Optimal. Leaf size=11 \[ b \log (x)-\frac{a}{x} \]
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Rubi [A] time = 0.0043358, antiderivative size = 11, 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} \[ b \log (x)-\frac{a}{x} \]
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*}
Mathematica [A] time = 0.0019118, size = 11, normalized size = 1. \[ b \log (x)-\frac{a}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 12, normalized size = 1.1 \begin{align*} -{\frac{a}{x}}+b\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01865, size = 15, normalized size = 1.36 \begin{align*} b \log \left (x\right ) - \frac{a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53353, size = 27, normalized size = 2.45 \begin{align*} \frac{b x \log \left (x\right ) - a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.379399, size = 7, normalized size = 0.64 \begin{align*} - \frac{a}{x} + b \log{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15994, size = 16, normalized size = 1.45 \begin{align*} b \log \left ({\left | x \right |}\right ) - \frac{a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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