Optimal. Leaf size=31 \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{b B}{x} \]
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Rubi [A] time = 0.015195, 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} \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{b B}{x} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right ) \left (A+B x^2\right )}{x^6} \, dx &=\int \left (\frac{a A}{x^6}+\frac{A b+a B}{x^4}+\frac{b B}{x^2}\right ) \, dx\\ &=-\frac{a A}{5 x^5}-\frac{A b+a B}{3 x^3}-\frac{b B}{x}\\ \end{align*}
Mathematica [A] time = 0.0109261, size = 33, normalized size = 1.06 \[ \frac{-a B-A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{b B}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 28, normalized size = 0.9 \begin{align*} -{\frac{Ab+Ba}{3\,{x}^{3}}}-{\frac{Aa}{5\,{x}^{5}}}-{\frac{Bb}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02129, size = 39, normalized size = 1.26 \begin{align*} -\frac{15 \, B b x^{4} + 5 \,{\left (B a + A b\right )} x^{2} + 3 \, A a}{15 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45562, size = 70, normalized size = 2.26 \begin{align*} -\frac{15 \, B b x^{4} + 5 \,{\left (B a + A b\right )} x^{2} + 3 \, A a}{15 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.482671, size = 32, normalized size = 1.03 \begin{align*} - \frac{3 A a + 15 B b x^{4} + x^{2} \left (5 A b + 5 B a\right )}{15 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10545, size = 42, normalized size = 1.35 \begin{align*} -\frac{15 \, B b x^{4} + 5 \, B a x^{2} + 5 \, A b x^{2} + 3 \, A a}{15 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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