Optimal. Leaf size=19 \[ \frac{1}{3} \log \left (a-b x^3-c x^6\right ) \]
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Rubi [A] time = 0.0240185, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, 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 = 0.0064442, size = 19, 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., size = 18, normalized size = 1. \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 = 0.978929, size = 23, normalized size = 1.21 \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 = 1.01625, size = 38, normalized size = 2. \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 = 0.512, size = 14, normalized size = 0.74 \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 = 1.33209, size = 23, normalized size = 1.21 \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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