Optimal. Leaf size=22 \[ -\sqrt{x}+x \tan ^{-1}\left (\sqrt{x}\right )+\tan ^{-1}\left (\sqrt{x}\right ) \]
[Out]
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Rubi [A] time = 0.0125779, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.667 \[ -\sqrt{x}+x \tan ^{-1}\left (\sqrt{x}\right )+\tan ^{-1}\left (\sqrt{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[ArcTan[Sqrt[x]],x]
[Out]
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Rubi in Sympy [A] time = 1.3685, size = 19, normalized size = 0.86 \[ - \sqrt{x} + x \operatorname{atan}{\left (\sqrt{x} \right )} + \operatorname{atan}{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(atan(x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0106311, size = 18, normalized size = 0.82 \[ (x+1) \tan ^{-1}\left (\sqrt{x}\right )-\sqrt{x} \]
Antiderivative was successfully verified.
[In] Integrate[ArcTan[Sqrt[x]],x]
[Out]
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Maple [A] time = 0.003, size = 17, normalized size = 0.8 \[ \arctan \left ( \sqrt{x} \right ) +x\arctan \left ( \sqrt{x} \right ) -\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(arctan(x^(1/2)),x)
[Out]
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Maxima [A] time = 1.53953, size = 22, normalized size = 1. \[ x \arctan \left (\sqrt{x}\right ) - \sqrt{x} + \arctan \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arctan(sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217494, size = 19, normalized size = 0.86 \[{\left (x + 1\right )} \arctan \left (\sqrt{x}\right ) - \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arctan(sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.13534, size = 19, normalized size = 0.86 \[ - \sqrt{x} + x \operatorname{atan}{\left (\sqrt{x} \right )} + \operatorname{atan}{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(atan(x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.214596, size = 22, normalized size = 1. \[ x \arctan \left (\sqrt{x}\right ) - \sqrt{x} + \arctan \left (\sqrt{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arctan(sqrt(x)),x, algorithm="giac")
[Out]