\(\int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 (25 x^4-10 x^5+x^6)}{25-10 e^x x+e^{2 x} x^2}} (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3)+e^x (3375 x+1575 x^3+150 x^5)+e^{2 x} (-675 x^2-315 x^4-30 x^6)+e^{3 x} (45 x^3+21 x^5+2 x^7)+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} (-285 x^2-60 x^4)+e^{3 x} (19 x^3+4 x^5)+e^x (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8))}{-3125-1250 x^2-125 x^4+e^{\frac {2 (25 x^4-10 x^5+x^6)}{25-10 e^x x+e^{2 x} x^2}} (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3)+e^x (1875 x+750 x^3+75 x^5)+e^{2 x} (-375 x^2-150 x^4-15 x^6)+e^{3 x} (25 x^3+10 x^5+x^7)+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} (-1250-250 x^2+e^x (750 x+150 x^3)+e^{2 x} (-150 x^2-30 x^4)+e^{3 x} (10 x^3+2 x^5))} \, dx\) [400]

Optimal result

Integrand size = 497, antiderivative size = 37 \[ \int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3\right )+e^x \left (3375 x+1575 x^3+150 x^5\right )+e^{2 x} \left (-675 x^2-315 x^4-30 x^6\right )+e^{3 x} \left (45 x^3+21 x^5+2 x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} \left (-285 x^2-60 x^4\right )+e^{3 x} \left (19 x^3+4 x^5\right )+e^x \left (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8\right )\right )}{-3125-1250 x^2-125 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3\right )+e^x \left (1875 x+750 x^3+75 x^5\right )+e^{2 x} \left (-375 x^2-150 x^4-15 x^6\right )+e^{3 x} \left (25 x^3+10 x^5+x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-1250-250 x^2+e^x \left (750 x+150 x^3\right )+e^{2 x} \left (-150 x^2-30 x^4\right )+e^{3 x} \left (10 x^3+2 x^5\right )\right )} \, dx=2 x-\frac {x}{5+e^{\frac {(5-x)^2 x^4}{\left (5-e^x x\right )^2}}+x^2} \] Output:

2*x-x/(exp(x^4*(5-x)^2/(5-exp(x)*x)^2)+x^2+5)
 

Mathematica [A] (verified)

Time = 0.66 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.81 \[ \int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3\right )+e^x \left (3375 x+1575 x^3+150 x^5\right )+e^{2 x} \left (-675 x^2-315 x^4-30 x^6\right )+e^{3 x} \left (45 x^3+21 x^5+2 x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} \left (-285 x^2-60 x^4\right )+e^{3 x} \left (19 x^3+4 x^5\right )+e^x \left (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8\right )\right )}{-3125-1250 x^2-125 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3\right )+e^x \left (1875 x+750 x^3+75 x^5\right )+e^{2 x} \left (-375 x^2-150 x^4-15 x^6\right )+e^{3 x} \left (25 x^3+10 x^5+x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-1250-250 x^2+e^x \left (750 x+150 x^3\right )+e^{2 x} \left (-150 x^2-30 x^4\right )+e^{3 x} \left (10 x^3+2 x^5\right )\right )} \, dx=x \left (2-\frac {e^{\frac {10 x^5}{\left (-5+e^x x\right )^2}}}{e^{\frac {x^4 \left (25+x^2\right )}{\left (-5+e^x x\right )^2}}+e^{\frac {10 x^5}{\left (-5+e^x x\right )^2}} \left (5+x^2\right )}\right ) \] Input:

