Optimal. Leaf size=21 \[ -\frac{\sqrt{a+b x^4}}{2 a x^2} \]
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Rubi [A] time = 0.0042104, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, 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 = 0.0037933, size = 21, 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 = 18, 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 = 0.985541, size = 23, normalized size = 1.1 \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 = 1.43842, size = 41, normalized size = 1.95 \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 = 0.870087, size = 20, normalized size = 0.95 \begin{align*} - \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} + 1}}{2 a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10376, size = 19, normalized size = 0.9 \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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