Optimal. Leaf size=13 \[ a \log (x)+\frac{b x^2}{2} \]
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Rubi [A] time = 0.0047781, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {14} \[ a \log (x)+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a x+b x^3}{x^2} \, dx &=\int \left (\frac{a}{x}+b x\right ) \, dx\\ &=\frac{b x^2}{2}+a \log (x)\\ \end{align*}
Mathematica [A] time = 0.0009369, size = 13, normalized size = 1. \[ a \log (x)+\frac{b x^2}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.9 \begin{align*}{\frac{b{x}^{2}}{2}}+a\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03596, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{2} \, b x^{2} + a \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.33364, size = 30, normalized size = 2.31 \begin{align*} \frac{1}{2} \, b x^{2} + a \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.077242, size = 10, normalized size = 0.77 \begin{align*} a \log{\left (x \right )} + \frac{b x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18372, size = 19, normalized size = 1.46 \begin{align*} \frac{1}{2} \, b x^{2} + \frac{1}{2} \, a \log \left (x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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