\(\int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x (49-16 x+x^2)+(280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)) \log (x)+(15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)) \log ^2(x)+(100 e^x+100 e^{2 x}) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+(140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)) \log (x)+(170+300 e^x+140 e^{2 x}+10 x) \log ^2(x)+(100+100 e^x) \log ^3(x)+25 \log ^4(x)} \, dx\) [674]

Optimal result

Integrand size = 261, antiderivative size = 30 \[ \int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx=e^x-\frac {3 x}{-2+e^{2 x}-x-5 \left (1+e^x+\log (x)\right )^2} \] Output:

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

Mathematica [A] (verified)

Time = 0.11 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.37 \[ \int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx=e^x+\frac {3 x}{7+10 e^x+4 e^{2 x}+x+10 \log (x)+10 e^x \log (x)+5 \log ^2(x)} \] Input:

Integrate[(-9 + 80*E^(4*x) + 16*E^(5*x) + E^(2*x)*(152 - 4*x) + E^(3*x)*(1 
56 + 8*x) + E^x*(49 - 16*x + x^2) + (280*E^(3*x) + 80*E^(4*x) + E^x*(170 - 
 10*x) + E^(2*x)*(340 + 20*x))*Log[x] + (15 + 300*E^(2*x) + 140*E^(3*x) + 
E^x*(170 + 10*x))*Log[x]^2 + (100*E^x + 100*E^(2*x))*Log[x]^3 + 25*E^x*Log 
[x]^4)/(49 + 80*E^(3*x) + 16*E^(4*x) + 14*x + x^2 + E^(2*x)*(156 + 8*x) + 
E^x*(140 + 20*x) + (140 + 280*E^(2*x) + 80*E^(3*x) + 20*x + E^x*(340 + 20* 
x))*Log[x] + (170 + 300*E^x + 140*E^(2*x) + 10*x)*Log[x]^2 + (100 + 100*E^ 
x)*Log[x]^3 + 25*Log[x]^4),x]
 

Output:

E^x + (3*x)/(7 + 10*E^x + 4*E^(2*x) + x + 10*Log[x] + 10*E^x*Log[x] + 5*Lo 
g[x]^2)
 

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.

\(\displaystyle \int \frac {e^x \left (x^2-16 x+49\right )+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (8 x+156)+25 e^x \log ^4(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+\left (e^x (10 x+170)+300 e^{2 x}+140 e^{3 x}+15\right ) \log ^2(x)+\left (e^x (170-10 x)+280 e^{3 x}+80 e^{4 x}+e^{2 x} (20 x+340)\right ) \log (x)-9}{x^2+80 e^{3 x}+16 e^{4 x}+14 x+e^{2 x} (8 x+156)+e^x (20 x+140)+25 \log ^4(x)+\left (100 e^x+100\right ) \log ^3(x)+\left (10 x+300 e^x+140 e^{2 x}+170\right ) \log ^2(x)+\left (20 x+280 e^{2 x}+80 e^{3 x}+e^x (20 x+340)+140\right ) \log (x)+49} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {e^x \left (x^2-16 x+49\right )+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (8 x+156)+25 e^x \log ^4(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+\left (e^x (10 x+170)+300 e^{2 x}+140 e^{3 x}+15\right ) \log ^2(x)+\left (e^x (170-10 x)+280 e^{3 x}+80 e^{4 x}+e^{2 x} (20 x+340)\right ) \log (x)-9}{\left (10 e^x+4 e^{2 x}+x+5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+7\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {3 \left (2 x^2+10 e^x x+13 x-10 e^x+10 x \log ^2(x)+10 e^x x \log (x)+20 x \log (x)-10 \log (x)-10\right )}{\left (10 e^x+4 e^{2 x}+x+5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+7\right )^2}+e^x-\frac {3 (2 x-1)}{10 e^x+4 e^{2 x}+x+5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+7}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 6 \int \frac {x^2}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx-30 \int \frac {1}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx-30 \int \frac {e^x}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx+39 \int \frac {x}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx+30 \int \frac {e^x x}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx-30 \int \frac {\log (x)}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx+60 \int \frac {x \log (x)}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx+30 \int \frac {e^x x \log (x)}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx+30 \int \frac {x \log ^2(x)}{\left (5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7\right )^2}dx+3 \int \frac {1}{5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7}dx-6 \int \frac {x}{5 \log ^2(x)+10 e^x \log (x)+10 \log (x)+10 e^x+4 e^{2 x}+x+7}dx+e^x\)

