Optimal. Leaf size=21 \[ -e^{-x+x^{\frac {e^3+4 x}{x}}} \]
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Rubi [F] time = 1.34, 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 {e^{-x+x^{\frac {e^3+4 x}{x}}} \left (x^2+x^{\frac {e^3+4 x}{x}} \left (-e^3-4 x+e^3 \log (x)\right )\right )}{x^2} \, 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^{-x+x^{\frac {e^3+4 x}{x}}}-e^{-x+x^{\frac {e^3+4 x}{x}}} x^{2+\frac {e^3}{x}} \left (e^3+4 x-e^3 \log (x)\right )\right ) \, dx\\ &=\int e^{-x+x^{\frac {e^3+4 x}{x}}} \, dx-\int e^{-x+x^{\frac {e^3+4 x}{x}}} x^{2+\frac {e^3}{x}} \left (e^3+4 x-e^3 \log (x)\right ) \, dx\\ &=\int e^{-x+x^{\frac {e^3+4 x}{x}}} \, dx-\int \left (e^{3-x+x^{\frac {e^3+4 x}{x}}} x^{2+\frac {e^3}{x}}+4 e^{-x+x^{\frac {e^3+4 x}{x}}} x^{3+\frac {e^3}{x}}-e^{3-x+x^{\frac {e^3+4 x}{x}}} x^{2+\frac {e^3}{x}} \log (x)\right ) \, dx\\ &=-\left (4 \int e^{-x+x^{\frac {e^3+4 x}{x}}} x^{3+\frac {e^3}{x}} \, dx\right )+\int e^{-x+x^{\frac {e^3+4 x}{x}}} \, dx-\int e^{3-x+x^{\frac {e^3+4 x}{x}}} x^{2+\frac {e^3}{x}} \, dx+\int e^{3-x+x^{\frac {e^3+4 x}{x}}} x^{2+\frac {e^3}{x}} \log (x) \, dx\\ &=-\left (4 \int e^{-x+x^{\frac {e^3+4 x}{x}}} x^{3+\frac {e^3}{x}} \, dx\right )+\log (x) \int e^{3-x+x^{\frac {e^3+4 x}{x}}} x^{2+\frac {e^3}{x}} \, dx+\int e^{-x+x^{\frac {e^3+4 x}{x}}} \, dx-\int e^{3-x+x^{\frac {e^3+4 x}{x}}} x^{2+\frac {e^3}{x}} \, dx-\int \frac {\int e^{3-x+x^{4+\frac {e^3}{x}}} x^{2+\frac {e^3}{x}} \, dx}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.32, size = 19, normalized size = 0.90 \begin {gather*} -e^{-x+x^{4+\frac {e^3}{x}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 19, normalized size = 0.90 \begin {gather*} -e^{\left (x^{\frac {4 \, x + e^{3}}{x}} - x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 17, normalized size = 0.81 \begin {gather*} -e^{\left (x^{\frac {e^{3}}{x} + 4} - x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 0.95
method | result | size |
risch | \(-{\mathrm e}^{x^{\frac {{\mathrm e}^{3}+4 x}{x}}-x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 19, normalized size = 0.90 \begin {gather*} -e^{\left (x^{4} x^{\frac {e^{3}}{x}} - x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.48, size = 17, normalized size = 0.81 \begin {gather*} -{\mathrm {e}}^{x^{\frac {{\mathrm {e}}^3}{x}+4}}\,{\mathrm {e}}^{-x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.72, size = 17, normalized size = 0.81 \begin {gather*} - e^{- x + e^{\frac {\left (4 x + e^{3}\right ) \log {\relax (x )}}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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