Optimal. Leaf size=74 \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{7} x^7 (A c+b C)+\frac{1}{6} b B x^6+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9 \]
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Rubi [A] time = 0.0815531, antiderivative size = 74, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038, Rules used = {1628} \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{7} x^7 (A c+b C)+\frac{1}{6} b B x^6+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9 \]
Antiderivative was successfully verified.
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Rule 1628
Rubi steps
\begin{align*} \int x^2 \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right ) \, dx &=\int \left (a A x^2+a B x^3+(A b+a C) x^4+b B x^5+(A c+b C) x^6+B c x^7+c C x^8\right ) \, dx\\ &=\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{5} (A b+a C) x^5+\frac{1}{6} b B x^6+\frac{1}{7} (A c+b C) x^7+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9\\ \end{align*}
Mathematica [A] time = 0.0154219, size = 74, normalized size = 1. \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{7} x^7 (A c+b C)+\frac{1}{6} b B x^6+\frac{1}{8} B c x^8+\frac{1}{9} c C x^9 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 61, normalized size = 0.8 \begin{align*}{\frac{aA{x}^{3}}{3}}+{\frac{aB{x}^{4}}{4}}+{\frac{ \left ( Ab+aC \right ){x}^{5}}{5}}+{\frac{bB{x}^{6}}{6}}+{\frac{ \left ( Ac+bC \right ){x}^{7}}{7}}+{\frac{Bc{x}^{8}}{8}}+{\frac{cC{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.931994, size = 81, normalized size = 1.09 \begin{align*} \frac{1}{9} \, C c x^{9} + \frac{1}{8} \, B c x^{8} + \frac{1}{6} \, B b x^{6} + \frac{1}{7} \,{\left (C b + A c\right )} x^{7} + \frac{1}{4} \, B a x^{4} + \frac{1}{5} \,{\left (C a + A b\right )} x^{5} + \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 = 1.0522, size = 169, normalized size = 2.28 \begin{align*} \frac{1}{9} x^{9} c C + \frac{1}{8} x^{8} c B + \frac{1}{7} x^{7} b C + \frac{1}{7} x^{7} c A + \frac{1}{6} x^{6} b B + \frac{1}{5} x^{5} a C + \frac{1}{5} x^{5} b 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 = 0.086636, size = 68, normalized size = 0.92 \begin{align*} \frac{A a x^{3}}{3} + \frac{B a x^{4}}{4} + \frac{B b x^{6}}{6} + \frac{B c x^{8}}{8} + \frac{C c x^{9}}{9} + x^{7} \left (\frac{A c}{7} + \frac{C b}{7}\right ) + x^{5} \left (\frac{A b}{5} + \frac{C a}{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09347, size = 86, normalized size = 1.16 \begin{align*} \frac{1}{9} \, C c x^{9} + \frac{1}{8} \, B c x^{8} + \frac{1}{7} \, C b x^{7} + \frac{1}{7} \, A c x^{7} + \frac{1}{6} \, B b x^{6} + \frac{1}{5} \, C a x^{5} + \frac{1}{5} \, A b 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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