Input:

Int[(-9 + 80*E^(4*x) + 16*E^(5*x) + E^(2*x)*(152 - 4*x) + E^(3*x)*(156 + 8 
*x) + E^x*(49 - 16*x + x^2) + (280*E^(3*x) + 80*E^(4*x) + E^x*(170 - 10*x) 
 + E^(2*x)*(340 + 20*x))*Log[x] + (15 + 300*E^(2*x) + 140*E^(3*x) + E^x*(1 
70 + 10*x))*Log[x]^2 + (100*E^x + 100*E^(2*x))*Log[x]^3 + 25*E^x*Log[x]^4) 
/(49 + 80*E^(3*x) + 16*E^(4*x) + 14*x + x^2 + E^(2*x)*(156 + 8*x) + E^x*(1 
40 + 20*x) + (140 + 280*E^(2*x) + 80*E^(3*x) + 20*x + E^x*(340 + 20*x))*Lo 
g[x] + (170 + 300*E^x + 140*E^(2*x) + 10*x)*Log[x]^2 + (100 + 100*E^x)*Log 
[x]^3 + 25*Log[x]^4),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.27

\[{\mathrm e}^{x}+\frac {3 x}{4 \,{\mathrm e}^{2 x}+10 \,{\mathrm e}^{x} \ln \left (x \right )+5 \ln \left (x \right )^{2}+10 \,{\mathrm e}^{x}+10 \ln \left (x \right )+x +7}\]

Input:

int((25*exp(x)*ln(x)^4+(100*exp(x)^2+100*exp(x))*ln(x)^3+(140*exp(x)^3+300 
*exp(x)^2+(10*x+170)*exp(x)+15)*ln(x)^2+(80*exp(x)^4+280*exp(x)^3+(20*x+34 
0)*exp(x)^2+(-10*x+170)*exp(x))*ln(x)+16*exp(x)^5+80*exp(x)^4+(8*x+156)*ex 
p(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*ln(x)^4+(100*exp(x) 
+100)*ln(x)^3+(140*exp(x)^2+300*exp(x)+10*x+170)*ln(x)^2+(80*exp(x)^3+280* 
exp(x)^2+(20*x+340)*exp(x)+20*x+140)*ln(x)+16*exp(x)^4+80*exp(x)^3+(8*x+15 
6)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x)
 

Output:

exp(x)+3*x/(4*exp(2*x)+10*exp(x)*ln(x)+5*ln(x)^2+10*exp(x)+10*ln(x)+x+7)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (27) = 54\).

Time = 0.09 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37 \[ \int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx=\frac {5 \, e^{x} \log \left (x\right )^{2} + {\left (x + 7\right )} e^{x} + 10 \, {\left (e^{\left (2 \, x\right )} + e^{x}\right )} \log \left (x\right ) + 3 \, x + 4 \, e^{\left (3 \, x\right )} + 10 \, e^{\left (2 \, x\right )}}{10 \, {\left (e^{x} + 1\right )} \log \left (x\right ) + 5 \, \log \left (x\right )^{2} + x + 4 \, e^{\left (2 \, x\right )} + 10 \, e^{x} + 7} \] Input:

integrate((25*exp(x)*log(x)^4+(100*exp(x)^2+100*exp(x))*log(x)^3+(140*exp( 
x)^3+300*exp(x)^2+(10*x+170)*exp(x)+15)*log(x)^2+(80*exp(x)^4+280*exp(x)^3 
+(20*x+340)*exp(x)^2+(-10*x+170)*exp(x))*log(x)+16*exp(x)^5+80*exp(x)^4+(8 
*x+156)*exp(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*log(x)^4+ 
(100*exp(x)+100)*log(x)^3+(140*exp(x)^2+300*exp(x)+10*x+170)*log(x)^2+(80* 
exp(x)^3+280*exp(x)^2+(20*x+340)*exp(x)+20*x+140)*log(x)+16*exp(x)^4+80*ex 
p(x)^3+(8*x+156)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x, algorithm="fri 
cas")
 

