Optimal. Leaf size=12 \[ \frac{x^2}{2 \sqrt{a}} \]
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Rubi [A] time = 0.0012983, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.136, Rules used = {2, 12, 30} \[ \frac{x^2}{2 \sqrt{a}} \]
Antiderivative was successfully verified.
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Rule 2
Rule 12
Rule 30
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx &=\int \frac{x}{\sqrt{a}} \, dx\\ &=\frac{\int x \, dx}{\sqrt{a}}\\ &=\frac{x^2}{2 \sqrt{a}}\\ \end{align*}
Mathematica [A] time = 0.0004321, size = 12, normalized size = 1. \[ \frac{x^2}{2 \sqrt{a}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 9, normalized size = 0.8 \begin{align*}{\frac{{x}^{2}}{2}{\frac{1}{\sqrt{a}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.951067, size = 11, normalized size = 0.92 \begin{align*} \frac{x^{2}}{2 \, \sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.20608, size = 23, normalized size = 1.92 \begin{align*} \frac{x^{2}}{2 \, \sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.054073, size = 8, normalized size = 0.67 \begin{align*} \frac{x^{2}}{2 \sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16745, size = 11, normalized size = 0.92 \begin{align*} \frac{x^{2}}{2 \, \sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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