Optimal. Leaf size=14 \[ 2 \sqrt{x-1}+2 \log (x) \]
[Out]
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Rubi [A] time = 0.193232, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ 2 \sqrt{x-1}+2 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(2*Sqrt[-1 + x] + x)/(Sqrt[-1 + x]*x),x]
[Out]
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Rubi in Sympy [A] time = 11.3264, size = 12, normalized size = 0.86 \[ 2 \sqrt{x - 1} + 2 \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x+2*(-1+x)**(1/2))/x/(-1+x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00777559, size = 14, normalized size = 1. \[ 2 \sqrt{x-1}+2 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(2*Sqrt[-1 + x] + x)/(Sqrt[-1 + x]*x),x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[ 2\,\ln \left ( x \right ) +2\,\sqrt{-1+x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x+2*(-1+x)^(1/2))/x/(-1+x)^(1/2),x)
[Out]
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Maxima [A] time = 0.801496, size = 16, normalized size = 1.14 \[ 2 \, \sqrt{x - 1} + 2 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2*sqrt(x - 1))/(sqrt(x - 1)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.26912, size = 16, normalized size = 1.14 \[ 2 \, \sqrt{x - 1} + 2 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2*sqrt(x - 1))/(sqrt(x - 1)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.347121, size = 12, normalized size = 0.86 \[ 2 \sqrt{x - 1} + 2 \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x+2*(-1+x)**(1/2))/x/(-1+x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.264567, size = 16, normalized size = 1.14 \[ 2 \, \sqrt{x - 1} + 2 \,{\rm ln}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2*sqrt(x - 1))/(sqrt(x - 1)*x),x, algorithm="giac")
[Out]