Optimal. Leaf size=10 \[ \log \left (a x+b x^3\right ) \]
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Rubi [A] time = 0.0090229, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {1587} \[ \log \left (a x+b x^3\right ) \]
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin{align*} \int \frac{a+3 b x^2}{a x+b x^3} \, dx &=\log \left (a x+b x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0059126, size = 11, normalized size = 1.1 \[ \log \left (a+b x^2\right )+\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 1.1 \begin{align*} \ln \left ( x \left ( b{x}^{2}+a \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.965325, size = 14, normalized size = 1.4 \begin{align*} \log \left (b x^{3} + a x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.978201, size = 24, normalized size = 2.4 \begin{align*} \log \left (b x^{3} + a x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.27362, size = 8, normalized size = 0.8 \begin{align*} \log{\left (a x + b x^{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09781, size = 22, normalized size = 2.2 \begin{align*} \frac{1}{2} \, \log \left (x^{2}\right ) + \log \left ({\left | b x^{2} + a \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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