Integrand size = 240, antiderivative size = 28 \[ \int \frac {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} \left (12000+e^{e^x+x} (22500+12000 x+15000 \log (3))\right )}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+\left (135000+231000 x+123200 x^2+20480 x^3\right ) \log (3)+\left (135000+149000 x+38400 x^2\right ) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} \left (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3)\right )+e^{e^{e^x}} \left (-405000-693000 x-369600 x^2-61440 x^3+\left (-810000-894000 x-230400 x^2\right ) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3)\right )} \, dx=\frac {1}{x+\left (5-2 \left (4-3 e^{e^{e^x}}+\frac {4 x}{5}+\log (3)\right )\right )^2} \]
Leaf count is larger than twice the leaf count of optimal. \(57\) vs. \(2(28)=56\).
Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.04 \[ \int \frac {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} \left (12000+e^{e^x+x} (22500+12000 x+15000 \log (3))\right )}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+\left (135000+231000 x+123200 x^2+20480 x^3\right ) \log (3)+\left (135000+149000 x+38400 x^2\right ) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} \left (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3)\right )+e^{e^{e^x}} \left (-405000-693000 x-369600 x^2-61440 x^3+\left (-810000-894000 x-230400 x^2\right ) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3)\right )} \, dx=\frac {25}{900 e^{2 e^{e^x}}+64 x^2+5 x (53+32 \log (3))+25 (3+\log (9))^2-60 e^{e^{e^x}} (8 x+5 (3+\log (9)))} \]
Integrate[(-6625 - 45000*E^(2*E^E^x + E^x + x) - 3200*x - 4000*Log[3] + E^ E^E^x*(12000 + E^(E^x + x)*(22500 + 12000*x + 15000*Log[3])))/(50625 + 810 000*E^(4*E^E^x) + 119250*x + 99025*x^2 + 33920*x^3 + 4096*x^4 + E^(3*E^E^x )*(-1620000 - 864000*x - 1080000*Log[3]) + (135000 + 231000*x + 123200*x^2 + 20480*x^3)*Log[3] + (135000 + 149000*x + 38400*x^2)*Log[3]^2 + (60000 + 32000*x)*Log[3]^3 + 10000*Log[3]^4 + E^(2*E^E^x)*(1215000 + 1341000*x + 3 45600*x^2 + (1620000 + 864000*x)*Log[3] + 540000*Log[3]^2) + E^E^E^x*(-405 000 - 693000*x - 369600*x^2 - 61440*x^3 + (-810000 - 894000*x - 230400*x^2 )*Log[3] + (-540000 - 288000*x)*Log[3]^2 - 120000*Log[3]^3)),x]
25/(900*E^(2*E^E^x) + 64*x^2 + 5*x*(53 + 32*Log[3]) + 25*(3 + Log[9])^2 - 60*E^E^E^x*(8*x + 5*(3 + Log[9])))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-3200 x-45000 e^{x+2 e^{e^x}+e^x}+e^{e^{e^x}} \left (e^{x+e^x} (12000 x+22500+15000 \log (3))+12000\right )-6625-4000 \log (3)}{4096 x^4+33920 x^3+99025 x^2+e^{2 e^{e^x}} \left (345600 x^2+1341000 x+(864000 x+1620000) \log (3)+1215000+540000 \log ^2(3)\right )+\left (38400 x^2+149000 x+135000\right ) \log ^2(3)+e^{e^{e^x}} \left (-61440 x^3-369600 x^2+\left (-230400 x^2-894000 x-810000\right ) \log (3)-693000 x+(-288000 x-540000) \log ^2(3)-405000-120000 \log ^3(3)\right )+\left (20480 x^3+123200 x^2+231000 x+135000\right ) \log (3)+119250 x+810000 e^{4 e^{e^x}}+(32000 x+60000) \log ^3(3)+e^{3 e^{e^x}} (-864000 x-1620000-1080000 \log (3))+50625+10000 \log ^4(3)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {25 \left (-128 x+480 e^{e^{e^x}}-1800 e^{x+2 e^{e^x}+e^x}+60 e^{x+e^{e^x}+e^x} (8 x+5 (3+\log (9)))-265 \left (1+\frac {32 \log (3)}{53}\right )\right )}{\left (64 x^2+900 e^{2 e^{e^x}}+5 x (53+32 \log (3))-60 e^{e^{e^x}} (8 x+5 (3+\log (9)))+25 (3+\log (9))^2\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 25 \int \frac {-128 x+480 e^{e^{e^x}}-1800 e^{x+2 e^{e^x}+e^x}+60 e^{x+e^{e^x}+e^x} (8 x+5 (3+\log (9)))-5 (53+32 \log (3))}{\left (64 x^2+5 (53+32 \log (3)) x+900 e^{2 e^{e^x}}-60 e^{e^{e^x}} (8 x+5 (3+\log (9)))+25 (3+\log (9))^2\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 25 \int \left (-\frac {128 x}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}+\frac {480 e^{e^{e^x}}}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}+\frac {60 e^{x+e^{e^x}+e^x} \left (8 x-30 e^{e^{e^x}}+15 \left (1+\frac {2 \log (3)}{3}\right )\right )}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}+\frac {5 (-53-32 \log (3))}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 25 \left (-5 (53+32 \log (3)) \int \frac {1}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}dx+480 \int \frac {e^{e^{e^x}}}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}dx+300 (3+\log (9)) \int \frac {e^{x+e^{e^x}+e^x}}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}dx-1800 \int \frac {e^{x+2 e^{e^x}+e^x}}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}dx-128 \int \frac {x}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}dx+480 \int \frac {e^{x+e^{e^x}+e^x} x}{\left (64 x^2-480 e^{e^{e^x}} x+265 \left (1+\frac {32 \log (3)}{53}\right ) x+900 e^{2 e^{e^x}}+225 \left (1+\frac {2}{9} (3+\log (3)) \log (9)\right )-900 e^{e^{e^x}} \left (1+\frac {2 \log (3)}{3}\right )\right )^2}dx\right )\) |
Int[(-6625 - 45000*E^(2*E^E^x + E^x + x) - 3200*x - 4000*Log[3] + E^E^E^x* (12000 + E^(E^x + x)*(22500 + 12000*x + 15000*Log[3])))/(50625 + 810000*E^ (4*E^E^x) + 119250*x + 99025*x^2 + 33920*x^3 + 4096*x^4 + E^(3*E^E^x)*(-16 20000 - 864000*x - 1080000*Log[3]) + (135000 + 231000*x + 123200*x^2 + 204 80*x^3)*Log[3] + (135000 + 149000*x + 38400*x^2)*Log[3]^2 + (60000 + 32000 *x)*Log[3]^3 + 10000*Log[3]^4 + E^(2*E^E^x)*(1215000 + 1341000*x + 345600* x^2 + (1620000 + 864000*x)*Log[3] + 540000*Log[3]^2) + E^E^E^x*(-405000 - 693000*x - 369600*x^2 - 61440*x^3 + (-810000 - 894000*x - 230400*x^2)*Log[ 3] + (-540000 - 288000*x)*Log[3]^2 - 120000*Log[3]^3)),x]
3.12.76.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(21)=42\).
Time = 1.46 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.11
| method | result | size |
| risch | \(\frac {25}{100 \ln \left (3\right )^{2}-600 \ln \left (3\right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+160 x \ln \left (3\right )+900 \,{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}-480 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}} x +64 x^{2}+300 \ln \left (3\right )-900 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+265 x +225}\) | \(59\) |
| parallelrisch | \(\frac {25}{100 \ln \left (3\right )^{2}-600 \ln \left (3\right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+160 x \ln \left (3\right )+900 \,{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}-480 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}} x +64 x^{2}+300 \ln \left (3\right )-900 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+265 x +225}\) | \(59\) |
int((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))^2+((15000*ln(3)+12000*x+22 500)*exp(x)*exp(exp(x))+12000)*exp(exp(exp(x)))-4000*ln(3)-3200*x-6625)/(8 10000*exp(exp(exp(x)))^4+(-1080000*ln(3)-864000*x-1620000)*exp(exp(exp(x)) )^3+(540000*ln(3)^2+(864000*x+1620000)*ln(3)+345600*x^2+1341000*x+1215000) *exp(exp(exp(x)))^2+(-120000*ln(3)^3+(-288000*x-540000)*ln(3)^2+(-230400*x ^2-894000*x-810000)*ln(3)-61440*x^3-369600*x^2-693000*x-405000)*exp(exp(ex p(x)))+10000*ln(3)^4+(32000*x+60000)*ln(3)^3+(38400*x^2+149000*x+135000)*l n(3)^2+(20480*x^3+123200*x^2+231000*x+135000)*ln(3)+4096*x^4+33920*x^3+990 25*x^2+119250*x+50625),x,method=_RETURNVERBOSE)
25/(100*ln(3)^2-600*ln(3)*exp(exp(exp(x)))+160*x*ln(3)+900*exp(2*exp(exp(x )))-480*exp(exp(exp(x)))*x+64*x^2+300*ln(3)-900*exp(exp(exp(x)))+265*x+225 )
