Optimal. Leaf size=12 \[ a x+\frac{b x^3}{3} \]
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Rubi [A] time = 0.0033423, antiderivative size = 12, 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} \[ a x+\frac{b x^3}{3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a x+b x^3}{x} \, dx &=\int \left (a+b x^2\right ) \, dx\\ &=a x+\frac{b x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0004057, size = 12, normalized size = 1. \[ a x+\frac{b x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 11, normalized size = 0.9 \begin{align*} ax+{\frac{b{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04063, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{3} \, b x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.3455, size = 23, normalized size = 1.92 \begin{align*} \frac{1}{3} \, b x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.051531, size = 8, normalized size = 0.67 \begin{align*} a x + \frac{b x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23919, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{3} \, b x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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