Optimal. Leaf size=53 \[ -\frac{a^2 A}{4 x^4}+\frac{1}{2} b x^2 (2 a B+A b)-\frac{a (a B+2 A b)}{x}+\frac{1}{5} b^2 B x^5 \]
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Rubi [A] time = 0.030959, 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} \[ -\frac{a^2 A}{4 x^4}+\frac{1}{2} b x^2 (2 a B+A b)-\frac{a (a B+2 A b)}{x}+\frac{1}{5} b^2 B x^5 \]
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^5} \, dx &=\int \left (\frac{a^2 A}{x^5}+\frac{a (2 A b+a B)}{x^2}+b (A b+2 a B) x+b^2 B x^4\right ) \, dx\\ &=-\frac{a^2 A}{4 x^4}-\frac{a (2 A b+a B)}{x}+\frac{1}{2} b (A b+2 a B) x^2+\frac{1}{5} b^2 B x^5\\ \end{align*}
Mathematica [A] time = 0.0156971, size = 51, normalized size = 0.96 \[ \frac{-5 a^2 A+10 b x^6 (2 a B+A b)-20 a x^3 (a B+2 A b)+4 b^2 B x^9}{20 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 50, normalized size = 0.9 \begin{align*}{\frac{{b}^{2}B{x}^{5}}{5}}+{\frac{A{x}^{2}{b}^{2}}{2}}+B{x}^{2}ab-{\frac{A{a}^{2}}{4\,{x}^{4}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17113, size = 72, normalized size = 1.36 \begin{align*} \frac{1}{5} \, B b^{2} x^{5} + \frac{1}{2} \,{\left (2 \, B a b + A b^{2}\right )} x^{2} - \frac{4 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + A a^{2}}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70558, size = 119, normalized size = 2.25 \begin{align*} \frac{4 \, B b^{2} x^{9} + 10 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} - 20 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 5 \, A a^{2}}{20 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.442399, size = 51, normalized size = 0.96 \begin{align*} \frac{B b^{2} x^{5}}{5} + x^{2} \left (\frac{A b^{2}}{2} + B a b\right ) - \frac{A a^{2} + x^{3} \left (8 A a b + 4 B a^{2}\right )}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1991, size = 73, normalized size = 1.38 \begin{align*} \frac{1}{5} \, B b^{2} x^{5} + B a b x^{2} + \frac{1}{2} \, A b^{2} x^{2} - \frac{4 \, B a^{2} x^{3} + 8 \, A a b x^{3} + A a^{2}}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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