Optimal. Leaf size=12 \[ \frac{1}{3} \log \left (x^3+3 x\right ) \]
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Rubi [A] time = 0.006125, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {1587} \[ \frac{1}{3} \log \left (x^3+3 x\right ) \]
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin{align*} \int \frac{1+x^2}{3 x+x^3} \, dx &=\frac{1}{3} \log \left (3 x+x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0034966, size = 17, normalized size = 1.42 \[ \frac{1}{3} \log \left (x^2+3\right )+\frac{\log (x)}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.9 \begin{align*}{\frac{\ln \left ( x \left ({x}^{2}+3 \right ) \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.993105, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{3} \, \log \left (x^{3} + 3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.948328, size = 27, normalized size = 2.25 \begin{align*} \frac{1}{3} \, \log \left (x^{3} + 3 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.083129, size = 8, normalized size = 0.67 \begin{align*} \frac{\log{\left (x^{3} + 3 x \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1117, size = 20, normalized size = 1.67 \begin{align*} \frac{1}{3} \, \log \left (x^{2} + 3\right ) + \frac{1}{6} \, \log \left (x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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