Optimal. Leaf size=26 \[ x-\log \left (\log ^4\left (e^{\frac {-4+x-x^2}{x}}-x\right )\right ) \]
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Rubi [A] time = 0.83, antiderivative size = 22, normalized size of antiderivative = 0.85, number of steps used = 3, number of rules used = 2, integrand size = 120, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6688, 6684} \begin {gather*} x-4 \log \left (\log \left (e^{-x-\frac {4}{x}+1}-x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {4 \left (e^{\frac {4}{x}+x} x^2+e \left (-4+x^2\right )\right )}{x^2 \left (-e+e^{\frac {4}{x}+x} x\right ) \log \left (e^{1-\frac {4}{x}-x}-x\right )}\right ) \, dx\\ &=x-4 \int \frac {e^{\frac {4}{x}+x} x^2+e \left (-4+x^2\right )}{x^2 \left (-e+e^{\frac {4}{x}+x} x\right ) \log \left (e^{1-\frac {4}{x}-x}-x\right )} \, dx\\ &=x-4 \log \left (\log \left (e^{1-\frac {4}{x}-x}-x\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.43, size = 22, normalized size = 0.85 \begin {gather*} x-4 \log \left (\log \left (e^{1-\frac {4}{x}-x}-x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 24, normalized size = 0.92 \begin {gather*} x - 4 \, \log \left (\log \left (-x + e^{\left (-\frac {x^{2} - x + 4}{x}\right )}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 24, normalized size = 0.92 \begin {gather*} x - 4 \, \log \left (\log \left (-x + e^{\left (-\frac {x^{2} - x + 4}{x}\right )}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 24, normalized size = 0.92
method | result | size |
norman | \(x -4 \ln \left (\ln \left ({\mathrm e}^{\frac {-x^{2}+x -4}{x}}-x \right )\right )\) | \(24\) |
risch | \(x -4 \ln \left (\ln \left ({\mathrm e}^{-\frac {x^{2}-x +4}{x}}-x \right )\right )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 33, normalized size = 1.27 \begin {gather*} x - 4 \, \log \left (-\frac {x^{2} - x \log \left (-x e^{\left (x + \frac {4}{x}\right )} + e\right ) + 4}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.59, size = 23, normalized size = 0.88 \begin {gather*} x-4\,\ln \left (\ln \left ({\mathrm {e}}^{-x}\,\mathrm {e}\,{\mathrm {e}}^{-\frac {4}{x}}-x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.58, size = 17, normalized size = 0.65 \begin {gather*} x - 4 \log {\left (\log {\left (- x + e^{\frac {- x^{2} + x - 4}{x}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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