Optimal. Leaf size=21 \[ \frac{x^2}{2 a \sqrt{a+b x^4}} \]
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Rubi [A] time = 0.0036308, 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} \[ \frac{x^2}{2 a \sqrt{a+b x^4}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{x}{\left (a+b x^4\right )^{3/2}} \, dx &=\frac{x^2}{2 a \sqrt{a+b x^4}}\\ \end{align*}
Mathematica [A] time = 0.0031739, size = 21, normalized size = 1. \[ \frac{x^2}{2 a \sqrt{a+b x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 0.9 \begin{align*}{\frac{{x}^{2}}{2\,a}{\frac{1}{\sqrt{b{x}^{4}+a}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.951382, size = 23, normalized size = 1.1 \begin{align*} \frac{x^{2}}{2 \, \sqrt{b x^{4} + a} a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49794, size = 55, normalized size = 2.62 \begin{align*} \frac{\sqrt{b x^{4} + a} x^{2}}{2 \,{\left (a b x^{4} + a^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.570206, size = 20, normalized size = 0.95 \begin{align*} \frac{x^{2}}{2 a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{4}}{a}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12439, size = 23, normalized size = 1.1 \begin{align*} \frac{x^{2}}{2 \, \sqrt{b x^{4} + a} a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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