Optimal. Leaf size=16 \[ -\frac {1}{4 x^2 \sqrt {c x^4}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, 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*}
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Mathematica [A] time = 0.00, 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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fricas [A] time = 0.48, size = 15, normalized size = 0.94 \[ -\frac {\sqrt {c x^{4}}}{4 \, c x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 8, normalized size = 0.50 \[ -\frac {1}{4 \, \sqrt {c} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ -\frac {1}{4 \sqrt {c \,x^{4}}\, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.05, size = 12, normalized size = 0.75 \[ -\frac {1}{4 \, \sqrt {c x^{4}} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.27, size = 13, normalized size = 0.81 \[ -\frac {1}{4\,\sqrt {c}\,x^2\,\sqrt {x^4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.66, size = 19, normalized size = 1.19 \[ - \frac {1}{4 \sqrt {c} x^{2} \sqrt {x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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