Optimal. Leaf size=37 \[ \frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{5} A c x^5+\frac{1}{6} B c x^6 \]
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Rubi [A] time = 0.0291948, 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} \[ \frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{5} A c x^5+\frac{1}{6} B c x^6 \]
Antiderivative was successfully verified.
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Rule 766
Rubi steps
\begin{align*} \int x^2 (A+B x) \left (a+c x^2\right ) \, dx &=\int \left (a A x^2+a B x^3+A c x^4+B c x^5\right ) \, dx\\ &=\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{5} A c x^5+\frac{1}{6} B c x^6\\ \end{align*}
Mathematica [A] time = 0.0020048, size = 37, normalized size = 1. \[ \frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{5} A c x^5+\frac{1}{6} B c x^6 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 30, normalized size = 0.8 \begin{align*}{\frac{aA{x}^{3}}{3}}+{\frac{aB{x}^{4}}{4}}+{\frac{Ac{x}^{5}}{5}}+{\frac{Bc{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0607, size = 39, normalized size = 1.05 \begin{align*} \frac{1}{6} \, B c x^{6} + \frac{1}{5} \, A c x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{3} \, A a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.33028, size = 74, normalized size = 2. \begin{align*} \frac{1}{6} x^{6} c B + \frac{1}{5} x^{5} c A + \frac{1}{4} x^{4} a B + \frac{1}{3} x^{3} a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.102037, size = 32, normalized size = 0.86 \begin{align*} \frac{A a x^{3}}{3} + \frac{A c x^{5}}{5} + \frac{B a x^{4}}{4} + \frac{B c x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1808, size = 39, normalized size = 1.05 \begin{align*} \frac{1}{6} \, B c x^{6} + \frac{1}{5} \, A c x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{3} \, A a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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