Optimal. Leaf size=13 \[ \frac{\cos ^3(x)}{3}-\cos (x) \]
[Out]
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Rubi [A] time = 0.0111025, antiderivative size = 13, 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 \[ \frac{\cos ^3(x)}{3}-\cos (x) \]
Antiderivative was successfully verified.
[In] Int[Sin[x]^3,x]
[Out]
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Rubi in Sympy [A] time = 0.642657, size = 8, normalized size = 0.62 \[ \frac{\cos ^{3}{\left (x \right )}}{3} - \cos{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(sin(x)**3,x)
[Out]
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Mathematica [A] time = 0.00280369, size = 15, normalized size = 1.15 \[ \frac{1}{12} \cos (3 x)-\frac{3 \cos (x)}{4} \]
Antiderivative was successfully verified.
[In] Integrate[Sin[x]^3,x]
[Out]
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Maple [A] time = 0.036, size = 11, normalized size = 0.9 \[ -{\frac{ \left ( 2+ \left ( \sin \left ( x \right ) \right ) ^{2} \right ) \cos \left ( x \right ) }{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(sin(x)^3,x)
[Out]
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Maxima [A] time = 1.39823, size = 15, normalized size = 1.15 \[ \frac{1}{3} \, \cos \left (x\right )^{3} - \cos \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232486, size = 15, normalized size = 1.15 \[ \frac{1}{3} \, \cos \left (x\right )^{3} - \cos \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.040446, size = 8, normalized size = 0.62 \[ \frac{\cos ^{3}{\left (x \right )}}{3} - \cos{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.208975, size = 15, normalized size = 1.15 \[ \frac{1}{3} \, \cos \left (x\right )^{3} - \cos \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sin(x)^3,x, algorithm="giac")
[Out]