Optimal. Leaf size=50 \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac{1}{4} b^2 B x^4 \]
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Rubi [A] time = 0.0283431, 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} \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac{1}{4} b^2 B x^4 \]
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^6} \, dx &=\int \left (b (A b+2 a B)+\frac{a^2 A}{x^6}+\frac{a (2 A b+a B)}{x^3}+b^2 B x^3\right ) \, dx\\ &=-\frac{a^2 A}{5 x^5}-\frac{a (2 A b+a B)}{2 x^2}+b (A b+2 a B) x+\frac{1}{4} b^2 B x^4\\ \end{align*}
Mathematica [A] time = 0.0182721, size = 50, normalized size = 1. \[ -\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac{1}{4} b^2 B x^4 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 46, normalized size = 0.9 \begin{align*}{\frac{{b}^{2}B{x}^{4}}{4}}+{b}^{2}Ax+2\,abBx-{\frac{a \left ( 2\,Ab+Ba \right ) }{2\,{x}^{2}}}-{\frac{A{a}^{2}}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.28127, size = 69, normalized size = 1.38 \begin{align*} \frac{1}{4} \, B b^{2} x^{4} +{\left (2 \, B a b + A b^{2}\right )} x - \frac{5 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + 2 \, A a^{2}}{10 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69, size = 119, normalized size = 2.38 \begin{align*} \frac{5 \, B b^{2} x^{9} + 20 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} - 10 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 4 \, A a^{2}}{20 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.470905, size = 51, normalized size = 1.02 \begin{align*} \frac{B b^{2} x^{4}}{4} + x \left (A b^{2} + 2 B a b\right ) - \frac{2 A a^{2} + x^{3} \left (10 A a b + 5 B a^{2}\right )}{10 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12228, size = 69, normalized size = 1.38 \begin{align*} \frac{1}{4} \, B b^{2} x^{4} + 2 \, B a b x + A b^{2} x - \frac{5 \, B a^{2} x^{3} + 10 \, A a b x^{3} + 2 \, A a^{2}}{10 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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