Optimal. Leaf size=21 \[ \frac{x^2 \sqrt{a+\frac{b}{x^4}}}{2 a} \]
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Rubi [A] time = 0.0046884, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {264} \[ \frac{x^2 \sqrt{a+\frac{b}{x^4}}}{2 a} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{a+\frac{b}{x^4}}} \, dx &=\frac{\sqrt{a+\frac{b}{x^4}} x^2}{2 a}\\ \end{align*}
Mathematica [A] time = 0.0092191, size = 21, normalized size = 1. \[ \frac{x^2 \sqrt{a+\frac{b}{x^4}}}{2 a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 29, normalized size = 1.4 \begin{align*}{\frac{a{x}^{4}+b}{2\,a{x}^{2}}{\frac{1}{\sqrt{{\frac{a{x}^{4}+b}{{x}^{4}}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.964356, size = 23, normalized size = 1.1 \begin{align*} \frac{\sqrt{a + \frac{b}{x^{4}}} x^{2}}{2 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45134, size = 45, normalized size = 2.14 \begin{align*} \frac{x^{2} \sqrt{\frac{a x^{4} + b}{x^{4}}}}{2 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.729963, size = 19, normalized size = 0.9 \begin{align*} \frac{\sqrt{b} \sqrt{\frac{a x^{4}}{b} + 1}}{2 a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{\sqrt{a + \frac{b}{x^{4}}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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