Optimal. Leaf size=14 \[ 2 \sqrt {x-1}+2 \log (x) \]
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Rubi [A] time = 0.12, 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 = {6688} \[ 2 \sqrt {x-1}+2 \log (x) \]
Antiderivative was successfully verified.
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Rule 6688
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 \[ 2 \sqrt {x-1}+2 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 12, normalized size = 0.86 \[ 2 \, \sqrt {x - 1} + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.40, size = 12, normalized size = 0.86 \[ 2 \, \sqrt {x - 1} + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.93 \[ 2 \ln \relax (x )+2 \sqrt {x -1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 12, normalized size = 0.86 \[ 2 \, \sqrt {x - 1} + 2 \, \log \relax (x) \]
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 \[ 2\,\ln \relax (x)+2\,\sqrt {x-1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 12, normalized size = 0.86 \[ 2 \sqrt {x - 1} + 2 \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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