Optimal. Leaf size=12 \[ -\frac {1}{3 \sqrt {a} x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, 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} \[ -\frac {1}{3 \sqrt {a} x^3} \]
Antiderivative was successfully verified.
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Rule 2
Rule 12
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{x^4 \sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx &=\int \frac {1}{\sqrt {a} x^4} \, dx\\ &=\frac {\int \frac {1}{x^4} \, dx}{\sqrt {a}}\\ &=-\frac {1}{3 \sqrt {a} x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ -\frac {1}{3 \sqrt {a} x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 8, normalized size = 0.67 \[ -\frac {1}{3 \, \sqrt {a} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 8, normalized size = 0.67 \[ -\frac {1}{3 \, \sqrt {a} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.75 \[ -\frac {1}{3 \sqrt {a}\, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.00, size = 8, normalized size = 0.67 \[ -\frac {1}{3 \, \sqrt {a} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.33, size = 8, normalized size = 0.67 \[ -\frac {1}{3\,\sqrt {a}\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 12, normalized size = 1.00 \[ - \frac {1}{3 \sqrt {a} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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