Optimal. Leaf size=17 \[ x^{5+e^{e^{e^{16 e^{-x}}}}} \]
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Rubi [F] time = 1.29, 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 e^{-x} x^{4+e^{e^{e^{16 e^{-x}}}}} \left (5 e^x+e^{e^{e^{16 e^{-x}}}} \left (e^x-16 e^{e^{16 e^{-x}}+16 e^{-x}} x \log (x)\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5 x^{4+e^{e^{e^{16 e^{-x}}}}}+e^{e^{e^{16 e^{-x}}}-x} x^{4+e^{e^{e^{16 e^{-x}}}}} \left (e^x-16 e^{e^{16 e^{-x}}+16 e^{-x}} x \log (x)\right )\right ) \, dx\\ &=5 \int x^{4+e^{e^{e^{16 e^{-x}}}}} \, dx+\int e^{e^{e^{16 e^{-x}}}-x} x^{4+e^{e^{e^{16 e^{-x}}}}} \left (e^x-16 e^{e^{16 e^{-x}}+16 e^{-x}} x \log (x)\right ) \, dx\\ &=5 \int x^{4+e^{e^{e^{16 e^{-x}}}}} \, dx+\int \left (e^{e^{e^{16 e^{-x}}}} x^{4+e^{e^{e^{16 e^{-x}}}}}-16 \exp \left (e^{e^{16 e^{-x}}}+e^{-x} \left (16+e^{16 e^{-x}+x}\right )-x\right ) x^{5+e^{e^{e^{16 e^{-x}}}}} \log (x)\right ) \, dx\\ &=5 \int x^{4+e^{e^{e^{16 e^{-x}}}}} \, dx-16 \int \exp \left (e^{e^{16 e^{-x}}}+e^{-x} \left (16+e^{16 e^{-x}+x}\right )-x\right ) x^{5+e^{e^{e^{16 e^{-x}}}}} \log (x) \, dx+\int e^{e^{e^{16 e^{-x}}}} x^{4+e^{e^{e^{16 e^{-x}}}}} \, dx\\ &=5 \int x^{4+e^{e^{e^{16 e^{-x}}}}} \, dx+16 \int \frac {\int e^{e^{e^{16 e^{-x}}}+e^{16 e^{-x}}+16 e^{-x}-x} x^{5+e^{e^{e^{16 e^{-x}}}}} \, dx}{x} \, dx-(16 \log (x)) \int \exp \left (e^{e^{16 e^{-x}}}+e^{-x} \left (16+e^{16 e^{-x}+x}\right )-x\right ) x^{5+e^{e^{e^{16 e^{-x}}}}} \, dx+\int e^{e^{e^{16 e^{-x}}}} x^{4+e^{e^{e^{16 e^{-x}}}}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.59, size = 17, normalized size = 1.00 \begin {gather*} x^{5+e^{e^{e^{16 e^{-x}}}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.54, size = 34, normalized size = 2.00 \begin {gather*} e^{\left (e^{\left (e^{\left ({\left (e^{\left (x + 16 \, e^{\left (-x\right )}\right )} + 16\right )} e^{\left (-x\right )} - 16 \, e^{\left (-x\right )}\right )}\right )} \log \relax (x) + 5 \, \log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left ({\left (16 \, x e^{\left (16 \, e^{\left (-x\right )} + e^{\left (16 \, e^{\left (-x\right )}\right )}\right )} \log \relax (x) - e^{x}\right )} e^{\left (e^{\left (e^{\left (16 \, e^{\left (-x\right )}\right )}\right )}\right )} - 5 \, e^{x}\right )} e^{\left (e^{\left (e^{\left (e^{\left (16 \, e^{\left (-x\right )}\right )}\right )}\right )} \log \relax (x) - x + 5 \, \log \relax (x)\right )}}{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 16, normalized size = 0.94
method | result | size |
risch | \(x^{{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{16 \,{\mathrm e}^{-x}}}}} x^{5}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 15, normalized size = 0.88 \begin {gather*} x^{5} x^{e^{\left (e^{\left (e^{\left (16 \, e^{\left (-x\right )}\right )}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.90, size = 15, normalized size = 0.88 \begin {gather*} x^{{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{16\,{\mathrm {e}}^{-x}}}}}\,x^5 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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