Optimal. Leaf size=46 \[ a^2 A \log (x)+\frac{2}{3} a A b x^3+\frac{B \left (a+b x^3\right )^3}{9 b}+\frac{1}{6} A b^2 x^6 \]
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Rubi [A] time = 0.0326931, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15, Rules used = {446, 80, 43} \[ a^2 A \log (x)+\frac{2}{3} a A b x^3+\frac{B \left (a+b x^3\right )^3}{9 b}+\frac{1}{6} A b^2 x^6 \]
Antiderivative was successfully verified.
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Rule 446
Rule 80
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^2 (A+B x)}{x} \, dx,x,x^3\right )\\ &=\frac{B \left (a+b x^3\right )^3}{9 b}+\frac{1}{3} A \operatorname{Subst}\left (\int \frac{(a+b x)^2}{x} \, dx,x,x^3\right )\\ &=\frac{B \left (a+b x^3\right )^3}{9 b}+\frac{1}{3} A \operatorname{Subst}\left (\int \left (2 a b+\frac{a^2}{x}+b^2 x\right ) \, dx,x,x^3\right )\\ &=\frac{2}{3} a A b x^3+\frac{1}{6} A b^2 x^6+\frac{B \left (a+b x^3\right )^3}{9 b}+a^2 A \log (x)\\ \end{align*}
Mathematica [A] time = 0.0142697, size = 51, normalized size = 1.11 \[ a^2 A \log (x)+\frac{1}{6} b x^6 (2 a B+A b)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{9} b^2 B x^9 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 52, normalized size = 1.1 \begin{align*}{\frac{B{b}^{2}{x}^{9}}{9}}+{\frac{A{b}^{2}{x}^{6}}{6}}+{\frac{B{x}^{6}ab}{3}}+{\frac{2\,aAb{x}^{3}}{3}}+{\frac{B{x}^{3}{a}^{2}}{3}}+{a}^{2}A\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.21736, size = 70, normalized size = 1.52 \begin{align*} \frac{1}{9} \, B b^{2} x^{9} + \frac{1}{6} \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + \frac{1}{3} \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + \frac{1}{3} \, A a^{2} \log \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44867, size = 116, normalized size = 2.52 \begin{align*} \frac{1}{9} \, B b^{2} x^{9} + \frac{1}{6} \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + \frac{1}{3} \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + A a^{2} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.282266, size = 53, normalized size = 1.15 \begin{align*} A a^{2} \log{\left (x \right )} + \frac{B b^{2} x^{9}}{9} + x^{6} \left (\frac{A b^{2}}{6} + \frac{B a b}{3}\right ) + x^{3} \left (\frac{2 A a b}{3} + \frac{B a^{2}}{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11482, size = 70, normalized size = 1.52 \begin{align*} \frac{1}{9} \, B b^{2} x^{9} + \frac{1}{3} \, B a b x^{6} + \frac{1}{6} \, A b^{2} x^{6} + \frac{1}{3} \, B a^{2} x^{3} + \frac{2}{3} \, A a b x^{3} + A a^{2} \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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