Optimal. Leaf size=26 \[ 5+\left (x+\left (3+\log ^2\left (\left (5-e^{e^x}\right )^2\right )\right )^2\right ) \log (\log (3)) \]
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Rubi [A] time = 1.12, antiderivative size = 39, normalized size of antiderivative = 1.50, number of steps used = 31, number of rules used = 21, integrand size = 85, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.247, Rules used = {2282, 12, 6742, 36, 31, 29, 2411, 2344, 2302, 30, 2317, 2374, 6589, 2301, 2391, 2383, 14, 2394, 2315, 2396, 2433} \begin {gather*} \log (\log (3)) \log ^4\left (\left (e^{e^x}-5\right )^2\right )+6 \log (\log (3)) \log ^2\left (\left (e^{e^x}-5\right )^2\right )+x \log (\log (3)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 29
Rule 30
Rule 31
Rule 36
Rule 2282
Rule 2301
Rule 2302
Rule 2315
Rule 2317
Rule 2344
Rule 2374
Rule 2383
Rule 2391
Rule 2394
Rule 2396
Rule 2411
Rule 2433
Rule 6589
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {\left (5-e^x-24 e^x x \log \left (\left (-5+e^x\right )^2\right )-8 e^x x \log ^3\left (\left (-5+e^x\right )^2\right )\right ) \log (\log (3))}{\left (5-e^x\right ) x} \, dx,x,e^x\right )\\ &=\log (\log (3)) \operatorname {Subst}\left (\int \frac {5-e^x-24 e^x x \log \left (\left (-5+e^x\right )^2\right )-8 e^x x \log ^3\left (\left (-5+e^x\right )^2\right )}{\left (5-e^x\right ) x} \, dx,x,e^x\right )\\ &=\log (\log (3)) \operatorname {Subst}\left (\int \left (\frac {40 \log \left (\left (-5+e^x\right )^2\right ) \left (3+\log ^2\left (\left (-5+e^x\right )^2\right )\right )}{-5+e^x}+\frac {1+24 x \log \left (\left (-5+e^x\right )^2\right )+8 x \log ^3\left (\left (-5+e^x\right )^2\right )}{x}\right ) \, dx,x,e^x\right )\\ &=\log (\log (3)) \operatorname {Subst}\left (\int \frac {1+24 x \log \left (\left (-5+e^x\right )^2\right )+8 x \log ^3\left (\left (-5+e^x\right )^2\right )}{x} \, dx,x,e^x\right )+(40 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (\left (-5+e^x\right )^2\right ) \left (3+\log ^2\left (\left (-5+e^x\right )^2\right )\right )}{-5+e^x} \, dx,x,e^x\right )\\ &=\log (\log (3)) \operatorname {Subst}\left (\int \left (\frac {1}{x}+24 \log \left (\left (-5+e^x\right )^2\right )+8 \log ^3\left (\left (-5+e^x\right )^2\right )\right ) \, dx,x,e^x\right )+(40 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left ((-5+x)^2\right ) \left (3+\log ^2\left ((-5+x)^2\right )\right )}{(-5+x) x} \, dx,x,e^{e^x}\right )\\ &=x \log (\log (3))+(8 \log (\log (3))) \operatorname {Subst}\left (\int \log ^3\left (\left (-5+e^x\right )^2\right ) \, dx,x,e^x\right )+(24 \log (\log (3))) \operatorname {Subst}\left (\int \log \left (\left (-5+e^x\right )^2\right ) \, dx,x,e^x\right )+(40 \log (\log (3))) \operatorname {Subst}\left (\int \left (\frac {3 \log \left ((-5+x)^2\right )}{(-5+x) x}+\frac {\log ^3\left ((-5+x)^2\right )}{(-5+x) x}\right ) \, dx,x,e^{e^x}\right )\\ &=x \log (\log (3))+(8 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log ^3\left ((-5+x)^2\right )}{x} \, dx,x,e^{e^x}\right )+(24 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left ((-5+x)^2\right )}{x} \, dx,x,e^{e^x}\right )+(40 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log ^3\left ((-5+x)^2\right )}{(-5+x) x} \, dx,x,e^{e^x}\right )+(120 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left ((-5+x)^2\right )}{(-5+x) x} \, dx,x,e^{e^x}\right )\\ &=x \log (\log (3))+24 \log \left (\frac {e^{e^x}}{5}\right ) \log \left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+8 \log \left (\frac {e^{e^x}}{5}\right ) \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+(40 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log ^3\left (x^2\right )}{x (5+x)} \, dx,x,-5+e^{e^x}\right )-(48 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (\frac {x}{5}\right )}{-5+x} \, dx,x,e^{e^x}\right )-(48 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log ^2\left ((-5+x)^2\right ) \log \left (\frac {x}{5}\right )}{-5+x} \, dx,x,e^{e^x}\right )+(120 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (x^2\right )}{x (5+x)} \, dx,x,-5+e^{e^x}\right )\\ &=x \log (\log (3))+24 \log \left (\frac {e^{e^x}}{5}\right ) \log \left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+8 \log \left (\frac {e^{e^x}}{5}\right ) \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+48 \log (\log (3)) \text {Li}_2\left (1-\frac {e^{e^x}}{5}\right )+(8 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log ^3\left (x^2\right )}{x} \, dx,x,-5+e^{e^x}\right )-(8 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log ^3\left (x^2\right )}{5+x} \, dx,x,-5+e^{e^x}\right )+(24 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (x^2\right )}{x} \, dx,x,-5+e^{e^x}\right )-(24 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (x^2\right )}{5+x} \, dx,x,-5+e^{e^x}\right )-(48 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log ^2\left (x^2\right ) \log \left (\frac {5+x}{5}\right )}{x} \, dx,x,-5+e^{e^x}\right )\\ &=x \log (\log (3))+24 \log \left (\frac {e^{e^x}}{5}\right ) \log \left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+6 \log ^2\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+8 \log \left (\frac {e^{e^x}}{5}\right ) \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))-24 \log \left (\left (-5+e^{e^x}\right )^2\right ) \log \left (1+\frac {1}{5} \left (-5+e^{e^x}\right )\right ) \log (\log (3))-8 \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log \left (1+\frac {1}{5} \left (-5+e^{e^x}\right )\right ) \log (\log (3))+48 \log ^2\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3)) \text {Li}_2\left (\frac {1}{5} \left (5-e^{e^x}\right )\right )+48 \log (\log (3)) \text {Li}_2\left (1-\frac {e^{e^x}}{5}\right )+(4 \log (\log (3))) \operatorname {Subst}\left (\int x^3 \, dx,x,\log \left (\left (-5+e^{e^x}\right )^2\right )\right )+(48 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {x}{5}\right )}{x} \, dx,x,-5+e^{e^x}\right )+(48 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {x}{5}\right ) \log ^2\left (x^2\right )}{x} \, dx,x,-5+e^{e^x}\right )-(192 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (x^2\right ) \text {Li}_2\left (-\frac {x}{5}\right )}{x} \, dx,x,-5+e^{e^x}\right )\\ &=x \log (\log (3))+24 \log \left (\frac {e^{e^x}}{5}\right ) \log \left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+6 \log ^2\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+8 \log \left (\frac {e^{e^x}}{5}\right ) \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+\log ^4\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))-24 \log \left (\left (-5+e^{e^x}\right )^2\right ) \log \left (1+\frac {1}{5} \left (-5+e^{e^x}\right )\right ) \log (\log (3))-8 \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log \left (1+\frac {1}{5} \left (-5+e^{e^x}\right )\right ) \log (\log (3))-48 \log (\log (3)) \text {Li}_2\left (\frac {1}{5} \left (5-e^{e^x}\right )\right )+48 \log (\log (3)) \text {Li}_2\left (1-\frac {e^{e^x}}{5}\right )-192 \log \left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3)) \text {Li}_3\left (\frac {1}{5} \left (5-e^{e^x}\right )\right )+(192 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\log \left (x^2\right ) \text {Li}_2\left (-\frac {x}{5}\right )}{x} \, dx,x,-5+e^{e^x}\right )+(384 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\text {Li}_3\left (-\frac {x}{5}\right )}{x} \, dx,x,-5+e^{e^x}\right )\\ &=x \log (\log (3))+24 \log \left (\frac {e^{e^x}}{5}\right ) \log \left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+6 \log ^2\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+8 \log \left (\frac {e^{e^x}}{5}\right ) \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+\log ^4\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))-24 \log \left (\left (-5+e^{e^x}\right )^2\right ) \log \left (1+\frac {1}{5} \left (-5+e^{e^x}\right )\right ) \log (\log (3))-8 \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log \left (1+\frac {1}{5} \left (-5+e^{e^x}\right )\right ) \log (\log (3))-48 \log (\log (3)) \text {Li}_2\left (\frac {1}{5} \left (5-e^{e^x}\right )\right )+48 \log (\log (3)) \text {Li}_2\left (1-\frac {e^{e^x}}{5}\right )+384 \log (\log (3)) \text {Li}_4\left (\frac {1}{5} \left (5-e^{e^x}\right )\right )-(384 \log (\log (3))) \operatorname {Subst}\left (\int \frac {\text {Li}_3\left (-\frac {x}{5}\right )}{x} \, dx,x,-5+e^{e^x}\right )\\ &=x \log (\log (3))+24 \log \left (\frac {e^{e^x}}{5}\right ) \log \left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+6 \log ^2\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+8 \log \left (\frac {e^{e^x}}{5}\right ) \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))+\log ^4\left (\left (-5+e^{e^x}\right )^2\right ) \log (\log (3))-24 \log \left (\left (-5+e^{e^x}\right )^2\right ) \log \left (1+\frac {1}{5} \left (-5+e^{e^x}\right )\right ) \log (\log (3))-8 \log ^3\left (\left (-5+e^{e^x}\right )^2\right ) \log \left (1+\frac {1}{5} \left (-5+e^{e^x}\right )\right ) \log (\log (3))-48 \log (\log (3)) \text {Li}_2\left (\frac {1}{5} \left (5-e^{e^x}\right )\right )+48 \log (\log (3)) \text {Li}_2\left (1-\frac {e^{e^x}}{5}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 22, normalized size = 0.85 \begin {gather*} \left (x+\left (3+\log ^2\left (\left (-5+e^{e^x}\right )^2\right )\right )^2\right ) \log (\log (3)) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.58, size = 81, normalized size = 3.12 \begin {gather*} \log \left ({\left (25 \, e^{\left (2 \, x\right )} + e^{\left (2 \, x + 2 \, e^{x}\right )} - 10 \, e^{\left (2 \, x + e^{x}\right )}\right )} e^{\left (-2 \, x\right )}\right )^{4} \log \left (\log \relax (3)\right ) + 6 \, \log \left ({\left (25 \, e^{\left (2 \, x\right )} + e^{\left (2 \, x + 2 \, e^{x}\right )} - 10 \, e^{\left (2 \, x + e^{x}\right )}\right )} e^{\left (-2 \, x\right )}\right )^{2} \log \left (\log \relax (3)\right ) + x \log \left (\log \relax (3)\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 {8 \, e^{\left (x + e^{x}\right )} \log \left (e^{\left (2 \, e^{x}\right )} - 10 \, e^{\left (e^{x}\right )} + 25\right )^{3} \log \left (\log \relax (3)\right ) + 24 \, e^{\left (x + e^{x}\right )} \log \left (e^{\left (2 \, e^{x}\right )} - 10 \, e^{\left (e^{x}\right )} + 25\right ) \log \left (\log \relax (3)\right ) + e^{\left (e^{x}\right )} \log \left (\log \relax (3)\right ) - 5 \, \log \left (\log \relax (3)\right )}{e^{\left (e^{x}\right )} - 5}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.25, size = 155, normalized size = 5.96
method | result | size |
derivativedivides | \(24 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2} \ln \left (\ln \relax (3)\right ) \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )-2 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{2}+24 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2} \ln \left (\ln \relax (3)\right )+8 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )-2 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{3}+24 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )-2 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )+16 \ln \left (\ln \relax (3)\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{4}+32 \ln \left (\ln \relax (3)\right ) \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )-2 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{3}+\ln \left (\ln \relax (3)\right ) \ln \left ({\mathrm e}^{x}\right )\) | \(155\) |
