Optimal. Leaf size=26 \[ -\frac {a B+A b}{x}-\frac {a A}{3 x^3}+b B x \]
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Rubi [A] time = 0.02, antiderivative size = 26, normalized size of antiderivative = 1.00, 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} \[ -\frac {a B+A b}{x}-\frac {a A}{3 x^3}+b B x \]
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^4} \, dx &=\int \left (b B+\frac {a A}{x^4}+\frac {A b+a B}{x^2}\right ) \, dx\\ &=-\frac {a A}{3 x^3}-\frac {A b+a B}{x}+b B x\\ \end {align*}
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Mathematica [A] time = 0.03, size = 27, normalized size = 1.04 \[ \frac {-a B-A b}{x}-\frac {a A}{3 x^3}+b B x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 29, normalized size = 1.12 \[ \frac {3 \, B b x^{4} - 3 \, {\left (B a + A b\right )} x^{2} - A a}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 28, normalized size = 1.08 \[ B b x - \frac {3 \, B a x^{2} + 3 \, A b x^{2} + A a}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.96 \[ B b x -\frac {A a}{3 x^{3}}-\frac {A b +B a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 26, normalized size = 1.00 \[ B b x - \frac {3 \, {\left (B a + A b\right )} x^{2} + A a}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 26, normalized size = 1.00 \[ B\,b\,x-\frac {\left (A\,b+B\,a\right )\,x^2+\frac {A\,a}{3}}{x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 27, normalized size = 1.04 \[ B b x + \frac {- A a + x^{2} \left (- 3 A b - 3 B a\right )}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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