Optimal. Leaf size=17 \[ -\frac{a}{4 x^4}-\frac{b}{2 x^2} \]
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Rubi [A] time = 0.0046325, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {14} \[ -\frac{a}{4 x^4}-\frac{b}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+b x^2}{x^5} \, dx &=\int \left (\frac{a}{x^5}+\frac{b}{x^3}\right ) \, dx\\ &=-\frac{a}{4 x^4}-\frac{b}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0018084, size = 17, normalized size = 1. \[ -\frac{a}{4 x^4}-\frac{b}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.8 \begin{align*} -{\frac{a}{4\,{x}^{4}}}-{\frac{b}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.49268, size = 18, normalized size = 1.06 \begin{align*} -\frac{2 \, b x^{2} + a}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4151, size = 32, normalized size = 1.88 \begin{align*} -\frac{2 \, b x^{2} + a}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.268826, size = 14, normalized size = 0.82 \begin{align*} - \frac{a + 2 b x^{2}}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.42417, size = 18, normalized size = 1.06 \begin{align*} -\frac{2 \, b x^{2} + a}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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