Optimal. Leaf size=8 \[ \frac{\log (x)}{\sqrt{a}} \]
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Rubi [A] time = 0.001119, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {2, 12, 29} \[ \frac{\log (x)}{\sqrt{a}} \]
Antiderivative was successfully verified.
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Rule 2
Rule 12
Rule 29
Rubi steps
\begin{align*} \int \frac{1}{x \sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx &=\int \frac{1}{\sqrt{a} x} \, dx\\ &=\frac{\int \frac{1}{x} \, dx}{\sqrt{a}}\\ &=\frac{\log (x)}{\sqrt{a}}\\ \end{align*}
Mathematica [A] time = 0.0004301, size = 8, normalized size = 1. \[ \frac{\log (x)}{\sqrt{a}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 7, normalized size = 0.9 \begin{align*}{\ln \left ( x \right ){\frac{1}{\sqrt{a}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.944304, size = 8, normalized size = 1. \begin{align*} \frac{\log \left (x\right )}{\sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.25804, size = 22, normalized size = 2.75 \begin{align*} \frac{\log \left (x\right )}{\sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.061173, size = 7, normalized size = 0.88 \begin{align*} \frac{\log{\left (x \right )}}{\sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21322, size = 9, normalized size = 1.12 \begin{align*} \frac{\log \left ({\left | x \right |}\right )}{\sqrt{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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