3.17.100 \(\int \frac {e^{x \log ^{-\frac {2}{3 x}}(50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3))} \log ^{-1-\frac {2}{3 x}}(50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3)) (8 x+(-45 x+3 e^5 x-3 x^2) \log (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3))+(-30+2 e^5-2 x) \log (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3)) \log (\log (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} (1350+180 x+6 x^2)+e^5 (-13500-2700 x-180 x^2-4 x^3))))}{-45 x+3 e^5 x-3 x^2} \, dx\) [1700]

3.17.100.1 Optimal result

Integrand size = 392, antiderivative size = 23 \[ \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )} \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{-45 x+3 e^5 x-3 x^2} \, dx=e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \]

output

exp(x/exp(1/3*ln(ln((15-exp(5)+x)^4))/x)^2)
 

3.17.100.2 Mathematica [A] (verified)

Time = 0.09 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )} \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{-45 x+3 e^5 x-3 x^2} \, dx=e^{x \log ^{-\frac {2}{3 x}}\left (\left (15-e^5+x\right )^4\right )} \]

input

Integrate[(E^(x/Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 
 60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x 
^2 - 4*x^3)]^(2/(3*x)))*Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 13 
50*x^2 + 60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x 
 - 180*x^2 - 4*x^3)]^(-1 - 2/(3*x))*(8*x + (-45*x + 3*E^5*x - 3*x^2)*Log[5 
0625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10* 
(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)] + (-30 + 
 2*E^5 - 2*x)*Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 6 
0*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 
 - 4*x^3)]*Log[Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 
60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^ 
2 - 4*x^3)]]))/(-45*x + 3*E^5*x - 3*x^2),x]
 

output

E^(x/Log[(15 - E^5 + x)^4]^(2/(3*x)))
 

3.17.100.3 Rubi [F]

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.

\(\displaystyle \int \frac {\log ^{-\frac {2}{3 x}-1}\left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right ) \left (\left (-3 x^2+3 e^5 x-45 x\right ) \log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )+\left (-2 x+2 e^5-30\right ) \log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right ) \log \left (\log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )\right )+8 x\right ) \exp \left (x \log ^{-\frac {2}{3 x}}\left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )\right )}{-3 x^2+3 e^5 x-45 x} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {\log ^{-\frac {2}{3 x}-1}\left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right ) \left (\left (-3 x^2+3 e^5 x-45 x\right ) \log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )+\left (-2 x+2 e^5-30\right ) \log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right ) \log \left (\log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )\right )+8 x\right ) \exp \left (x \log ^{-\frac {2}{3 x}}\left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )\right )}{\left (3 e^5-45\right ) x-3 x^2}dx\)

\(\Big \downarrow \) 2026

\(\displaystyle \int \frac {\log ^{-\frac {2}{3 x}-1}\left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right ) \left (\left (-3 x^2+3 e^5 x-45 x\right ) \log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )+\left (-2 x+2 e^5-30\right ) \log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right ) \log \left (\log \left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )\right )+8 x\right ) \exp \left (x \log ^{-\frac {2}{3 x}}\left (x^4+60 x^3+1350 x^2+e^{10} \left (6 x^2+180 x+1350\right )+e^5 \left (-4 x^3-180 x^2-2700 x-13500\right )+13500 x+e^{15} (-4 x-60)+e^{20}+50625\right )\right )}{\left (-3 x-3 \left (15-e^5\right )\right ) x}dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )} \log ^{-\frac {2}{3 x}-1}\left (\left (x-e^5+15\right )^4\right ) \left (-8 x-\left (-x+e^5-15\right ) \log \left (\left (x-e^5+15\right )^4\right ) \left (3 x+2 \log \left (\log \left (\left (x-e^5+15\right )^4\right )\right )\right )\right )}{3 x \left (x-e^5+15\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{3} \int -\frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right ) \left (8 x-\left (x-e^5+15\right ) \log \left (\left (x-e^5+15\right )^4\right ) \left (3 x+2 \log \left (\log \left (\left (x-e^5+15\right )^4\right )\right )\right )\right )}{x \left (x-e^5+15\right )}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -\frac {1}{3} \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right ) \left (8 x-\left (x-e^5+15\right ) \log \left (\left (x-e^5+15\right )^4\right ) \left (3 x+2 \log \left (\log \left (\left (x-e^5+15\right )^4\right )\right )\right )\right )}{x \left (x-e^5+15\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {1}{3} \int \left (\frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right ) \left (-3 x \log \left (\left (x-e^5+15\right )^4\right )-45 \left (1-\frac {e^5}{15}\right ) \log \left (\left (x-e^5+15\right )^4\right )+8\right )}{x-e^5+15}-\frac {2 e^{x \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right ) \log \left (\log \left (\left (x-e^5+15\right )^4\right )\right )}{x}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \frac {1}{3} \left (8 \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )} \log ^{-1-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )}{-x+e^5-15}dx+3 \int e^{x \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )dx+2 \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right )} \log ^{-\frac {2}{3 x}}\left (\left (x-e^5+15\right )^4\right ) \log \left (\log \left (\left (x-e^5+15\right )^4\right )\right )}{x}dx\right )\)

