Optimal. Leaf size=30 \[ e^{e^x}+x+\frac {x}{\log \left (2-e^{4 x}\right )+e^x (2+\log (x))} \]
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Rubi [F]
time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A]
time = 0.36, size = 30, normalized size = 1.00 \begin {gather*} e^{e^x}+x+\frac {x}{\log \left (2-e^{4 x}\right )+e^x (2+\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.31, size = 29, normalized size = 0.97
method | result | size |
risch | \(x +{\mathrm e}^{{\mathrm e}^{x}}+\frac {x}{{\mathrm e}^{x} \ln \left (x \right )+2 \,{\mathrm e}^{x}+\ln \left (-{\mathrm e}^{4 x}+2\right )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 58 vs.
\(2 (26) = 52\).
time = 0.70, size = 58, normalized size = 1.93 \begin {gather*} \frac {{\left (\log \left (x\right ) + 2\right )} e^{\left (x + e^{x}\right )} + {\left (x \log \left (x\right ) + 2 \, x\right )} e^{x} + {\left (x + e^{\left (e^{x}\right )}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + x}{{\left (\log \left (x\right ) + 2\right )} e^{x} + \log \left (-e^{\left (4 \, x\right )} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 64 vs.
\(2 (26) = 52\).
time = 0.42, size = 64, normalized size = 2.13 \begin {gather*} \frac {x e^{x} \log \left (x\right ) + 2 \, x e^{x} + {\left (e^{x} \log \left (x\right ) + 2 \, e^{x}\right )} e^{\left (e^{x}\right )} + {\left (x + e^{\left (e^{x}\right )}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + x}{e^{x} \log \left (x\right ) + 2 \, e^{x} + \log \left (-e^{\left (4 \, x\right )} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.46, size = 27, normalized size = 0.90 \begin {gather*} x + \frac {x}{e^{x} \log {\left (x \right )} + 2 e^{x} + \log {\left (2 - e^{4 x} \right )}} + e^{e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 736 vs.
\(2 (26) = 52\).
time = 0.65, size = 736, normalized size = 24.53 \begin {gather*} \frac {x^{2} e^{\left (6 \, x\right )} \log \left (x\right )^{2} - 2 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} + x^{2} e^{\left (5 \, x\right )} \log \left (x\right ) \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 2 \, x^{2} e^{x} \log \left (x\right ) \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 4 \, x^{2} e^{\left (6 \, x\right )} \log \left (x\right ) + 5 \, x^{2} e^{\left (5 \, x\right )} \log \left (x\right ) - 8 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right ) - 2 \, x^{2} e^{x} \log \left (x\right ) + x e^{\left (6 \, x + e^{x}\right )} \log \left (x\right )^{2} - 2 \, x e^{\left (2 \, x + e^{x}\right )} \log \left (x\right )^{2} + 2 \, x^{2} e^{\left (5 \, x\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 4 \, x^{2} e^{\left (4 \, x\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 4 \, x^{2} e^{x} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + x e^{\left (5 \, x + e^{x}\right )} \log \left (x\right ) \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 2 \, x e^{\left (x + e^{x}\right )} \log \left (x\right ) \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 4 \, x^{2} e^{\left (6 \, x\right )} + 10 \, x^{2} e^{\left (5 \, x\right )} + 4 \, x^{2} e^{\left (4 \, x\right )} - 8 \, x^{2} e^{\left (2 \, x\right )} - 4 \, x^{2} e^{x} + x e^{\left (6 \, x\right )} \log \left (x\right ) - 2 \, x e^{\left (2 \, x\right )} \log \left (x\right ) + 4 \, x e^{\left (6 \, x + e^{x}\right )} \log \left (x\right ) + 4 \, x e^{\left (5 \, x + e^{x}\right )} \log \left (x\right ) - 8 \, x e^{\left (2 \, x + e^{x}\right )} \log \left (x\right ) + x e^{\left (5 \, x\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 2 \, x e^{\left (5 \, x + e^{x}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 4 \, x e^{\left (4 \, x + e^{x}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 4 \, x e^{\left (x + e^{x}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 2 \, x