Optimal. Leaf size=14 \[ 2 \sqrt {-1+x}+2 \log (x) \]
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Rubi [A]
time = 0.08, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {6820}
\begin {gather*} 2 \sqrt {x-1}+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6820
Rubi steps
\begin {align*} \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx &=\int \left (\frac {1}{\sqrt {-1+x}}+\frac {2}{x}\right ) \, dx\\ &=2 \sqrt {-1+x}+2 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} 2 \sqrt {-1+x}+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.51, size = 13, normalized size = 0.93
method | result | size |
derivativedivides | \(2 \ln \left (x \right )+2 \sqrt {-1+x}\) | \(13\) |
default | \(2 \ln \left (x \right )+2 \sqrt {-1+x}\) | \(13\) |
trager | \(2 \sqrt {-1+x}-2 \ln \left (\frac {1}{x}\right )\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 12, normalized size = 0.86 \begin {gather*} 2 \, \sqrt {x - 1} + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 12, normalized size = 0.86 \begin {gather*} 2 \, \sqrt {x - 1} + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.86 \begin {gather*} 2 \sqrt {x - 1} + 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.79, size = 12, normalized size = 0.86 \begin {gather*} 2 \, \sqrt {x - 1} + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.39, size = 12, normalized size = 0.86 \begin {gather*} 2\,\ln \left (x\right )+2\,\sqrt {x-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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