Optimal. Leaf size=11 \[ b \log (x)-\frac {a}{x} \]
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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 = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {43} \begin {gather*} b \log (x)-\frac {a}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^2} \, dx &=\int \left (\frac {a}{x^2}+\frac {b}{x}\right ) \, dx\\ &=-\frac {a}{x}+b \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} b \log (x)-\frac {a}{x} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a+b x}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.41, size = 13, normalized size = 1.18 \begin {gather*} \frac {b x \log \relax (x) - a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 12, normalized size = 1.09 \begin {gather*} b \log \left ({\left | x \right |}\right ) - \frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 12, normalized size = 1.09 \begin {gather*} b \ln \relax (x )-\frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 11, normalized size = 1.00 \begin {gather*} b \log \relax (x) - \frac {a}{x} \end {gather*}
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 \begin {gather*} b\,\ln \relax (x)-\frac {a}{x} \end {gather*}
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 \begin {gather*} - \frac {a}{x} + b \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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