right )}}{6} + \frac{3 \sin{\left (3 x \right )} \cos{\left (x \right )} \cos{\left (2 x \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)*cos(2*x)*cos(3*x),x)
[Out]
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GIAC/XCAS [A] time = 0.204311, size = 30, normalized size = 1. \[ \frac{1}{4} \, x + \frac{1}{24} \, \sin \left (6 \, x\right ) + \frac{1}{16} \, \sin \left (4 \, x\right ) + \frac{1}{8} \, \sin \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(3*x)*cos(2*x)*cos(x),x, algorithm="giac")
[Out]