Optimal. Leaf size=8 \[ a \log (x)+b x \]
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Rubi [A] time = 0.0030192, antiderivative size = 8, normalized size of antiderivative = 1., 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} \[ a \log (x)+b x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{x} \, dx &=\int \left (b+\frac{a}{x}\right ) \, dx\\ &=b x+a \log (x)\\ \end{align*}
Mathematica [A] time = 0.0008298, size = 8, normalized size = 1. \[ a \log (x)+b x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 9, normalized size = 1.1 \begin{align*} bx+a\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0344, size = 11, normalized size = 1.38 \begin{align*} b x + a \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55437, size = 22, normalized size = 2.75 \begin{align*} b x + a \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.116574, size = 7, normalized size = 0.88 \begin{align*} a \log{\left (x \right )} + b x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15128, size = 12, normalized size = 1.5 \begin{align*} b x + a \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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