Optimal. Leaf size=11 \[ \sin (x)-\frac{\sin ^3(x)}{3} \]
[Out]
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Rubi [A] time = 0.0107204, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \sin (x)-\frac{\sin ^3(x)}{3} \]
Antiderivative was successfully verified.
[In] Int[Cos[x]^3,x]
[Out]
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Rubi in Sympy [A] time = 0.671478, size = 8, normalized size = 0.73 \[ - \frac{\sin ^{3}{\left (x \right )}}{3} + \sin{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(x)**3,x)
[Out]
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Mathematica [A] time = 0.00293136, size = 15, normalized size = 1.36 \[ \frac{3 \sin (x)}{4}+\frac{1}{12} \sin (3 x) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[x]^3,x]
[Out]
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Maple [A] time = 0.04, size = 11, normalized size = 1. \[{\frac{ \left ( 2+ \left ( \cos \left ( x \right ) \right ) ^{2} \right ) \sin \left ( x \right ) }{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(x)^3,x)
[Out]
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Maxima [A] time = 1.35495, size = 12, normalized size = 1.09 \[ -\frac{1}{3} \, \sin \left (x\right )^{3} + \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206491, size = 14, normalized size = 1.27 \[ \frac{1}{3} \,{\left (\cos \left (x\right )^{2} + 2\right )} \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.040248, size = 8, normalized size = 0.73 \[ - \frac{\sin ^{3}{\left (x \right )}}{3} + \sin{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.234835, size = 12, normalized size = 1.09 \[ -\frac{1}{3} \, \sin \left (x\right )^{3} + \sin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(x)^3,x, algorithm="giac")
[Out]