Integrand size = 334, antiderivative size = 31 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=e^{e^{e^4 (1+3 x) \left (\frac {5 e^{-x}}{x}+x-\log (2)\right )^2}} \]
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Timed out. \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
\[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=\int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx \]
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Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(29)=58\).
Time = 0.48 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.19
\[{\mathrm e}^{{\mathrm e}^{-\frac {\left (-\ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{2}+2 \ln \left (2\right ) {\mathrm e}^{2 x} x^{3}-{\mathrm e}^{2 x} x^{4}+10 x \ln \left (2\right ) {\mathrm e}^{x}-10 \,{\mathrm e}^{x} x^{2}-25\right ) \left (1+3 x \right ) {\mathrm e}^{4-2 x}}{x^{2}}}}\]
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Leaf count of result is larger than twice the leaf count of optimal. 311 vs. \(2 (27) = 54\).
Time = 0.27 (sec) , antiderivative size = 311, normalized size of antiderivative = 10.03 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=e^{\left (2 \, x + \frac {{\left (x^{2} e^{\left (2 \, x + \frac {{\left (25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}}\right )} + 25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, x^{3} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}} - \frac {{\left (25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (24) = 48\).
Time = 6.05 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.39 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=e^{e^{\frac {\left (\left (75 x + 25\right ) e^{4} + \left (\left (- 30 x^{2} - 10 x\right ) e^{4} \log {\left (2 \right )} + \left (30 x^{3} + 10 x^{2}\right ) e^{4}\right ) e^{x} + \left (\left (3 x^{3} + x^{2}\right ) e^{4} \log {\left (2 \right )}^{2} + \left (- 6 x^{4} - 2 x^{3}\right ) e^{4} \log {\left (2 \right )} + \left (3 x^{5} + x^{4}\right ) e^{4}\right ) e^{2 x}\right ) e^{- 2 x}}{x^{2}}}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (27) = 54\).
Time = 2.43 (sec) , antiderivative size = 110, normalized size of antiderivative = 3.55 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=e^{\left (e^{\left (3 \, x^{3} e^{4} - 6 \, x^{2} e^{4} \log \left (2\right ) + 3 \, x e^{4} \log \left (2\right )^{2} + x^{2} e^{4} - 2 \, x e^{4} \log \left (2\right ) + e^{4} \log \left (2\right )^{2} + 30 \, x e^{\left (-x + 4\right )} - 30 \, e^{\left (-x + 4\right )} \log \left (2\right ) - \frac {10 \, e^{\left (-x + 4\right )} \log \left (2\right )}{x} + \frac {75 \, e^{\left (-2 \, x + 4\right )}}{x} + \frac {25 \, e^{\left (-2 \, x + 4\right )}}{x^{2}} + 10 \, e^{\left (-x + 4\right )}\right )}\right )} \]
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\[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx=\int { -\frac {{\left (25 \, {\left (6 \, x^{2} + 5 \, x + 2\right )} e^{4} - {\left (3 \, x^{3} e^{4} \log \left (2\right )^{2} - 2 \, {\left (6 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (9 \, x^{5} + 2 \, x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{3} + x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{4} - 2 \, x^{3}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x + \frac {{\left (25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}} + e^{\left (\frac {{\left (25 \, {\left (3 \, x + 1\right )} e^{4} + {\left ({\left (3 \, x^{3} + x^{2}\right )} e^{4} \log \left (2\right )^{2} - 2 \, {\left (3 \, x^{4} + x^{3}\right )} e^{4} \log \left (2\right ) + {\left (3 \, x^{5} + x^{4}\right )} e^{4}\right )} e^{\left (2 \, x\right )} - 10 \, {\left ({\left (3 \, x^{2} + x\right )} e^{4} \log \left (2\right ) - {\left (3 \, x^{3} + x^{2}\right )} e^{4}\right )} e^{x}\right )} e^{\left (-2 \, x\right )}}{x^{2}}\right )}\right )}}{x^{3}} \,d x } \]
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Time = 9.23 (sec) , antiderivative size = 125, normalized size of antiderivative = 4.03 \[ \int \frac {e^{e^{\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}}-2 x+\frac {e^{-2 x} \left (e^4 (25+75 x)+e^x \left (e^4 \left (10 x^2+30 x^3\right )+e^4 \left (-10 x-30 x^2\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (x^4+3 x^5\right )+e^4 \left (-2 x^3-6 x^4\right ) \log (2)+e^4 \left (x^2+3 x^3\right ) \log ^2(2)\right )\right )}{x^2}} \left (e^4 \left (-50-125 x-150 x^2\right )+e^x \left (e^4 \left (20 x^3-30 x^4\right )+e^4 \left (10 x+10 x^2+30 x^3\right ) \log (2)\right )+e^{2 x} \left (e^4 \left (2 x^4+9 x^5\right )+e^4 \left (-2 x^3-12 x^4\right ) \log (2)+3 e^4 x^3 \log ^2(2)\right )\right )}{x^3} \, dx={\mathrm {e}}^{\frac {{\mathrm {e}}^{x^2\,{\mathrm {e}}^4}\,{\mathrm {e}}^{3\,x^3\,{\mathrm {e}}^4}\,{\mathrm {e}}^{\frac {25\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^4}{x^2}}\,{\mathrm {e}}^{\frac {75\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^4}{x}}\,{\mathrm {e}}^{10\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{3\,x\,{\mathrm {e}}^4\,{\ln \left (2\right )}^2}\,{\mathrm {e}}^{30\,x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{{\mathrm {e}}^4\,{\ln \left (2\right )}^2}}{2^{\frac {10\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4}{x}}\,2^{30\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4}\,2^{2\,x\,{\mathrm {e}}^4}\,2^{6\,x^2\,{\mathrm {e}}^4}}} \]
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