e^{x} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 2 \, x e^{\left (6 \, x\right )} + x e^{\left (5 \, x\right )} - 4 \, x e^{\left (2 \, x\right )} + 4 \, x e^{\left (6 \, x + e^{x}\right )} + 8 \, x e^{\left (5 \, x + e^{x}\right )} - 8 \, x e^{\left (2 \, x + e^{x}\right )} - 2 \, x e^{x} + e^{\left (6 \, x + e^{x}\right )} \log \left (x\right ) - 2 \, e^{\left (2 \, x + e^{x}\right )} \log \left (x\right ) + e^{\left (5 \, x + e^{x}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 2 \, e^{\left (x + e^{x}\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 2 \, e^{\left (6 \, x + e^{x}\right )} - 4 \, e^{\left (2 \, x + e^{x}\right )}}{x e^{\left (6 \, x\right )} \log \left (x\right )^{2} - 2 \, x e^{\left (2 \, x\right )} \log \left (x\right )^{2} + x e^{\left (5 \, x\right )} \log \left (x\right ) \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 2 \, x e^{x} \log \left (x\right ) \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 4 \, x e^{\left (6 \, x\right )} \log \left (x\right ) + 4 \, x e^{\left (5 \, x\right )} \log \left (x\right ) - 8 \, x e^{\left (2 \, x\right )} \log \left (x\right ) + 2 \, x e^{\left (5 \, x\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 4 \, x e^{\left (4 \, x\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 4 \, x e^{x} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 4 \, x e^{\left (6 \, x\right )} + 8 \, x e^{\left (5 \, x\right )} - 8 \, x e^{\left (2 \, x\right )} + e^{\left (6 \, x\right )} \log \left (x\right ) - 2 \, e^{\left (2 \, x\right )} \log \left (x\right ) + e^{\left (5 \, x\right )} \log \left (-e^{\left (4 \, x\right )} + 2\right ) - 2 \, e^{x} \log \left (-e^{\left (4 \, x\right )} + 2\right ) + 2 \, e^{\left (6 \, x\right )} - 4 \, e^{\left (2 \, x\right )}} \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 = -0.03 \begin {gather*} \int \frac {8\,{\mathrm {e}}^{2\,x}+\ln \left (2-{\mathrm {e}}^{4\,x}\right )\,\left (8\,{\mathrm {e}}^x+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}+\ln \left (x\right )\,\left (4\,{\mathrm {e}}^{2\,x}-2\,{\mathrm {e}}^{6\,x}\right )\right )-{\mathrm {e}}^{4\,x}\,\left (4\,{\mathrm {e}}^x+1\right )-\ln \left (x\right )\,\left (2\,{\mathrm {e}}^{5\,x}-4\,{\mathrm {e}}^x\right )+2\right )+{\ln \left (x\right )}^2\,\left (2\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^{6\,x}\right )-{\ln \left (2-{\mathrm {e}}^{4\,x}\right )}^2\,\left ({\mathrm {e}}^{4\,x}+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left ({\mathrm {e}}^{5\,x}-2\,{\mathrm {e}}^x\right )-2\right )+{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (\left (2\,{\mathrm {e}}^{3\,x}-{\mathrm {e}}^{7\,x}\right )\,{\ln \left (x\right )}^2+\left (8\,{\mathrm {e}}^{3\,x}-4\,{\mathrm {e}}^{7\,x}\right )\,\ln \left (x\right )+8\,{\mathrm {e}}^{3\,x}-4\,{\mathrm {e}}^{7\,x}\right )-\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (2\,x-2\right )-8\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^{4\,x}\,\left (4\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^x\,\left (x-1\right )\right )\right )-{\mathrm {e}}^x\,\left (4\,x-2\right )+{\mathrm {e}}^{4\,x}\,\left (4\,x-4\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^x\,\left (2\,x-1\right )\right )}{8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}+{\ln \left (x\right )}^2\,\left (2\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^{6\,x}\right )-\ln \left (2-{\mathrm {e}}^{4\,x}\right )\,\left (4\,{\mathrm {e}}^{5\,x}-8\,{\mathrm {e}}^x+\ln \left (x\right )\,\left (2\,{\mathrm {e}}^{5\,x}-4\,{\mathrm {e}}^x\right )\right )-{\ln \left (2-{\mathrm {e}}^{4\,x}\right )}^2\,\left ({\mathrm {e}}^{4\,x}-2\right )+\ln \left (x\right )\,\left (8\,{\mathrm {e}}^{2\,x}-4\,{\mathrm {e}}^{6\,x}\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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