Output:

(5*e^x*log(x)^2 + (x + 7)*e^x + 10*(e^(2*x) + e^x)*log(x) + 3*x + 4*e^(3*x 
) + 10*e^(2*x))/(10*(e^x + 1)*log(x) + 5*log(x)^2 + x + 4*e^(2*x) + 10*e^x 
 + 7)
 

Sympy [A] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23 \[ \int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx=\frac {3 x}{x + \left (10 \log {\left (x \right )} + 10\right ) e^{x} + 4 e^{2 x} + 5 \log {\left (x \right )}^{2} + 10 \log {\left (x \right )} + 7} + e^{x} \] Input:

integrate((25*exp(x)*ln(x)**4+(100*exp(x)**2+100*exp(x))*ln(x)**3+(140*exp 
(x)**3+300*exp(x)**2+(10*x+170)*exp(x)+15)*ln(x)**2+(80*exp(x)**4+280*exp( 
x)**3+(20*x+340)*exp(x)**2+(-10*x+170)*exp(x))*ln(x)+16*exp(x)**5+80*exp(x 
)**4+(8*x+156)*exp(x)**3+(-4*x+152)*exp(x)**2+(x**2-16*x+49)*exp(x)-9)/(25 
*ln(x)**4+(100*exp(x)+100)*ln(x)**3+(140*exp(x)**2+300*exp(x)+10*x+170)*ln 
(x)**2+(80*exp(x)**3+280*exp(x)**2+(20*x+340)*exp(x)+20*x+140)*ln(x)+16*ex 
p(x)**4+80*exp(x)**3+(8*x+156)*exp(x)**2+(20*x+140)*exp(x)+x**2+14*x+49),x 
)
 

Output:

3*x/(x + (10*log(x) + 10)*exp(x) + 4*exp(2*x) + 5*log(x)**2 + 10*log(x) + 
7) + exp(x)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (27) = 54\).

Time = 0.21 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.20 \[ \int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx=\frac {10 \, {\left (\log \left (x\right ) + 1\right )} e^{\left (2 \, x\right )} + {\left (5 \, \log \left (x\right )^{2} + x + 10 \, \log \left (x\right ) + 7\right )} e^{x} + 3 \, x + 4 \, e^{\left (3 \, x\right )}}{10 \, {\left (\log \left (x\right ) + 1\right )} e^{x} + 5 \, \log \left (x\right )^{2} + x + 4 \, e^{\left (2 \, x\right )} + 10 \, \log \left (x\right ) + 7} \] Input:

integrate((25*exp(x)*log(x)^4+(100*exp(x)^2+100*exp(x))*log(x)^3+(140*exp( 
x)^3+300*exp(x)^2+(10*x+170)*exp(x)+15)*log(x)^2+(80*exp(x)^4+280*exp(x)^3 
+(20*x+340)*exp(x)^2+(-10*x+170)*exp(x))*log(x)+16*exp(x)^5+80*exp(x)^4+(8 
*x+156)*exp(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*log(x)^4+ 
(100*exp(x)+100)*log(x)^3+(140*exp(x)^2+300*exp(x)+10*x+170)*log(x)^2+(80* 
exp(x)^3+280*exp(x)^2+(20*x+340)*exp(x)+20*x+140)*log(x)+16*exp(x)^4+80*ex 
p(x)^3+(8*x+156)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x, algorithm="max 
ima")
 

Output:

(10*(log(x) + 1)*e^(2*x) + (5*log(x)^2 + x + 10*log(x) + 7)*e^x + 3*x + 4* 
e^(3*x))/(10*(log(x) + 1)*e^x + 5*log(x)^2 + x + 4*e^(2*x) + 10*log(x) + 7 
)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 5359 vs. \(2 (27) = 54\).

