Optimal. Leaf size=93 \[ \frac{1}{2} a^2 A c x^6+\frac{1}{4} a^3 A x^4+\frac{3}{7} a^2 B c x^7+\frac{1}{5} a^3 B x^5+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11} \]
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Rubi [A] time = 0.100903, antiderivative size = 93, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {766} \[ \frac{1}{2} a^2 A c x^6+\frac{1}{4} a^3 A x^4+\frac{3}{7} a^2 B c x^7+\frac{1}{5} a^3 B x^5+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11} \]
Antiderivative was successfully verified.
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Rule 766
Rubi steps
\begin{align*} \int x^3 (A+B x) \left (a+c x^2\right )^3 \, dx &=\int \left (a^3 A x^3+a^3 B x^4+3 a^2 A c x^5+3 a^2 B c x^6+3 a A c^2 x^7+3 a B c^2 x^8+A c^3 x^9+B c^3 x^{10}\right ) \, dx\\ &=\frac{1}{4} a^3 A x^4+\frac{1}{5} a^3 B x^5+\frac{1}{2} a^2 A c x^6+\frac{3}{7} a^2 B c x^7+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11}\\ \end{align*}
Mathematica [A] time = 0.0035024, size = 93, normalized size = 1. \[ \frac{1}{2} a^2 A c x^6+\frac{1}{4} a^3 A x^4+\frac{3}{7} a^2 B c x^7+\frac{1}{5} a^3 B x^5+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 78, normalized size = 0.8 \begin{align*}{\frac{{a}^{3}A{x}^{4}}{4}}+{\frac{{a}^{3}B{x}^{5}}{5}}+{\frac{{a}^{2}Ac{x}^{6}}{2}}+{\frac{3\,{a}^{2}Bc{x}^{7}}{7}}+{\frac{3\,aA{c}^{2}{x}^{8}}{8}}+{\frac{aB{c}^{2}{x}^{9}}{3}}+{\frac{A{c}^{3}{x}^{10}}{10}}+{\frac{B{c}^{3}{x}^{11}}{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02378, size = 104, normalized size = 1.12 \begin{align*} \frac{1}{11} \, B c^{3} x^{11} + \frac{1}{10} \, A c^{3} x^{10} + \frac{1}{3} \, B a c^{2} x^{9} + \frac{3}{8} \, A a c^{2} x^{8} + \frac{3}{7} \, B a^{2} c x^{7} + \frac{1}{2} \, A a^{2} c x^{6} + \frac{1}{5} \, B a^{3} x^{5} + \frac{1}{4} \, A a^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57675, size = 188, normalized size = 2.02 \begin{align*} \frac{1}{11} x^{11} c^{3} B + \frac{1}{10} x^{10} c^{3} A + \frac{1}{3} x^{9} c^{2} a B + \frac{3}{8} x^{8} c^{2} a A + \frac{3}{7} x^{7} c a^{2} B + \frac{1}{2} x^{6} c a^{2} A + \frac{1}{5} x^{5} a^{3} B + \frac{1}{4} x^{4} a^{3} A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.079366, size = 90, normalized size = 0.97 \begin{align*} \frac{A a^{3} x^{4}}{4} + \frac{A a^{2} c x^{6}}{2} + \frac{3 A a c^{2} x^{8}}{8} + \frac{A c^{3} x^{10}}{10} + \frac{B a^{3} x^{5}}{5} + \frac{3 B a^{2} c x^{7}}{7} + \frac{B a c^{2} x^{9}}{3} + \frac{B c^{3} x^{11}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09873, size = 104, normalized size = 1.12 \begin{align*} \frac{1}{11} \, B c^{3} x^{11} + \frac{1}{10} \, A c^{3} x^{10} + \frac{1}{3} \, B a c^{2} x^{9} + \frac{3}{8} \, A a c^{2} x^{8} + \frac{3}{7} \, B a^{2} c x^{7} + \frac{1}{2} \, A a^{2} c x^{6} + \frac{1}{5} \, B a^{3} x^{5} + \frac{1}{4} \, A a^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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