Optimal. Leaf size=25 \[ -3+e^4 \left (-e^{e^{-x} x}+x\right )+2 \log \left (x^2\right ) \]
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Rubi [F] time = 0.22, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {4+e^4 x+e^{4-x+e^{-x} x} (-1+x) x}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{4+\left (-1+e^{-x}\right ) x} (-1+x)+\frac {4+e^4 x}{x}\right ) \, dx\\ &=\int e^{4+\left (-1+e^{-x}\right ) x} (-1+x) \, dx+\int \frac {4+e^4 x}{x} \, dx\\ &=\int \left (e^4+\frac {4}{x}\right ) \, dx+\int \left (-e^{4+\left (-1+e^{-x}\right ) x}+e^{4+\left (-1+e^{-x}\right ) x} x\right ) \, dx\\ &=e^4 x+4 \log (x)-\int e^{4+\left (-1+e^{-x}\right ) x} \, dx+\int e^{4+\left (-1+e^{-x}\right ) x} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 23, normalized size = 0.92 \begin {gather*} -e^{4+e^{-x} x}+e^4 x+4 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 43, normalized size = 1.72 \begin {gather*} {\left ({\left (x e^{4} + 4 \, \log \relax (x)\right )} e^{\left (-x + \log \relax (x)\right )} - e^{\left (-x + e^{\left (-x + \log \relax (x)\right )} + \log \relax (x) + 4\right )}\right )} e^{\left (x - \log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 34, normalized size = 1.36 \begin {gather*} {\left (x e^{\left (-x + 4\right )} + 4 \, e^{\left (-x\right )} \log \relax (x) - e^{\left (x e^{\left (-x\right )} - x + 4\right )}\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 21, normalized size = 0.84
method | result | size |
risch | \(x \,{\mathrm e}^{4}+4 \ln \relax (x )-{\mathrm e}^{4+x \,{\mathrm e}^{-x}}\) | \(21\) |
default | \(x \,{\mathrm e}^{4}+4 \ln \relax (x )-{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{\ln \relax (x )-x}}\) | \(22\) |
norman | \(x \,{\mathrm e}^{4}+4 \ln \relax (x )-{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{\ln \relax (x )-x}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 20, normalized size = 0.80 \begin {gather*} x e^{4} - e^{\left (x e^{\left (-x\right )} + 4\right )} + 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.15, size = 20, normalized size = 0.80 \begin {gather*} 4\,\ln \relax (x)+x\,{\mathrm {e}}^4-{\mathrm {e}}^4\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 19, normalized size = 0.76 \begin {gather*} x e^{4} - e^{4} e^{x e^{- x}} + 4 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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