Leaf count of result is larger than twice the leaf count of optimal. 52 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86 \[ \int \frac {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} \left (12000+e^{e^x+x} (22500+12000 x+15000 \log (3))\right )}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+\left (135000+231000 x+123200 x^2+20480 x^3\right ) \log (3)+\left (135000+149000 x+38400 x^2\right ) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} \left (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3)\right )+e^{e^{e^x}} \left (-405000-693000 x-369600 x^2-61440 x^3+\left (-810000-894000 x-230400 x^2\right ) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3)\right )} \, dx=\frac {25}{64 \, x^{2} - 60 \, {\left (8 \, x + 10 \, \log \left (3\right ) + 15\right )} e^{\left (e^{\left (e^{x}\right )}\right )} + 20 \, {\left (8 \, x + 15\right )} \log \left (3\right ) + 100 \, \log \left (3\right )^{2} + 265 \, x + 900 \, e^{\left (2 \, e^{\left (e^{x}\right )}\right )} + 225} \]
integrate((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))^2+((15000*log(3)+120 00*x+22500)*exp(x)*exp(exp(x))+12000)*exp(exp(exp(x)))-4000*log(3)-3200*x- 6625)/(810000*exp(exp(exp(x)))^4+(-1080000*log(3)-864000*x-1620000)*exp(ex p(exp(x)))^3+(540000*log(3)^2+(864000*x+1620000)*log(3)+345600*x^2+1341000 *x+1215000)*exp(exp(exp(x)))^2+(-120000*log(3)^3+(-288000*x-540000)*log(3) ^2+(-230400*x^2-894000*x-810000)*log(3)-61440*x^3-369600*x^2-693000*x-4050 00)*exp(exp(exp(x)))+10000*log(3)^4+(32000*x+60000)*log(3)^3+(38400*x^2+14 9000*x+135000)*log(3)^2+(20480*x^3+123200*x^2+231000*x+135000)*log(3)+4096 *x^4+33920*x^3+99025*x^2+119250*x+50625),x, algorithm=\
25/(64*x^2 - 60*(8*x + 10*log(3) + 15)*e^(e^(e^x)) + 20*(8*x + 15)*log(3) + 100*log(3)^2 + 265*x + 900*e^(2*e^(e^x)) + 225)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (24) = 48\).
Time = 0.27 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07 \[ \int \frac {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} \left (12000+e^{e^x+x} (22500+12000 x+15000 \log (3))\right )}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+\left (135000+231000 x+123200 x^2+20480 x^3\right ) \log (3)+\left (135000+149000 x+38400 x^2\right ) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} \left (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3)\right )+e^{e^{e^x}} \left (-405000-693000 x-369600 x^2-61440 x^3+\left (-810000-894000 x-230400 x^2\right ) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3)\right )} \, dx=\frac {25}{64 x^{2} + 160 x \log {\left (3 \right )} + 265 x + \left (- 480 x - 900 - 600 \log {\left (3 \right )}\right ) e^{e^{e^{x}}} + 900 e^{2 e^{e^{x}}} + 100 \log {\left (3 \right )}^{2} + 225 + 300 \log {\left (3 \right )}} \]
integrate((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))**2+((15000*ln(3)+120 00*x+22500)*exp(x)*exp(exp(x))+12000)*exp(exp(exp(x)))-4000*ln(3)-3200*x-6 625)/(810000*exp(exp(exp(x)))**4+(-1080000*ln(3)-864000*x-1620000)*exp(exp (exp(x)))**3+(540000*ln(3)**2+(864000*x+1620000)*ln(3)+345600*x**2+1341000 *x+1215000)*exp(exp(exp(x)))**2+(-120000*ln(3)**3+(-288000*x-540000)*ln(3) **2+(-230400*x**2-894000*x-810000)*ln(3)-61440*x**3-369600*x**2-693000*x-4 05000)*exp(exp(exp(x)))+10000*ln(3)**4+(32000*x+60000)*ln(3)**3+(38400*x** 2+149000*x+135000)*ln(3)**2+(20480*x**3+123200*x**2+231000*x+135000)*ln(3) +4096*x**4+33920*x**3+99025*x**2+119250*x+50625),x)
25/(64*x**2 + 160*x*log(3) + 265*x + (-480*x - 900 - 600*log(3))*exp(exp(e xp(x))) + 900*exp(2*exp(exp(x))) + 100*log(3)**2 + 225 + 300*log(3))
Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (25) = 50\).
