Optimal. Leaf size=50 \[ -\frac{a^2 A}{8 x^8}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B x \]
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Rubi [A] time = 0.0287994, antiderivative size = 50, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ -\frac{a^2 A}{8 x^8}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B x \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x^9} \, dx &=\int \left (b^2 B+\frac{a^2 A}{x^9}+\frac{a (2 A b+a B)}{x^6}+\frac{b (A b+2 a B)}{x^3}\right ) \, dx\\ &=-\frac{a^2 A}{8 x^8}-\frac{a (2 A b+a B)}{5 x^5}-\frac{b (A b+2 a B)}{2 x^2}+b^2 B x\\ \end{align*}
Mathematica [A] time = 0.021259, size = 50, normalized size = 1. \[ -\frac{a^2 A}{8 x^8}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 45, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{2}}{8\,{x}^{8}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{5\,{x}^{5}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{2\,{x}^{2}}}+{b}^{2}Bx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17527, size = 69, normalized size = 1.38 \begin{align*} B b^{2} x - \frac{20 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 8 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + 5 \, A a^{2}}{40 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.33918, size = 119, normalized size = 2.38 \begin{align*} \frac{40 \, B b^{2} x^{9} - 20 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} - 8 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 5 \, A a^{2}}{40 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.10184, size = 51, normalized size = 1.02 \begin{align*} B b^{2} x - \frac{5 A a^{2} + x^{6} \left (20 A b^{2} + 40 B a b\right ) + x^{3} \left (16 A a b + 8 B a^{2}\right )}{40 x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19952, size = 72, normalized size = 1.44 \begin{align*} B b^{2} x - \frac{40 \, B a b x^{6} + 20 \, A b^{2} x^{6} + 8 \, B a^{2} x^{3} + 16 \, A a b x^{3} + 5 \, A a^{2}}{40 \, x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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