Time = 1.17 (sec) , antiderivative size = 5359, normalized size of antiderivative = 178.63 \[ \int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx=\text {Too large to display} \] Input:

integrate((25*exp(x)*log(x)^4+(100*exp(x)^2+100*exp(x))*log(x)^3+(140*exp( 
x)^3+300*exp(x)^2+(10*x+170)*exp(x)+15)*log(x)^2+(80*exp(x)^4+280*exp(x)^3 
+(20*x+340)*exp(x)^2+(-10*x+170)*exp(x))*log(x)+16*exp(x)^5+80*exp(x)^4+(8 
*x+156)*exp(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*log(x)^4+ 
(100*exp(x)+100)*log(x)^3+(140*exp(x)^2+300*exp(x)+10*x+170)*log(x)^2+(80* 
exp(x)^3+280*exp(x)^2+(20*x+340)*exp(x)+20*x+140)*log(x)+16*exp(x)^4+80*ex 
p(x)^3+(8*x+156)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x, algorithm="gia 
c")
 

Output:

(2500*x^5*e^(3*x)*log(x)^6 - 1000*x^6*e^(3*x)*log(x)^4 + 3000*x^6*e^(2*x)* 
log(x)^4 + 5000*x^5*e^(4*x)*log(x)^5 + 15000*x^5*e^(3*x)*log(x)^5 + 750*x^ 
5*e^x*log(x)^5 - 2000*x^4*e^(5*x)*log(x)^6 + 4500*x^4*e^(3*x)*log(x)^6 + 5 
000*x^4*e^(2*x)*log(x)^6 + 125*x^4*e^x*log(x)^6 - 700*x^7*e^(3*x)*log(x)^2 
 - 1800*x^7*e^(2*x)*log(x)^2 - 3000*x^6*e^(4*x)*log(x)^3 - 4000*x^6*e^(3*x 
)*log(x)^3 + 12000*x^6*e^(2*x)*log(x)^3 - 450*x^6*e^x*log(x)^3 + 2800*x^5* 
e^(5*x)*log(x)^4 + 22600*x^5*e^(4*x)*log(x)^4 + 33200*x^5*e^(3*x)*log(x)^4 
 + 7300*x^5*e^(2*x)*log(x)^4 + 8200*x^5*e^x*log(x)^4 - 4000*x^4*e^(6*x)*lo 
g(x)^5 - 12000*x^4*e^(5*x)*log(x)^5 + 9000*x^4*e^(4*x)*log(x)^5 + 29000*x^ 
4*e^(3*x)*log(x)^5 + 24250*x^4*e^(2*x)*log(x)^5 - 5000*x^3*e^(4*x)*log(x)^ 
6 + 10000*x^3*e^(2*x)*log(x)^6 + 2500*x^3*e^x*log(x)^6 - 80*x^8*e^(3*x) - 
480*x^8*e^(2*x) - 800*x^7*e^(4*x)*log(x) - 1400*x^7*e^(3*x)*log(x) - 3600* 
x^7*e^(2*x)*log(x) - 120*x^7*e^x*log(x) - 640*x^6*e^(5*x)*log(x)^2 - 7560* 
x^6*e^(4*x)*log(x)^2 - 9760*x^6*e^(3*x)*log(x)^2 + 8920*x^6*e^(2*x)*log(x) 
^2 - 4085*x^6*e^x*log(x)^2 + 2400*x^5*e^(6*x)*log(x)^3 + 11200*x^5*e^(5*x) 
*log(x)^3 + 28000*x^5*e^(4*x)*log(x)^3 + 34600*x^5*e^(3*x)*log(x)^3 + 1765 
0*x^5*e^(2*x)*log(x)^3 + 24700*x^5*e^x*log(x)^3 + 75*x^5*log(x)^4 - 1600*x 
^4*e^(7*x)*log(x)^4 - 20000*x^4*e^(6*x)*log(x)^4 - 24400*x^4*e^(5*x)*log(x 
)^4 + 35000*x^4*e^(4*x)*log(x)^4 + 61100*x^4*e^(3*x)*log(x)^4 + 42050*x^4* 
e^(2*x)*log(x)^4 + 12750*x^4*e^x*log(x)^4 - 6000*x^3*e^(5*x)*log(x)^5 -...
 

