Optimal. Leaf size=12 \[ -\frac{x}{\sqrt{c x^4}} \]
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Rubi [A] time = 0.0014219, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.158, Rules used = {1, 15, 30} \[ -\frac{x}{\sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac{1}{\sqrt{c x^4}} \, dx\\ &=\frac{x^2 \int \frac{1}{x^2} \, dx}{\sqrt{c x^4}}\\ &=-\frac{x}{\sqrt{c x^4}}\\ \end{align*}
Mathematica [A] time = 0.001179, size = 12, normalized size = 1. \[ -\frac{x}{\sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.041, size = 11, normalized size = 0.9 \begin{align*} -{x{\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 = 0.948303, size = 14, normalized size = 1.17 \begin{align*} -\frac{x}{\sqrt{c x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.32357, size = 30, normalized size = 2.5 \begin{align*} -\frac{\sqrt{c x^{4}}}{c x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.383548, size = 14, normalized size = 1.17 \begin{align*} - \frac{x}{\sqrt{c} \sqrt{x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17937, size = 11, normalized size = 0.92 \begin{align*} -\frac{1}{\sqrt{c} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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