default | \(24 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2} \ln \left (\ln \relax (3)\right ) \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )-2 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{2}+24 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2} \ln \left (\ln \relax (3)\right )+8 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )-2 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{3}+24 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )-2 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )+16 \ln \left (\ln \relax (3)\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{4}+32 \ln \left (\ln \relax (3)\right ) \left (\ln \left (\left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )-2 \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{3}+\ln \left (\ln \relax (3)\right ) \ln \left ({\mathrm e}^{x}\right )\) | \(155\) |
risch | \(16 \ln \left (\ln \relax (3)\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{4}-16 i \ln \left (\ln \relax (3)\right ) \pi \,\mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right ) \left (\mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{2}-2 \,\mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )+\mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{2}\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{3}+\left (-6 \pi ^{2} \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{4} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{2}+24 \pi ^{2} \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{3} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{3}-36 \pi ^{2} \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{4}+24 \pi ^{2} \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{5}-6 \pi ^{2} \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{6}+24 \ln \left (\ln \relax (3)\right )\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}+i \pi ^{3} \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{6} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{3}-6 i \pi ^{3} \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{5} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{4}+15 i \pi ^{3} \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{4} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{5}-20 i \pi ^{3} \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{3} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{6}+15 i \pi ^{3} \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{7}-6 i \pi ^{3} \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{8}+i \pi ^{3} \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{9}-12 i \pi \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right )^{2} \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )+24 i \pi \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{2}-12 i \pi \ln \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right ) \ln \left (\ln \relax (3)\right ) \mathrm {csgn}\left (i \left ({\mathrm e}^{{\mathrm e}^{x}}-5\right )^{2}\right )^{3}+\ln \left (\ln \relax (3)\right ) x\) | \(611\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 32, normalized size = 1.23 \begin {gather*} 16 \, \log \left (e^{\left (e^{x}\right )} - 5\right )^{4} \log \left (\log \relax (3)\right ) + 24 \, \log \left (e^{\left (e^{x}\right )} - 5\right )^{2} \log \left (\log \relax (3)\right ) + x \log \left (\log \relax (3)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.37, size = 38, normalized size = 1.46 \begin {gather*} \ln \left (\ln \relax (3)\right )\,\left ({\ln \left ({\mathrm {e}}^{2\,{\mathrm {e}}^x}-10\,{\mathrm {e}}^{{\mathrm {e}}^x}+25\right )}^4+6\,{\ln \left ({\mathrm {e}}^{2\,{\mathrm {e}}^x}-10\,{\mathrm {e}}^{{\mathrm {e}}^x}+25\right )}^2+x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.42, size = 54, normalized size = 2.08 \begin {gather*} x \log {\left (\log {\relax (3 )} \right )} + \log {\left (e^{2 e^{x}} - 10 e^{e^{x}} + 25 \right )}^{4} \log {\left (\log {\relax (3 )} \right )} + 6 \log {\left (e^{2 e^{x}} - 10 e^{e^{x}} + 25 \right )}^{2} \log {\left (\log {\relax (3 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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