Optimal. Leaf size=31 \[ -\frac{a B+A b}{x}-\frac{a A}{4 x^4}+\frac{1}{2} b B x^2 \]
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Rubi [A] time = 0.0173916, antiderivative size = 31, 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} \[ -\frac{a B+A b}{x}-\frac{a A}{4 x^4}+\frac{1}{2} b B x^2 \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right ) \left (A+B x^3\right )}{x^5} \, dx &=\int \left (\frac{a A}{x^5}+\frac{A b+a B}{x^2}+b B x\right ) \, dx\\ &=-\frac{a A}{4 x^4}-\frac{A b+a B}{x}+\frac{1}{2} b B x^2\\ \end{align*}
Mathematica [A] time = 0.0118031, size = 32, normalized size = 1.03 \[ \frac{-a B-A b}{x}-\frac{a A}{4 x^4}+\frac{1}{2} b B x^2 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 28, normalized size = 0.9 \begin{align*}{\frac{bB{x}^{2}}{2}}-{\frac{Aa}{4\,{x}^{4}}}-{\frac{Ab+Ba}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.30636, size = 39, normalized size = 1.26 \begin{align*} \frac{1}{2} \, B b x^{2} - \frac{4 \,{\left (B a + A b\right )} x^{3} + A a}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.37449, size = 63, normalized size = 2.03 \begin{align*} \frac{2 \, B b x^{6} - 4 \,{\left (B a + A b\right )} x^{3} - A a}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.378447, size = 29, normalized size = 0.94 \begin{align*} \frac{B b x^{2}}{2} - \frac{A a + x^{3} \left (4 A b + 4 B a\right )}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20865, size = 42, normalized size = 1.35 \begin{align*} \frac{1}{2} \, B b x^{2} - \frac{4 \, B a x^{3} + 4 \, A b x^{3} + A a}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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