Optimal. Leaf size=16 \[ -\frac{1}{3 x \sqrt{c x^4}} \]
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Rubi [A] time = 0.0014903, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13, Rules used = {1, 15, 30} \[ -\frac{1}{3 x \sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x^2 \sqrt{2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac{1}{x^2 \sqrt{c x^4}} \, dx\\ &=\frac{x^2 \int \frac{1}{x^4} \, dx}{\sqrt{c x^4}}\\ &=-\frac{1}{3 x \sqrt{c x^4}}\\ \end{align*}
Mathematica [A] time = 0.0015786, size = 16, normalized size = 1. \[ -\frac{1}{3 x \sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.041, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{3\,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 = 0.947221, size = 16, normalized size = 1. \begin{align*} -\frac{1}{3 \, \sqrt{c x^{4}} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19101, size = 35, normalized size = 2.19 \begin{align*} -\frac{\sqrt{c x^{4}}}{3 \, c x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.482531, size = 17, normalized size = 1.06 \begin{align*} - \frac{1}{3 \sqrt{c} x \sqrt{x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15646, size = 11, normalized size = 0.69 \begin{align*} -\frac{1}{3 \, \sqrt{c} x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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