Optimal. Leaf size=20 \[ 1+\left (\frac {25}{4}+e^{1-x^6}\right ) (x+\log (x)) \]
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Rubi [A] time = 0.10, antiderivative size = 35, normalized size of antiderivative = 1.75, number of steps used = 6, number of rules used = 4, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 14, 43, 2288} \begin {gather*} \frac {e^{1-x^6} \left (x^7+x^6 \log (x)\right )}{x^6}+\frac {25 x}{4}+\frac {25 \log (x)}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 43
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {25+25 x+e^{1-x^6} \left (4+4 x-24 x^7\right )-24 e^{1-x^6} x^6 \log (x)}{x} \, dx\\ &=\frac {1}{4} \int \left (\frac {25 (1+x)}{x}-\frac {4 e^{1-x^6} \left (-1-x+6 x^7+6 x^6 \log (x)\right )}{x}\right ) \, dx\\ &=\frac {25}{4} \int \frac {1+x}{x} \, dx-\int \frac {e^{1-x^6} \left (-1-x+6 x^7+6 x^6 \log (x)\right )}{x} \, dx\\ &=\frac {e^{1-x^6} \left (x^7+x^6 \log (x)\right )}{x^6}+\frac {25}{4} \int \left (1+\frac {1}{x}\right ) \, dx\\ &=\frac {25 x}{4}+\frac {25 \log (x)}{4}+\frac {e^{1-x^6} \left (x^7+x^6 \log (x)\right )}{x^6}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 26, normalized size = 1.30 \begin {gather*} \frac {1}{4} e^{-x^6} \left (4 e+25 e^{x^6}\right ) (x+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.35, size = 30, normalized size = 1.50 \begin {gather*} x e^{\left (-x^{6} + 1\right )} + \frac {1}{4} \, {\left (4 \, e^{\left (-x^{6} + 1\right )} + 25\right )} \log \relax (x) + \frac {25}{4} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 29, normalized size = 1.45 \begin {gather*} x e^{\left (-x^{6} + 1\right )} + e^{\left (-x^{6} + 1\right )} \log \relax (x) + \frac {25}{4} \, x + \frac {25}{4} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 60, normalized size = 3.00
method | result | size |
risch | \({\mathrm e}^{-\left (x -1\right ) \left (x +1\right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right )} \ln \relax (x )+\frac {25 x}{4}+\frac {25 \ln \relax (x )}{4}+{\mathrm e}^{-\left (x -1\right ) \left (x +1\right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right )} x\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.43, size = 50, normalized size = 2.50 \begin {gather*} \frac {x^{7} e \Gamma \left (\frac {7}{6}, x^{6}\right )}{{\left (x^{6}\right )}^{\frac {7}{6}}} - \frac {x e \Gamma \left (\frac {1}{6}, x^{6}\right )}{6 \, {\left (x^{6}\right )}^{\frac {1}{6}}} + e^{\left (-x^{6} + 1\right )} \log \relax (x) + \frac {25}{4} \, x + \frac {25}{4} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {\frac {25\,x}{4}+\frac {{\mathrm {e}}^{1-x^6}\,\left (-24\,x^7+4\,x+4\right )}{4}-6\,x^6\,{\mathrm {e}}^{1-x^6}\,\ln \relax (x)+\frac {25}{4}}{x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 22, normalized size = 1.10 \begin {gather*} \frac {25 x}{4} + \left (x + \log {\relax (x )}\right ) e^{1 - x^{6}} + \frac {25 \log {\relax (x )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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