Optimal. Leaf size=17 \[ \frac{1}{3} \log \left (a+b x^3+c x^6\right ) \]
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Rubi [A] time = 0.0237446, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {1468, 628} \[ \frac{1}{3} \log \left (a+b x^3+c x^6\right ) \]
Antiderivative was successfully verified.
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Rule 1468
Rule 628
Rubi steps
\begin{align*} \int \frac{x^2 \left (b+2 c x^3\right )}{a+b x^3+c x^6} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{b+2 c x}{a+b x+c x^2} \, dx,x,x^3\right )\\ &=\frac{1}{3} \log \left (a+b x^3+c x^6\right )\\ \end{align*}
Mathematica [A] time = 0.0067678, size = 17, normalized size = 1. \[ \frac{1}{3} \log \left (a+b x^3+c x^6\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 16, normalized size = 0.9 \begin{align*}{\frac{\ln \left ( c{x}^{6}+b{x}^{3}+a \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02964, size = 20, normalized size = 1.18 \begin{align*} \frac{1}{3} \, \log \left (c x^{6} + b x^{3} + a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.98849, size = 38, normalized size = 2.24 \begin{align*} \frac{1}{3} \, \log \left (c x^{6} + b x^{3} + a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.529788, size = 14, normalized size = 0.82 \begin{align*} \frac{\log{\left (a + b x^{3} + c x^{6} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.36809, size = 20, normalized size = 1.18 \begin{align*} \frac{1}{3} \, \log \left (c x^{6} + b x^{3} + a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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