Optimal. Leaf size=15 \[ \frac{x^2 \log (x)}{\sqrt{c x^4}} \]
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Rubi [A] time = 0.0013116, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {1, 15, 29} \[ \frac{x^2 \log (x)}{\sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 29
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac{x}{\sqrt{c x^4}} \, dx\\ &=\frac{x^2 \int \frac{1}{x} \, dx}{\sqrt{c x^4}}\\ &=\frac{x^2 \log (x)}{\sqrt{c x^4}}\\ \end{align*}
Mathematica [A] time = 0.0015753, size = 15, normalized size = 1. \[ \frac{x^2 \log (x)}{\sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 14, normalized size = 0.9 \begin{align*}{{x}^{2}\ln \left ( x \right ){\frac{1}{\sqrt{c{x}^{4}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.951511, size = 18, normalized size = 1.2 \begin{align*} \frac{x^{2} \log \left (x\right )}{\sqrt{c x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29413, size = 38, normalized size = 2.53 \begin{align*} \frac{\sqrt{c x^{4}} \log \left (x\right )}{c x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{\sqrt{c x^{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17966, size = 9, normalized size = 0.6 \begin{align*} \frac{\log \left ({\left | x \right |}\right )}{\sqrt{c}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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