Optimal. Leaf size=19 \[ x-2 \sqrt{x}+2 \log \left (\sqrt{x}+1\right ) \]
[Out]
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Rubi [A] time = 0.028977, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ x-2 \sqrt{x}+2 \log \left (\sqrt{x}+1\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]/(1 + Sqrt[x]),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 2 \sqrt{x} + 2 \log{\left (\sqrt{x} + 1 \right )} + 2 \int ^{\sqrt{x}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(1/2)/(1+x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.00637374, size = 19, normalized size = 1. \[ x-2 \sqrt{x}+2 \log \left (\sqrt{x}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]/(1 + Sqrt[x]),x]
[Out]
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Maple [A] time = 0.003, size = 16, normalized size = 0.8 \[ x+2\,\ln \left ( 1+\sqrt{x} \right ) -2\,\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(1/2)/(1+x^(1/2)),x)
[Out]
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Maxima [A] time = 1.44349, size = 30, normalized size = 1.58 \[{\left (\sqrt{x} + 1\right )}^{2} - 4 \, \sqrt{x} + 2 \, \log \left (\sqrt{x} + 1\right ) - 4 \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(sqrt(x) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235673, size = 20, normalized size = 1.05 \[ x - 2 \, \sqrt{x} + 2 \, \log \left (\sqrt{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(sqrt(x) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.328301, size = 17, normalized size = 0.89 \[ - 2 \sqrt{x} + x + 2 \log{\left (\sqrt{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(1/2)/(1+x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.257443, size = 20, normalized size = 1.05 \[ x - 2 \, \sqrt{x} + 2 \,{\rm ln}\left (\sqrt{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(sqrt(x) + 1),x, algorithm="giac")
[Out]