Optimal. Leaf size=16 \[ -\frac{1}{4 x^2 \sqrt{c x^4}} \]
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Rubi [A] time = 0.0016737, 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} \[ -\frac{1}{4 x^2 \sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x^3 \sqrt{2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac{1}{x^3 \sqrt{c x^4}} \, dx\\ &=\frac{x^2 \int \frac{1}{x^5} \, dx}{\sqrt{c x^4}}\\ &=-\frac{1}{4 x^2 \sqrt{c x^4}}\\ \end{align*}
Mathematica [A] time = 0.0030231, size = 17, normalized size = 1.06 \[ -\frac{c x^2}{4 \left (c x^4\right )^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.042, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{4\,{x}^{2}}{\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 = 0.955371, size = 16, normalized size = 1. \begin{align*} -\frac{1}{4 \, \sqrt{c x^{4}} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.25511, size = 35, normalized size = 2.19 \begin{align*} -\frac{\sqrt{c x^{4}}}{4 \, c x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.546345, size = 19, normalized size = 1.19 \begin{align*} - \frac{1}{4 \sqrt{c} x^{2} \sqrt{x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19921, size = 11, normalized size = 0.69 \begin{align*} -\frac{1}{4 \, \sqrt{c} x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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