input

Int[(E^(x/Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^ 
3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4 
*x^3)]^(2/(3*x)))*Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 
 + 60*x^3 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180 
*x^2 - 4*x^3)]^(-1 - 2/(3*x))*(8*x + (-45*x + 3*E^5*x - 3*x^2)*Log[50625 + 
 E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 + x^4 + E^10*(1350 
+ 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x^3)] + (-30 + 2*E^5 
 - 2*x)*Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 
+ x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4*x 
^3)]*Log[Log[50625 + E^20 + E^15*(-60 - 4*x) + 13500*x + 1350*x^2 + 60*x^3 
 + x^4 + E^10*(1350 + 180*x + 6*x^2) + E^5*(-13500 - 2700*x - 180*x^2 - 4* 
x^3)]]))/(-45*x + 3*E^5*x - 3*x^2),x]
 

output

$Aborted
 

3.17.100.3.1 Defintions of rubi rules used

rule 6

Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v 
+ (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] &&  !FreeQ[Fx, x]
 

rule 25

Int[-(Fx_), x_Symbol] :> Simp[Identity[-1]   Int[Fx, x], x]
 

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 2009

Int[u_, x_Symbol] :> Simp[IntSum[u, x], x] /; SumQ[u]
 

rule 2026

Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p 
*r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ 
erQ[p] &&  !MonomialQ[Px, x] && (ILtQ[p, 0] ||  !PolyQ[u, x])
 

rule 7239

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl 
erIntegrandQ[v, u, x]]
 

rule 7293

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v] 
]
 

3.17.100.4 Maple [F]

\[\int \frac {\left (\left (2 \,{\mathrm e}^{5}-2 x -30\right ) \ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right ) \ln \left (\ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )\right )+\left (3 x \,{\mathrm e}^{5}-3 x^{2}-45 x \right ) \ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )+8 x \right ) {\mathrm e}^{x \,{\mathrm e}^{\frac {\ln \left (\frac {1}{\ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )^{\frac {2}{3}}}\right )}{x}}} {\mathrm e}^{\frac {\ln \left (\frac {1}{\ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )^{\frac {2}{3}}}\right )}{x}}}{\left (3 x \,{\mathrm e}^{5}-3 x^{2}-45 x \right ) \ln \left ({\mathrm e}^{20}+\left (-4 x -60\right ) {\mathrm e}^{15}+\left (6 x^{2}+180 x +1350\right ) {\mathrm e}^{10}+\left (-4 x^{3}-180 x^{2}-2700 x -13500\right ) {\mathrm e}^{5}+x^{4}+60 x^{3}+1350 x^{2}+13500 x +50625\right )}d x\]

input

int(((2*exp(5)-2*x-30)*ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*e 
xp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+5 
0625)*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^ 
3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))+(3*x*ex 
p(5)-3*x^2-45*x)*ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^ 
2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)+ 
8*x)*exp(x/exp(1/3*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*ex 
p(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50 
625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+ 
180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350* 
x^2+13500*x+50625)/exp(1/3*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+ 
1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13 
500*x+50625))/x)^2,x)
 

output

int(((2*exp(5)-2*x-30)*ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*e 
xp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+5 
0625)*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^ 
3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625))+(3*x*ex 
p(5)-3*x^2-45*x)*ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5)^ 
2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625)+ 
8*x)*exp(x/exp(1/3*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*ex 
p(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50 
625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+ 
180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350* 
x^2+13500*x+50625)/exp(1/3*ln(ln(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+ 
1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13 
500*x+50625))/x)^2,x)
 

3.17.100.5 Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (21) = 42\).

