Optimal. Leaf size=11 \[ a \log (x)-\frac {b}{x} \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ a \log (x)-\frac {b}{x} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+\frac {b}{x}}{x} \, dx &=\int \left (\frac {b}{x^2}+\frac {a}{x}\right ) \, dx\\ &=-\frac {b}{x}+a \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ a \log (x)-\frac {b}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 13, normalized size = 1.18 \[ \frac {a x \log \relax (x) - b}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 12, normalized size = 1.09 \[ a \log \left ({\left | x \right |}\right ) - \frac {b}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 12, normalized size = 1.09 \[ a \ln \relax (x )-\frac {b}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.03, size = 11, normalized size = 1.00 \[ a \log \relax (x) - \frac {b}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 11, normalized size = 1.00 \[ a\,\ln \relax (x)-\frac {b}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 7, normalized size = 0.64 \[ a \log {\relax (x )} - \frac {b}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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