Time = 0.63 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.89 \[ \int \frac {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} \left (12000+e^{e^x+x} (22500+12000 x+15000 \log (3))\right )}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+\left (135000+231000 x+123200 x^2+20480 x^3\right ) \log (3)+\left (135000+149000 x+38400 x^2\right ) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} \left (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3)\right )+e^{e^{e^x}} \left (-405000-693000 x-369600 x^2-61440 x^3+\left (-810000-894000 x-230400 x^2\right ) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3)\right )} \, dx=\frac {25}{64 \, x^{2} + 5 \, x {\left (32 \, \log \left (3\right ) + 53\right )} - 60 \, {\left (8 \, x + 10 \, \log \left (3\right ) + 15\right )} e^{\left (e^{\left (e^{x}\right )}\right )} + 100 \, \log \left (3\right )^{2} + 900 \, e^{\left (2 \, e^{\left (e^{x}\right )}\right )} + 300 \, \log \left (3\right ) + 225} \]
integrate((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))^2+((15000*log(3)+120 00*x+22500)*exp(x)*exp(exp(x))+12000)*exp(exp(exp(x)))-4000*log(3)-3200*x- 6625)/(810000*exp(exp(exp(x)))^4+(-1080000*log(3)-864000*x-1620000)*exp(ex p(exp(x)))^3+(540000*log(3)^2+(864000*x+1620000)*log(3)+345600*x^2+1341000 *x+1215000)*exp(exp(exp(x)))^2+(-120000*log(3)^3+(-288000*x-540000)*log(3) ^2+(-230400*x^2-894000*x-810000)*log(3)-61440*x^3-369600*x^2-693000*x-4050 00)*exp(exp(exp(x)))+10000*log(3)^4+(32000*x+60000)*log(3)^3+(38400*x^2+14 9000*x+135000)*log(3)^2+(20480*x^3+123200*x^2+231000*x+135000)*log(3)+4096 *x^4+33920*x^3+99025*x^2+119250*x+50625),x, algorithm=\
25/(64*x^2 + 5*x*(32*log(3) + 53) - 60*(8*x + 10*log(3) + 15)*e^(e^(e^x)) + 100*log(3)^2 + 900*e^(2*e^(e^x)) + 300*log(3) + 225)
\[ \int \frac {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} \left (12000+e^{e^x+x} (22500+12000 x+15000 \log (3))\right )}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+\left (135000+231000 x+123200 x^2+20480 x^3\right ) \log (3)+\left (135000+149000 x+38400 x^2\right ) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} \left (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3)\right )+e^{e^{e^x}} \left (-405000-693000 x-369600 x^2-61440 x^3+\left (-810000-894000 x-230400 x^2\right ) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3)\right )} \, dx=\int { \frac {25 \, {\left (60 \, {\left ({\left (8 \, x + 10 \, \log \left (3\right ) + 15\right )} e^{\left (x + e^{x}\right )} + 8\right )} e^{\left (e^{\left (e^{x}\right )}\right )} - 128 \, x - 1800 \, e^{\left (x + e^{x} + 2 \, e^{\left (e^{x}\right )}\right )} - 160 \, \log \left (3\right ) - 265\right )}}{4096 \, x^{4} + 4000 \, {\left (8 \, x + 15\right )} \log \left (3\right )^{3} + 10000 \, \log \left (3\right )^{4} + 33920 \, x^{3} + 200 \, {\left (192 \, x^{2} + 745 \, x + 675\right )} \log \left (3\right )^{2} + 99025 \, x^{2} - 108000 \, {\left (8 \, x + 10 \, \log \left (3\right ) + 15\right )} e^{\left (3 \, e^{\left (e^{x}\right )}\right )} + 1800 \, {\left (192 \, x^{2} + 60 \, {\left (8 \, x + 15\right )} \log \left (3\right ) + 300 \, \log \left (3\right )^{2} + 745 \, x + 675\right )} e^{\left (2 \, e^{\left (e^{x}\right )}\right )} - 120 \, {\left (512 \, x^{3} + 300 \, {\left (8 \, x + 15\right )} \log \left (3\right )^{2} + 1000 \, \log \left (3\right )^{3} + 3080 \, x^{2} + 10 \, {\left (192 \, x^{2} + 745 \, x + 675\right )} \log \left (3\right ) + 5775 \, x + 3375\right )} e^{\left (e^{\left (e^{x}\right )}\right )} + 40 \, {\left (512 \, x^{3} + 3080 \, x^{2} + 5775 \, x + 3375\right )} \log \left (3\right ) + 119250 \, x + 810000 \, e^{\left (4 \, e^{\left (e^{x}\right )}\right )} + 50625} \,d x } \]
integrate((-45000*exp(x)*exp(exp(x))*exp(exp(exp(x)))^2+((15000*log(3)+120 00*x+22500)*exp(x)*exp(exp(x))+12000)*exp(exp(exp(x)))-4000*log(3)-3200*x- 6625)/(810000*exp(exp(exp(x)))^4+(-1080000*log(3)-864000*x-1620000)*exp(ex p(exp(x)))^3+(540000*log(3)^2+(864000*x+1620000)*log(3)+345600*x^2+1341000 *x+1215000)*exp(exp(exp(x)))^2+(-120000*log(3)^3+(-288000*x-540000)*log(3) ^2+(-230400*x^2-894000*x-810000)*log(3)-61440*x^3-369600*x^2-693000*x-4050 00)*exp(exp(exp(x)))+10000*log(3)^4+(32000*x+60000)*log(3)^3+(38400*x^2+14 9000*x+135000)*log(3)^2+(20480*x^3+123200*x^2+231000*x+135000)*log(3)+4096 *x^4+33920*x^3+99025*x^2+119250*x+50625),x, algorithm=\
integrate(25*(60*((8*x + 10*log(3) + 15)*e^(x + e^x) + 8)*e^(e^(e^x)) - 12 8*x - 1800*e^(x + e^x + 2*e^(e^x)) - 160*log(3) - 265)/(4096*x^4 + 4000*(8 *x + 15)*log(3)^3 + 10000*log(3)^4 + 33920*x^3 + 200*(192*x^2 + 745*x + 67 5)*log(3)^2 + 99025*x^2 - 108000*(8*x + 10*log(3) + 15)*e^(3*e^(e^x)) + 18 00*(192*x^2 + 60*(8*x + 15)*log(3) + 300*log(3)^2 + 745*x + 675)*e^(2*e^(e ^x)) - 120*(512*x^3 + 300*(8*x + 15)*log(3)^2 + 1000*log(3)^3 + 3080*x^2 + 10*(192*x^2 + 745*x + 675)*log(3) + 5775*x + 3375)*e^(e^(e^x)) + 40*(512* x^3 + 3080*x^2 + 5775*x + 3375)*log(3) + 119250*x + 810000*e^(4*e^(e^x)) + 50625), x)
Timed out. \[ \int \frac {-6625-45000 e^{2 e^{e^x}+e^x+x}-3200 x-4000 \log (3)+e^{e^{e^x}} \left (12000+e^{e^x+x} (22500+12000 x+15000 \log (3))\right )}{50625+810000 e^{4 e^{e^x}}+119250 x+99025 x^2+33920 x^3+4096 x^4+e^{3 e^{e^x}} (-1620000-864000 x-1080000 \log (3))+\left (135000+231000 x+123200 x^2+20480 x^3\right ) \log (3)+\left (135000+149000 x+38400 x^2\right ) \log ^2(3)+(60000+32000 x) \log ^3(3)+10000 \log ^4(3)+e^{2 e^{e^x}} \left (1215000+1341000 x+345600 x^2+(1620000+864000 x) \log (3)+540000 \log ^2(3)\right )+e^{e^{e^x}} \left (-405000-693000 x-369600 x^2-61440 x^3+\left (-810000-894000 x-230400 x^2\right ) \log (3)+(-540000-288000 x) \log ^2(3)-120000 \log ^3(3)\right )} \, dx=\text {Hanged} \]
int(-(3200*x + 4000*log(3) - exp(exp(exp(x)))*(exp(exp(x))*exp(x)*(12000*x + 15000*log(3) + 22500) + 12000) + 45000*exp(2*exp(exp(x)))*exp(exp(x))*e xp(x) + 6625)/(119250*x + 810000*exp(4*exp(exp(x))) + exp(2*exp(exp(x)))*( 1341000*x + log(3)*(864000*x + 1620000) + 540000*log(3)^2 + 345600*x^2 + 1 215000) + log(3)^3*(32000*x + 60000) - exp(3*exp(exp(x)))*(864000*x + 1080 000*log(3) + 1620000) + log(3)*(231000*x + 123200*x^2 + 20480*x^3 + 135000 ) - exp(exp(exp(x)))*(693000*x + log(3)*(894000*x + 230400*x^2 + 810000) + log(3)^2*(288000*x + 540000) + 120000*log(3)^3 + 369600*x^2 + 61440*x^3 + 405000) + log(3)^2*(149000*x + 38400*x^2 + 135000) + 10000*log(3)^4 + 990 25*x^2 + 33920*x^3 + 4096*x^4 + 50625),x)