Optimal. Leaf size=37 \[ \frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7 \]
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Rubi [A] time = 0.035158, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {766} \[ \frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7 \]
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 ) \, dx &=\int \left (a A x^3+a B x^4+A c x^5+B c x^6\right ) \, dx\\ &=\frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7\\ \end{align*}
Mathematica [A] time = 0.002291, size = 37, normalized size = 1. \[ \frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 30, normalized size = 0.8 \begin{align*}{\frac{aA{x}^{4}}{4}}+{\frac{aB{x}^{5}}{5}}+{\frac{Ac{x}^{6}}{6}}+{\frac{Bc{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05521, size = 39, normalized size = 1.05 \begin{align*} \frac{1}{7} \, B c x^{7} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{4} \, A a x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.30428, size = 74, normalized size = 2. \begin{align*} \frac{1}{7} x^{7} c B + \frac{1}{6} x^{6} c A + \frac{1}{5} x^{5} a B + \frac{1}{4} x^{4} a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.061884, size = 32, normalized size = 0.86 \begin{align*} \frac{A a x^{4}}{4} + \frac{A c x^{6}}{6} + \frac{B a x^{5}}{5} + \frac{B c x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09268, size = 39, normalized size = 1.05 \begin{align*} \frac{1}{7} \, B c x^{7} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, B a x^{5} + \frac{1}{4} \, A a x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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