Time = 0.25 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.96 \[ \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )} \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{-45 x+3 e^5 x-3 x^2} \, dx=e^{\left (\frac {x}{\log \left (x^{4} + 60 \, x^{3} + 1350 \, x^{2} - 4 \, {\left (x + 15\right )} e^{15} + 6 \, {\left (x^{2} + 30 \, x + 225\right )} e^{10} - 4 \, {\left (x^{3} + 45 \, x^{2} + 675 \, x + 3375\right )} e^{5} + 13500 \, x + e^{20} + 50625\right )^{\frac {2}{3 \, x}}}\right )} \]

input

integrate(((2*exp(5)-2*x-30)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+ 
1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13 
500*x+50625)*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5) 
^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625) 
)+(3*x*exp(5)-3*x^2-45*x)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+135 
0)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500 
*x+50625)+8*x)*exp(x/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+18 
0*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^ 
2+13500*x+50625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/log(exp(5)^4+(-4*x-60)*exp 
(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4 
+60*x^3+1350*x^2+13500*x+50625)/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^ 
3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60* 
x^3+1350*x^2+13500*x+50625))/x)^2,x, algorithm=\
 

output

e^(x/log(x^4 + 60*x^3 + 1350*x^2 - 4*(x + 15)*e^15 + 6*(x^2 + 30*x + 225)* 
e^10 - 4*(x^3 + 45*x^2 + 675*x + 3375)*e^5 + 13500*x + e^20 + 50625)^(2/3/ 
x))
 

3.17.100.6 Sympy [F(-1)]

Timed out. \[ \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )} \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{-45 x+3 e^5 x-3 x^2} \, dx=\text {Timed out} \]

input

integrate(((2*exp(5)-2*x-30)*ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180* 
x+1350)*exp(5)**2+(-4*x**3-180*x**2-2700*x-13500)*exp(5)+x**4+60*x**3+1350 
*x**2+13500*x+50625)*ln(ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+135 
0)*exp(5)**2+(-4*x**3-180*x**2-2700*x-13500)*exp(5)+x**4+60*x**3+1350*x**2 
+13500*x+50625))+(3*x*exp(5)-3*x**2-45*x)*ln(exp(5)**4+(-4*x-60)*exp(5)**3 
+(6*x**2+180*x+1350)*exp(5)**2+(-4*x**3-180*x**2-2700*x-13500)*exp(5)+x**4 
+60*x**3+1350*x**2+13500*x+50625)+8*x)*exp(x/exp(1/3*ln(ln(exp(5)**4+(-4*x 
-60)*exp(5)**3+(6*x**2+180*x+1350)*exp(5)**2+(-4*x**3-180*x**2-2700*x-1350 
0)*exp(5)+x**4+60*x**3+1350*x**2+13500*x+50625))/x)**2)/(3*x*exp(5)-3*x**2 
-45*x)/ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+1350)*exp(5)**2+(-4* 
x**3-180*x**2-2700*x-13500)*exp(5)+x**4+60*x**3+1350*x**2+13500*x+50625)/e 
xp(1/3*ln(ln(exp(5)**4+(-4*x-60)*exp(5)**3+(6*x**2+180*x+1350)*exp(5)**2+( 
-4*x**3-180*x**2-2700*x-13500)*exp(5)+x**4+60*x**3+1350*x**2+13500*x+50625 
))/x)**2,x)
 

output

Timed out
 

3.17.100.7 Maxima [A] (verification not implemented)

Time = 0.46 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.13 \[ \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )} \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{-45 x+3 e^5 x-3 x^2} \, dx=e^{\left (x e^{\left (-\frac {4 \, \log \left (2\right )}{3 \, x} - \frac {2 \, \log \left (\log \left (x - e^{5} + 15\right )\right )}{3 \, x}\right )}\right )} \]

input

integrate(((2*exp(5)-2*x-30)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+ 
1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13 
500*x+50625)*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5) 
^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625) 
)+(3*x*exp(5)-3*x^2-45*x)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+135 
0)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500 
*x+50625)+8*x)*exp(x/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+18 
0*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^ 
2+13500*x+50625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/log(exp(5)^4+(-4*x-60)*exp 
(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4 
+60*x^3+1350*x^2+13500*x+50625)/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^ 
3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60* 
x^3+1350*x^2+13500*x+50625))/x)^2,x, algorithm=\
 

output

e^(x*e^(-4/3*log(2)/x - 2/3*log(log(x - e^5 + 15))/x))
 

