Optimal. Leaf size=28 \[ -\frac{a B+A b}{2 x^2}-\frac{a A}{5 x^5}+b B x \]
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Rubi [A] time = 0.0164566, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {448} \[ -\frac{a B+A b}{2 x^2}-\frac{a A}{5 x^5}+b B x \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right ) \left (A+B x^3\right )}{x^6} \, dx &=\int \left (b B+\frac{a A}{x^6}+\frac{A b+a B}{x^3}\right ) \, dx\\ &=-\frac{a A}{5 x^5}-\frac{A b+a B}{2 x^2}+b B x\\ \end{align*}
Mathematica [A] time = 0.0111974, size = 30, normalized size = 1.07 \[ \frac{-a B-A b}{2 x^2}-\frac{a A}{5 x^5}+b B x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 25, normalized size = 0.9 \begin{align*} bBx-{\frac{Ab+Ba}{2\,{x}^{2}}}-{\frac{Aa}{5\,{x}^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.33122, size = 36, normalized size = 1.29 \begin{align*} B b x - \frac{5 \,{\left (B a + A b\right )} x^{3} + 2 \, A a}{10 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40485, size = 69, normalized size = 2.46 \begin{align*} \frac{10 \, B b x^{6} - 5 \,{\left (B a + A b\right )} x^{3} - 2 \, A a}{10 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.408755, size = 27, normalized size = 0.96 \begin{align*} B b x - \frac{2 A a + x^{3} \left (5 A b + 5 B a\right )}{10 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13208, size = 39, normalized size = 1.39 \begin{align*} B b x - \frac{5 \, B a x^{3} + 5 \, A b x^{3} + 2 \, A a}{10 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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