Optimal. Leaf size=18 \[ x \cos ^{-1}(x)-\sqrt{1-x^2} \]
[Out]
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Rubi [A] time = 0.00999595, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 1. \[ x \cos ^{-1}(x)-\sqrt{1-x^2} \]
Antiderivative was successfully verified.
[In] Int[ArcCos[x],x]
[Out]
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Rubi in Sympy [A] time = 1.02105, size = 12, normalized size = 0.67 \[ x \operatorname{acos}{\left (x \right )} - \sqrt{- x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(acos(x),x)
[Out]
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Mathematica [A] time = 0.00474919, size = 18, normalized size = 1. \[ x \cos ^{-1}(x)-\sqrt{1-x^2} \]
Antiderivative was successfully verified.
[In] Integrate[ArcCos[x],x]
[Out]
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Maple [A] time = 0.001, size = 17, normalized size = 0.9 \[ x\arccos \left ( x \right ) -\sqrt{-{x}^{2}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(arccos(x),x)
[Out]
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Maxima [A] time = 1.48087, size = 22, normalized size = 1.22 \[ x \arccos \left (x\right ) - \sqrt{-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arccos(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225051, size = 22, normalized size = 1.22 \[ x \arccos \left (x\right ) - \sqrt{-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arccos(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.137691, size = 12, normalized size = 0.67 \[ x \operatorname{acos}{\left (x \right )} - \sqrt{- x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(acos(x),x)
[Out]
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GIAC/XCAS [A] time = 0.215181, size = 22, normalized size = 1.22 \[ x \arccos \left (x\right ) - \sqrt{-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arccos(x),x, algorithm="giac")
[Out]