Mupad [F(-1)]

Timed out. \[ \int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx=\int \frac {25\,{\mathrm {e}}^x\,{\ln \left (x\right )}^4+\left (100\,{\mathrm {e}}^{2\,x}+100\,{\mathrm {e}}^x\right )\,{\ln \left (x\right )}^3+\left (300\,{\mathrm {e}}^{2\,x}+140\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^x\,\left (10\,x+170\right )+15\right )\,{\ln \left (x\right )}^2+\left (280\,{\mathrm {e}}^{3\,x}+80\,{\mathrm {e}}^{4\,x}-{\mathrm {e}}^x\,\left (10\,x-170\right )+{\mathrm {e}}^{2\,x}\,\left (20\,x+340\right )\right )\,\ln \left (x\right )+80\,{\mathrm {e}}^{4\,x}+16\,{\mathrm {e}}^{5\,x}+{\mathrm {e}}^x\,\left (x^2-16\,x+49\right )-{\mathrm {e}}^{2\,x}\,\left (4\,x-152\right )+{\mathrm {e}}^{3\,x}\,\left (8\,x+156\right )-9}{14\,x+80\,{\mathrm {e}}^{3\,x}+16\,{\mathrm {e}}^{4\,x}+\ln \left (x\right )\,\left (20\,x+280\,{\mathrm {e}}^{2\,x}+80\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^x\,\left (20\,x+340\right )+140\right )+{\ln \left (x\right )}^3\,\left (100\,{\mathrm {e}}^x+100\right )+25\,{\ln \left (x\right )}^4+{\mathrm {e}}^x\,\left (20\,x+140\right )+{\ln \left (x\right )}^2\,\left (10\,x+140\,{\mathrm {e}}^{2\,x}+300\,{\mathrm {e}}^x+170\right )+{\mathrm {e}}^{2\,x}\,\left (8\,x+156\right )+x^2+49} \,d x \] Input:

int((80*exp(4*x) + 16*exp(5*x) + log(x)*(280*exp(3*x) + 80*exp(4*x) - exp( 
x)*(10*x - 170) + exp(2*x)*(20*x + 340)) + exp(x)*(x^2 - 16*x + 49) + 25*e 
xp(x)*log(x)^4 + log(x)^2*(300*exp(2*x) + 140*exp(3*x) + exp(x)*(10*x + 17 
0) + 15) - exp(2*x)*(4*x - 152) + exp(3*x)*(8*x + 156) + log(x)^3*(100*exp 
(2*x) + 100*exp(x)) - 9)/(14*x + 80*exp(3*x) + 16*exp(4*x) + log(x)*(20*x 
+ 280*exp(2*x) + 80*exp(3*x) + exp(x)*(20*x + 340) + 140) + log(x)^3*(100* 
exp(x) + 100) + 25*log(x)^4 + exp(x)*(20*x + 140) + log(x)^2*(10*x + 140*e 
xp(2*x) + 300*exp(x) + 170) + exp(2*x)*(8*x + 156) + x^2 + 49),x)
 

