Optimal. Leaf size=11 \[ -\frac {x}{1+x+x^5} \]
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Rubi [A]
time = 0.00, 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 = {1602}
\begin {gather*} -\frac {x}{x^5+x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 1602
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 = 0.00, size = 11, normalized size = 1.00 \begin {gather*} -\frac {x}{1+x+x^5} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(40\) vs.
\(2(11)=22\).
time = 0.02, size = 41, normalized size = 3.73
method | result | size |
gosper | \(-\frac {x}{x^{5}+x +1}\) | \(12\) |
norman | \(-\frac {x}{x^{5}+x +1}\) | \(12\) |
risch | \(-\frac {x}{x^{5}+x +1}\) | \(12\) |
default | \(-\frac {-3 x^{2}+5 x -1}{7 \left (x^{3}-x^{2}+1\right )}+\frac {-3 x -1}{7 x^{2}+7 x +7}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.10, size = 11, normalized size = 1.00 \begin {gather*} -\frac {x}{x^{5} + x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.04, size = 11, normalized size = 1.00 \begin {gather*} -\frac {x}{x^{5} + x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 8, normalized size = 0.73 \begin {gather*} - \frac {x}{x^{5} + x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 11, normalized size = 1.00 \begin {gather*} -\frac {x}{x^{5} + x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 11, normalized size = 1.00 \begin {gather*} -\frac {x}{x^5+x+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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