Optimal. Leaf size=19 \[ x-8 \sqrt{x}+32 \log \left (\sqrt{x}+4\right ) \]
[Out]
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Rubi [A] time = 0.0287146, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ x-8 \sqrt{x}+32 \log \left (\sqrt{x}+4\right ) \]
Antiderivative was successfully verified.
[In] Int[x/(4*Sqrt[x] + x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 8 \sqrt{x} + 32 \log{\left (\sqrt{x} + 4 \right )} + 2 \int ^{\sqrt{x}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x+4*x**(1/2)),x)
[Out]
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Mathematica [A] time = 0.0089928, size = 19, normalized size = 1. \[ x-8 \sqrt{x}+32 \log \left (\sqrt{x}+4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x/(4*Sqrt[x] + x),x]
[Out]
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Maple [A] time = 0.004, size = 16, normalized size = 0.8 \[ x+32\,\ln \left ( 4+\sqrt{x} \right ) -8\,\sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x+4*x^(1/2)),x)
[Out]
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Maxima [A] time = 0.690106, size = 20, normalized size = 1.05 \[ x - 8 \, \sqrt{x} + 32 \, \log \left (\sqrt{x} + 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x + 4*sqrt(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.26943, size = 20, normalized size = 1.05 \[ x - 8 \, \sqrt{x} + 32 \, \log \left (\sqrt{x} + 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x + 4*sqrt(x)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{4 \sqrt{x} + x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x+4*x**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.278019, size = 20, normalized size = 1.05 \[ x - 8 \, \sqrt{x} + 32 \,{\rm ln}\left (\sqrt{x} + 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x + 4*sqrt(x)),x, algorithm="giac")
[Out]