Optimal. Leaf size=65 \[ \frac{1}{6} x^6 (a C+A b)+\frac{1}{4} a A x^4+\frac{1}{7} x^7 (a D+b B)+\frac{1}{5} a B x^5+\frac{1}{8} b C x^8+\frac{1}{9} b D x^9 \]
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Rubi [A] time = 0.0742998, antiderivative size = 65, 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 = {1802} \[ \frac{1}{6} x^6 (a C+A b)+\frac{1}{4} a A x^4+\frac{1}{7} x^7 (a D+b B)+\frac{1}{5} a B x^5+\frac{1}{8} b C x^8+\frac{1}{9} b D x^9 \]
Antiderivative was successfully verified.
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Rule 1802
Rubi steps
\begin{align*} \int x^3 \left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right ) \, dx &=\int \left (a A x^3+a B x^4+(A b+a C) x^5+(b B+a D) x^6+b C x^7+b D x^8\right ) \, dx\\ &=\frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} (A b+a C) x^6+\frac{1}{7} (b B+a D) x^7+\frac{1}{8} b C x^8+\frac{1}{9} b D x^9\\ \end{align*}
Mathematica [A] time = 0.0152672, size = 65, normalized size = 1. \[ \frac{1}{6} x^6 (a C+A b)+\frac{1}{4} a A x^4+\frac{1}{7} x^7 (a D+b B)+\frac{1}{5} a B x^5+\frac{1}{8} b C x^8+\frac{1}{9} b D x^9 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 54, normalized size = 0.8 \begin{align*}{\frac{aA{x}^{4}}{4}}+{\frac{aB{x}^{5}}{5}}+{\frac{ \left ( Ab+aC \right ){x}^{6}}{6}}+{\frac{ \left ( Bb+aD \right ){x}^{7}}{7}}+{\frac{bC{x}^{8}}{8}}+{\frac{bD{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06304, size = 72, normalized size = 1.11 \begin{align*} \frac{1}{9} \, D b x^{9} + \frac{1}{8} \, C b x^{8} + \frac{1}{7} \,{\left (D a + B b\right )} x^{7} + \frac{1}{5} \, B a x^{5} + \frac{1}{6} \,{\left (C a + A b\right )} x^{6} + \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 = 1.23511, size = 150, normalized size = 2.31 \begin{align*} \frac{1}{9} x^{9} b D + \frac{1}{8} x^{8} b C + \frac{1}{7} x^{7} a D + \frac{1}{7} x^{7} b B + \frac{1}{6} x^{6} a C + \frac{1}{6} x^{6} b 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 = 0.06462, size = 60, normalized size = 0.92 \begin{align*} \frac{A a x^{4}}{4} + \frac{B a x^{5}}{5} + \frac{C b x^{8}}{8} + \frac{D b x^{9}}{9} + x^{7} \left (\frac{B b}{7} + \frac{D a}{7}\right ) + x^{6} \left (\frac{A b}{6} + \frac{C a}{6}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.56146, size = 77, normalized size = 1.18 \begin{align*} \frac{1}{9} \, D b x^{9} + \frac{1}{8} \, C b x^{8} + \frac{1}{7} \, D a x^{7} + \frac{1}{7} \, B b x^{7} + \frac{1}{6} \, C a x^{6} + \frac{1}{6} \, A b 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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