Optimal. Leaf size=42 \[ \frac{\left (a+b x^3\right )^3 (A b-a B)}{9 b^2}+\frac{B \left (a+b x^3\right )^4}{12 b^2} \]
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Rubi [A] time = 0.0721012, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {444, 43} \[ \frac{\left (a+b x^3\right )^3 (A b-a B)}{9 b^2}+\frac{B \left (a+b x^3\right )^4}{12 b^2} \]
Antiderivative was successfully verified.
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Rule 444
Rule 43
Rubi steps
\begin{align*} \int x^2 \left (a+b x^3\right )^2 \left (A+B x^3\right ) \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int (a+b x)^2 (A+B x) \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{(A b-a B) (a+b x)^2}{b}+\frac{B (a+b x)^3}{b}\right ) \, dx,x,x^3\right )\\ &=\frac{(A b-a B) \left (a+b x^3\right )^3}{9 b^2}+\frac{B \left (a+b x^3\right )^4}{12 b^2}\\ \end{align*}
Mathematica [A] time = 0.0145113, size = 51, normalized size = 1.21 \[ \frac{1}{36} x^3 \left (12 a^2 A+4 b x^6 (2 a B+A b)+6 a x^3 (a B+2 A b)+3 b^2 B x^9\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 52, normalized size = 1.2 \begin{align*}{\frac{{b}^{2}B{x}^{12}}{12}}+{\frac{ \left ({b}^{2}A+2\,abB \right ){x}^{9}}{9}}+{\frac{ \left ( 2\,abA+{a}^{2}B \right ){x}^{6}}{6}}+{\frac{{a}^{2}A{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12715, size = 69, normalized size = 1.64 \begin{align*} \frac{1}{12} \, B b^{2} x^{12} + \frac{1}{9} \,{\left (2 \, B a b + A b^{2}\right )} x^{9} + \frac{1}{6} \,{\left (B a^{2} + 2 \, A a b\right )} x^{6} + \frac{1}{3} \, A a^{2} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.26638, size = 131, normalized size = 3.12 \begin{align*} \frac{1}{12} x^{12} b^{2} B + \frac{2}{9} x^{9} b a B + \frac{1}{9} x^{9} b^{2} A + \frac{1}{6} x^{6} a^{2} B + \frac{1}{3} x^{6} b a A + \frac{1}{3} x^{3} a^{2} A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067793, size = 54, normalized size = 1.29 \begin{align*} \frac{A a^{2} x^{3}}{3} + \frac{B b^{2} x^{12}}{12} + x^{9} \left (\frac{A b^{2}}{9} + \frac{2 B a b}{9}\right ) + x^{6} \left (\frac{A a b}{3} + \frac{B a^{2}}{6}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18901, size = 72, normalized size = 1.71 \begin{align*} \frac{1}{12} \, B b^{2} x^{12} + \frac{2}{9} \, B a b x^{9} + \frac{1}{9} \, A b^{2} x^{9} + \frac{1}{6} \, B a^{2} x^{6} + \frac{1}{3} \, A a b x^{6} + \frac{1}{3} \, A a^{2} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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