Optimal. Leaf size=12 \[ -\frac{1}{2 \sqrt{a} x^2} \]
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Rubi [A] time = 0.001611, antiderivative size = 12, 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, 30} \[ -\frac{1}{2 \sqrt{a} x^2} \]
Antiderivative was successfully verified.
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Rule 2
Rule 12
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x^3 \sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx &=\int \frac{1}{\sqrt{a} x^3} \, dx\\ &=\frac{\int \frac{1}{x^3} \, dx}{\sqrt{a}}\\ &=-\frac{1}{2 \sqrt{a} x^2}\\ \end{align*}
Mathematica [A] time = 0.0004923, size = 12, normalized size = 1. \[ -\frac{1}{2 \sqrt{a} x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 9, normalized size = 0.8 \begin{align*} -{\frac{1}{2\,{x}^{2}}{\frac{1}{\sqrt{a}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.946884, size = 11, normalized size = 0.92 \begin{align*} -\frac{1}{2 \, \sqrt{a} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28153, size = 27, normalized size = 2.25 \begin{align*} -\frac{1}{2 \, \sqrt{a} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063928, size = 12, normalized size = 1. \begin{align*} - \frac{1}{2 \sqrt{a} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20006, size = 11, normalized size = 0.92 \begin{align*} -\frac{1}{2 \, \sqrt{a} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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