Optimal. Leaf size=12 \[ -\frac {x}{\sqrt {c x^4}} \]
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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 = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {1, 15, 30} \[ -\frac {x}{\sqrt {c x^4}} \]
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac {1}{\sqrt {c x^4}} \, dx\\ &=\frac {x^2 \int \frac {1}{x^2} \, dx}{\sqrt {c x^4}}\\ &=-\frac {x}{\sqrt {c x^4}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ -\frac {x}{\sqrt {c x^4}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 15, normalized size = 1.25 \[ -\frac {\sqrt {c x^{4}}}{c x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 8, normalized size = 0.67 \[ -\frac {1}{\sqrt {c} x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.92 \[ -\frac {x}{\sqrt {c \,x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 10, normalized size = 0.83 \[ -\frac {x}{\sqrt {c x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.30, size = 13, normalized size = 1.08 \[ -\frac {\sqrt {x^4}}{\sqrt {c}\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.47, size = 14, normalized size = 1.17 \[ - \frac {x}{\sqrt {c} \sqrt {x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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