Optimal. Leaf size=8 \[ \tan ^{-1}\left (\sqrt{x}\right )^2 \]
[Out]
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Rubi [A] time = 0.0553465, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ \tan ^{-1}\left (\sqrt{x}\right )^2 \]
Antiderivative was successfully verified.
[In] Int[ArcTan[Sqrt[x]]/(Sqrt[x]*(1 + x)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 2 \operatorname{atan}^{2}{\left (\sqrt{x} \right )} - \int \frac{\operatorname{atan}{\left (\sqrt{x} \right )}}{\sqrt{x} \left (x + 1\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(atan(x**(1/2))/(1+x)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00404746, size = 8, normalized size = 1. \[ \tan ^{-1}\left (\sqrt{x}\right )^2 \]
Antiderivative was successfully verified.
[In] Integrate[ArcTan[Sqrt[x]]/(Sqrt[x]*(1 + x)),x]
[Out]
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Maple [A] time = 0.006, size = 7, normalized size = 0.9 \[ \left ( \arctan \left ( \sqrt{x} \right ) \right ) ^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(arctan(x^(1/2))/(1+x)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.37559, size = 8, normalized size = 1. \[ \arctan \left (\sqrt{x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arctan(sqrt(x))/((x + 1)*sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231464, size = 8, normalized size = 1. \[ \arctan \left (\sqrt{x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arctan(sqrt(x))/((x + 1)*sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.55055, size = 7, normalized size = 0.88 \[ \operatorname{atan}^{2}{\left (\sqrt{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(atan(x**(1/2))/(1+x)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.218283, size = 8, normalized size = 1. \[ \arctan \left (\sqrt{x}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(arctan(sqrt(x))/((x + 1)*sqrt(x)),x, algorithm="giac")
[Out]