3.17.100.8 Giac [F]

\[ \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )} \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{-45 x+3 e^5 x-3 x^2} \, dx=\int { \frac {{\left (2 \, {\left (x - e^{5} + 15\right )} \log \left (x^{4} + 60 \, x^{3} + 1350 \, x^{2} - 4 \, {\left (x + 15\right )} e^{15} + 6 \, {\left (x^{2} + 30 \, x + 225\right )} e^{10} - 4 \, {\left (x^{3} + 45 \, x^{2} + 675 \, x + 3375\right )} e^{5} + 13500 \, x + e^{20} + 50625\right ) \log \left (\log \left (x^{4} + 60 \, x^{3} + 1350 \, x^{2} - 4 \, {\left (x + 15\right )} e^{15} + 6 \, {\left (x^{2} + 30 \, x + 225\right )} e^{10} - 4 \, {\left (x^{3} + 45 \, x^{2} + 675 \, x + 3375\right )} e^{5} + 13500 \, x + e^{20} + 50625\right )\right ) + 3 \, {\left (x^{2} - x e^{5} + 15 \, x\right )} \log \left (x^{4} + 60 \, x^{3} + 1350 \, x^{2} - 4 \, {\left (x + 15\right )} e^{15} + 6 \, {\left (x^{2} + 30 \, x + 225\right )} e^{10} - 4 \, {\left (x^{3} + 45 \, x^{2} + 675 \, x + 3375\right )} e^{5} + 13500 \, x + e^{20} + 50625\right ) - 8 \, x\right )} e^{\left (\frac {x}{\log \left (x^{4} + 60 \, x^{3} + 1350 \, x^{2} - 4 \, {\left (x + 15\right )} e^{15} + 6 \, {\left (x^{2} + 30 \, x + 225\right )} e^{10} - 4 \, {\left (x^{3} + 45 \, x^{2} + 675 \, x + 3375\right )} e^{5} + 13500 \, x + e^{20} + 50625\right )^{\frac {2}{3 \, x}}}\right )}}{3 \, {\left (x^{2} - x e^{5} + 15 \, x\right )} \log \left (x^{4} + 60 \, x^{3} + 1350 \, x^{2} - 4 \, {\left (x + 15\right )} e^{15} + 6 \, {\left (x^{2} + 30 \, x + 225\right )} e^{10} - 4 \, {\left (x^{3} + 45 \, x^{2} + 675 \, x + 3375\right )} e^{5} + 13500 \, x + e^{20} + 50625\right )^{\frac {2}{3 \, x}} \log \left (x^{4} + 60 \, x^{3} + 1350 \, x^{2} - 4 \, {\left (x + 15\right )} e^{15} + 6 \, {\left (x^{2} + 30 \, x + 225\right )} e^{10} - 4 \, {\left (x^{3} + 45 \, x^{2} + 675 \, x + 3375\right )} e^{5} + 13500 \, x + e^{20} + 50625\right )} \,d x } \]

input

integrate(((2*exp(5)-2*x-30)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+ 
1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13 
500*x+50625)*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+1350)*exp(5) 
^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500*x+50625) 
)+(3*x*exp(5)-3*x^2-45*x)*log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+180*x+135 
0)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^2+13500 
*x+50625)+8*x)*exp(x/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^3+(6*x^2+18 
0*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60*x^3+1350*x^ 
2+13500*x+50625))/x)^2)/(3*x*exp(5)-3*x^2-45*x)/log(exp(5)^4+(-4*x-60)*exp 
(5)^3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4 
+60*x^3+1350*x^2+13500*x+50625)/exp(1/3*log(log(exp(5)^4+(-4*x-60)*exp(5)^ 
3+(6*x^2+180*x+1350)*exp(5)^2+(-4*x^3-180*x^2-2700*x-13500)*exp(5)+x^4+60* 
x^3+1350*x^2+13500*x+50625))/x)^2,x, algorithm=\
 

