Optimal. Leaf size=22 \[ -\frac{\sqrt{a-b x^4}}{2 a x^2} \]
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Rubi [A] time = 0.0044414, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {264} \[ -\frac{\sqrt{a-b x^4}}{2 a x^2} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^3 \sqrt{a-b x^4}} \, dx &=-\frac{\sqrt{a-b x^4}}{2 a x^2}\\ \end{align*}
Mathematica [A] time = 0.0034588, size = 22, normalized size = 1. \[ -\frac{\sqrt{a-b x^4}}{2 a x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 19, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,a{x}^{2}}\sqrt{-b{x}^{4}+a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.962564, size = 24, normalized size = 1.09 \begin{align*} -\frac{\sqrt{-b x^{4} + a}}{2 \, a x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49038, size = 42, normalized size = 1.91 \begin{align*} -\frac{\sqrt{-b x^{4} + a}}{2 \, a x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.919776, size = 54, normalized size = 2.45 \begin{align*} \begin{cases} - \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} - 1}}{2 a} & \text{for}\: \frac{\left |{a}\right |}{\left |{b}\right | \left |{x^{4}}\right |} > 1 \\- \frac{i \sqrt{b} \sqrt{- \frac{a}{b x^{4}} + 1}}{2 a} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09172, size = 22, normalized size = 1. \begin{align*} -\frac{\sqrt{-b + \frac{a}{x^{4}}}}{2 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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