Optimal. Leaf size=53 \[ -\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{x}+\frac{1}{2} b^2 B x^2 \]
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Rubi [A] time = 0.0287355, antiderivative size = 53, 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} \[ -\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{x}+\frac{1}{2} b^2 B x^2 \]
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^8} \, dx &=\int \left (\frac{a^2 A}{x^8}+\frac{a (2 A b+a B)}{x^5}+\frac{b (A b+2 a B)}{x^2}+b^2 B x\right ) \, dx\\ &=-\frac{a^2 A}{7 x^7}-\frac{a (2 A b+a B)}{4 x^4}-\frac{b (A b+2 a B)}{x}+\frac{1}{2} b^2 B x^2\\ \end{align*}
Mathematica [A] time = 0.0151625, size = 54, normalized size = 1.02 \[ -\frac{a^2 \left (4 A+7 B x^3\right )+14 a b x^3 \left (A+4 B x^3\right )-14 b^2 x^6 \left (B x^3-2 A\right )}{28 x^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 48, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{2}}{7\,{x}^{7}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{4\,{x}^{4}}}-{\frac{b \left ( Ab+2\,Ba \right ) }{x}}+{\frac{{b}^{2}B{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.031, size = 73, normalized size = 1.38 \begin{align*} \frac{1}{2} \, B b^{2} x^{2} - \frac{28 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 7 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + 4 \, A a^{2}}{28 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44573, size = 119, normalized size = 2.25 \begin{align*} \frac{14 \, B b^{2} x^{9} - 28 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} - 7 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 4 \, A a^{2}}{28 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.0215, size = 54, normalized size = 1.02 \begin{align*} \frac{B b^{2} x^{2}}{2} - \frac{4 A a^{2} + x^{6} \left (28 A b^{2} + 56 B a b\right ) + x^{3} \left (14 A a b + 7 B a^{2}\right )}{28 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17072, size = 76, normalized size = 1.43 \begin{align*} \frac{1}{2} \, B b^{2} x^{2} - \frac{56 \, B a b x^{6} + 28 \, A b^{2} x^{6} + 7 \, B a^{2} x^{3} + 14 \, A a b x^{3} + 4 \, A a^{2}}{28 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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