Output:

int((80*exp(4*x) + 16*exp(5*x) + log(x)*(280*exp(3*x) + 80*exp(4*x) - exp( 
x)*(10*x - 170) + exp(2*x)*(20*x + 340)) + exp(x)*(x^2 - 16*x + 49) + 25*e 
xp(x)*log(x)^4 + log(x)^2*(300*exp(2*x) + 140*exp(3*x) + exp(x)*(10*x + 17 
0) + 15) - exp(2*x)*(4*x - 152) + exp(3*x)*(8*x + 156) + log(x)^3*(100*exp 
(2*x) + 100*exp(x)) - 9)/(14*x + 80*exp(3*x) + 16*exp(4*x) + log(x)*(20*x 
+ 280*exp(2*x) + 80*exp(3*x) + exp(x)*(20*x + 340) + 140) + log(x)^3*(100* 
exp(x) + 100) + 25*log(x)^4 + exp(x)*(20*x + 140) + log(x)^2*(10*x + 140*e 
xp(2*x) + 300*exp(x) + 170) + exp(2*x)*(8*x + 156) + x^2 + 49), x)
 

Reduce [B] (verification not implemented)

Time = 0.19 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.07 \[ \int \frac {-9+80 e^{4 x}+16 e^{5 x}+e^{2 x} (152-4 x)+e^{3 x} (156+8 x)+e^x \left (49-16 x+x^2\right )+\left (280 e^{3 x}+80 e^{4 x}+e^x (170-10 x)+e^{2 x} (340+20 x)\right ) \log (x)+\left (15+300 e^{2 x}+140 e^{3 x}+e^x (170+10 x)\right ) \log ^2(x)+\left (100 e^x+100 e^{2 x}\right ) \log ^3(x)+25 e^x \log ^4(x)}{49+80 e^{3 x}+16 e^{4 x}+14 x+x^2+e^{2 x} (156+8 x)+e^x (140+20 x)+\left (140+280 e^{2 x}+80 e^{3 x}+20 x+e^x (340+20 x)\right ) \log (x)+\left (170+300 e^x+140 e^{2 x}+10 x\right ) \log ^2(x)+\left (100+100 e^x\right ) \log ^3(x)+25 \log ^4(x)} \, dx=\frac {4 e^{3 x}+10 e^{2 x} \mathrm {log}\left (x \right )+6 e^{2 x}+5 e^{x} \mathrm {log}\left (x \right )^{2}+e^{x} x -3 e^{x}-5 \mathrm {log}\left (x \right )^{2}-10 \,\mathrm {log}\left (x \right )+2 x -7}{4 e^{2 x}+10 e^{x} \mathrm {log}\left (x \right )+10 e^{x}+5 \mathrm {log}\left (x \right )^{2}+10 \,\mathrm {log}\left (x \right )+x +7} \] Input:

int((25*exp(x)*log(x)^4+(100*exp(x)^2+100*exp(x))*log(x)^3+(140*exp(x)^3+3 
00*exp(x)^2+(10*x+170)*exp(x)+15)*log(x)^2+(80*exp(x)^4+280*exp(x)^3+(20*x 
+340)*exp(x)^2+(-10*x+170)*exp(x))*log(x)+16*exp(x)^5+80*exp(x)^4+(8*x+156 
)*exp(x)^3+(-4*x+152)*exp(x)^2+(x^2-16*x+49)*exp(x)-9)/(25*log(x)^4+(100*e 
xp(x)+100)*log(x)^3+(140*exp(x)^2+300*exp(x)+10*x+170)*log(x)^2+(80*exp(x) 
^3+280*exp(x)^2+(20*x+340)*exp(x)+20*x+140)*log(x)+16*exp(x)^4+80*exp(x)^3 
+(8*x+156)*exp(x)^2+(20*x+140)*exp(x)+x^2+14*x+49),x)
 

Output:

(4*e**(3*x) + 10*e**(2*x)*log(x) + 6*e**(2*x) + 5*e**x*log(x)**2 + e**x*x 
- 3*e**x - 5*log(x)**2 - 10*log(x) + 2*x - 7)/(4*e**(2*x) + 10*e**x*log(x) 
 + 10*e**x + 5*log(x)**2 + 10*log(x) + x + 7)