Optimal. Leaf size=11 \[ -\frac {x}{x^5+x+1} \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1588} \[ -\frac {x}{x^5+x+1} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin {align*} \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx &=-\frac {x}{1+x+x^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \[ -\frac {x}{x^5+x+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 11, normalized size = 1.00 \[ -\frac {x}{x^{5} + x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 11, normalized size = 1.00 \[ -\frac {x}{x^{5} + x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 41, normalized size = 3.73 \[ -\frac {-3 x^{2}+5 x -1}{7 \left (x^{3}-x^{2}+1\right )}+\frac {-3 x -1}{7 x^{2}+7 x +7} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 11, normalized size = 1.00 \[ -\frac {x}{x^{5} + x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.30, size = 11, normalized size = 1.00 \[ -\frac {x}{x^5+x+1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 8, normalized size = 0.73 \[ - \frac {x}{x^{5} + x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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