Optimal. Leaf size=15 \[ \frac{1}{3} \log \left (x^3+3 x^2+4\right ) \]
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Rubi [A] time = 0.0090738, antiderivative size = 15, 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} \[ \frac{1}{3} \log \left (x^3+3 x^2+4\right ) \]
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin{align*} \int \frac{2 x+x^2}{4+3 x^2+x^3} \, dx &=\frac{1}{3} \log \left (4+3 x^2+x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0042837, size = 15, normalized size = 1. \[ \frac{1}{3} \log \left (x^3+3 x^2+4\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 14, normalized size = 0.9 \begin{align*}{\frac{\ln \left ({x}^{3}+3\,{x}^{2}+4 \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.927364, size = 18, normalized size = 1.2 \begin{align*} \frac{1}{3} \, \log \left (x^{3} + 3 \, x^{2} + 4\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.84928, size = 35, normalized size = 2.33 \begin{align*} \frac{1}{3} \, \log \left (x^{3} + 3 \, x^{2} + 4\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.080973, size = 12, normalized size = 0.8 \begin{align*} \frac{\log{\left (x^{3} + 3 x^{2} + 4 \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06531, size = 19, normalized size = 1.27 \begin{align*} \frac{1}{3} \, \log \left ({\left | x^{3} + 3 \, x^{2} + 4 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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