output

integrate(1/3*(2*(x - e^5 + 15)*log(x^4 + 60*x^3 + 1350*x^2 - 4*(x + 15)*e 
^15 + 6*(x^2 + 30*x + 225)*e^10 - 4*(x^3 + 45*x^2 + 675*x + 3375)*e^5 + 13 
500*x + e^20 + 50625)*log(log(x^4 + 60*x^3 + 1350*x^2 - 4*(x + 15)*e^15 + 
6*(x^2 + 30*x + 225)*e^10 - 4*(x^3 + 45*x^2 + 675*x + 3375)*e^5 + 13500*x 
+ e^20 + 50625)) + 3*(x^2 - x*e^5 + 15*x)*log(x^4 + 60*x^3 + 1350*x^2 - 4* 
(x + 15)*e^15 + 6*(x^2 + 30*x + 225)*e^10 - 4*(x^3 + 45*x^2 + 675*x + 3375 
)*e^5 + 13500*x + e^20 + 50625) - 8*x)*e^(x/log(x^4 + 60*x^3 + 1350*x^2 - 
4*(x + 15)*e^15 + 6*(x^2 + 30*x + 225)*e^10 - 4*(x^3 + 45*x^2 + 675*x + 33 
75)*e^5 + 13500*x + e^20 + 50625)^(2/3/x))/((x^2 - x*e^5 + 15*x)*log(x^4 + 
 60*x^3 + 1350*x^2 - 4*(x + 15)*e^15 + 6*(x^2 + 30*x + 225)*e^10 - 4*(x^3 
+ 45*x^2 + 675*x + 3375)*e^5 + 13500*x + e^20 + 50625)^(2/3/x)*log(x^4 + 6 
0*x^3 + 1350*x^2 - 4*(x + 15)*e^15 + 6*(x^2 + 30*x + 225)*e^10 - 4*(x^3 + 
45*x^2 + 675*x + 3375)*e^5 + 13500*x + e^20 + 50625)), x)
 

3.17.100.9 Mupad [B] (verification not implemented)

Time = 13.35 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.48 \[ \int \frac {e^{x \log ^{-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )} \log ^{-1-\frac {2}{3 x}}\left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \left (8 x+\left (-45 x+3 e^5 x-3 x^2\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )+\left (-30+2 e^5-2 x\right ) \log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right ) \log \left (\log \left (50625+e^{20}+e^{15} (-60-4 x)+13500 x+1350 x^2+60 x^3+x^4+e^{10} \left (1350+180 x+6 x^2\right )+e^5 \left (-13500-2700 x-180 x^2-4 x^3\right )\right )\right )\right )}{-45 x+3 e^5 x-3 x^2} \, dx={\mathrm {e}}^{\frac {x}{{\ln \left (13500\,x-13500\,{\mathrm {e}}^5+1350\,{\mathrm {e}}^{10}-60\,{\mathrm {e}}^{15}+{\mathrm {e}}^{20}-2700\,x\,{\mathrm {e}}^5+180\,x\,{\mathrm {e}}^{10}-4\,x\,{\mathrm {e}}^{15}-180\,x^2\,{\mathrm {e}}^5-4\,x^3\,{\mathrm {e}}^5+6\,x^2\,{\mathrm {e}}^{10}+1350\,x^2+60\,x^3+x^4+50625\right )}^{\frac {2}{3\,x}}}} \]

input

int((exp(x*exp(-(2*log(log(13500*x + exp(20) + exp(10)*(180*x + 6*x^2 + 13 
50) - exp(5)*(2700*x + 180*x^2 + 4*x^3 + 13500) + 1350*x^2 + 60*x^3 + x^4 
- exp(15)*(4*x + 60) + 50625)))/(3*x)))*exp(-(2*log(log(13500*x + exp(20) 
+ exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 180*x^2 + 4*x^3 + 1350 
0) + 1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625)))/(3*x))*(log(1 
3500*x + exp(20) + exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 180*x 
^2 + 4*x^3 + 13500) + 1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625 
)*(45*x - 3*x*exp(5) + 3*x^2) - 8*x + log(log(13500*x + exp(20) + exp(10)* 
(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 180*x^2 + 4*x^3 + 13500) + 1350* 
x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625))*log(13500*x + exp(20) + 
exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2700*x + 180*x^2 + 4*x^3 + 13500) 
 + 1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x + 60) + 50625)*(2*x - 2*exp(5) + 
 30)))/(log(13500*x + exp(20) + exp(10)*(180*x + 6*x^2 + 1350) - exp(5)*(2 
700*x + 180*x^2 + 4*x^3 + 13500) + 1350*x^2 + 60*x^3 + x^4 - exp(15)*(4*x 
+ 60) + 50625)*(45*x - 3*x*exp(5) + 3*x^2)),x)
 

output

exp(x/log(13500*x - 13500*exp(5) + 1350*exp(10) - 60*exp(15) + exp(20) - 2 
700*x*exp(5) + 180*x*exp(10) - 4*x*exp(15) - 180*x^2*exp(5) - 4*x^3*exp(5) 
 + 6*x^2*exp(10) + 1350*x^2 + 60*x^3 + x^4 + 50625)^(2/(3*x)))