Integrate[(-5625 - 2625*x^2 - 250*x^4 + E^((2*(25*x^4 - 10*x^5 + x^6))/(25 
 - 10*E^x*x + E^(2*x)*x^2))*(-250 + 150*E^x*x - 30*E^(2*x)*x^2 + 2*E^(3*x) 
*x^3) + E^x*(3375*x + 1575*x^3 + 150*x^5) + E^(2*x)*(-675*x^2 - 315*x^4 - 
30*x^6) + E^(3*x)*(45*x^3 + 21*x^5 + 2*x^7) + E^((25*x^4 - 10*x^5 + x^6)/( 
25 - 10*E^x*x + E^(2*x)*x^2))*(-2375 - 500*x^2 - 500*x^4 + 250*x^5 - 30*x^ 
6 + E^(2*x)*(-285*x^2 - 60*x^4) + E^(3*x)*(19*x^3 + 4*x^5) + E^x*(1425*x + 
 300*x^3 + 50*x^5 - 80*x^6 + 24*x^7 - 2*x^8)))/(-3125 - 1250*x^2 - 125*x^4 
 + E^((2*(25*x^4 - 10*x^5 + x^6))/(25 - 10*E^x*x + E^(2*x)*x^2))*(-125 + 7 
5*E^x*x - 15*E^(2*x)*x^2 + E^(3*x)*x^3) + E^x*(1875*x + 750*x^3 + 75*x^5) 
+ E^(2*x)*(-375*x^2 - 150*x^4 - 15*x^6) + E^(3*x)*(25*x^3 + 10*x^5 + x^7) 
+ E^((25*x^4 - 10*x^5 + x^6)/(25 - 10*E^x*x + E^(2*x)*x^2))*(-1250 - 250*x 
^2 + E^x*(750*x + 150*x^3) + E^(2*x)*(-150*x^2 - 30*x^4) + E^(3*x)*(10*x^3 
 + 2*x^5))),x]
 

Output:

x*(2 - E^((10*x^5)/(-5 + E^x*x)^2)/(E^((x^4*(25 + x^2))/(-5 + E^x*x)^2) + 
E^((10*x^5)/(-5 + E^x*x)^2)*(5 + 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.

\(\displaystyle \int \frac {\left (2 e^{3 x} x^3-30 e^{2 x} x^2+150 e^x x-250\right ) \exp \left (\frac {2 \left (x^6-10 x^5+25 x^4\right )}{e^{2 x} x^2-10 e^x x+25}\right )-250 x^4-2625 x^2+e^x \left (150 x^5+1575 x^3+3375 x\right )+e^{3 x} \left (2 x^7+21 x^5+45 x^3\right )+e^{2 x} \left (-30 x^6-315 x^4-675 x^2\right )+e^{\frac {x^6-10 x^5+25 x^4}{e^{2 x} x^2-10 e^x x+25}} \left (-30 x^6+250 x^5-500 x^4-500 x^2+e^{3 x} \left (4 x^5+19 x^3\right )+e^{2 x} \left (-60 x^4-285 x^2\right )+e^x \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )-2375\right )-5625}{\left (e^{3 x} x^3-15 e^{2 x} x^2+75 e^x x-125\right ) \exp \left (\frac {2 \left (x^6-10 x^5+25 x^4\right )}{e^{2 x} x^2-10 e^x x+25}\right )-125 x^4-1250 x^2+e^x \left (75 x^5+750 x^3+1875 x\right )+e^{3 x} \left (x^7+10 x^5+25 x^3\right )+e^{2 x} \left (-15 x^6-150 x^4-375 x^2\right )+e^{\frac {x^6-10 x^5+25 x^4}{e^{2 x} x^2-10 e^x x+25}} \left (e^x \left (150 x^3+750 x\right )-250 x^2+e^{3 x} \left (2 x^5+10 x^3\right )+e^{2 x} \left (-30 x^4-150 x^2\right )-1250\right )-3125} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (250 x^4-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (e^x x-5\right )^3+2625 x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (-15 e^{2 x} \left (4 x^2+19\right ) x^2+e^{3 x} \left (4 x^2+19\right ) x^3-5 \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )+e^x \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )+5625\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} \left (-150 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x+250 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}-2 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3+30 e^{\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2+15 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} \left (4 x^2+19\right ) x^2+15 e^{2 x} \left (2 x^4+21 x^2+45\right ) x^2-75 e^x \left (2 x^4+21 x^2+45\right ) x+125 \left (2 x^4+21 x^2+45\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} \left (4 x^2+19\right ) x^3-e^{3 x} \left (2 x^4+21 x^2+45\right ) x^3+5 e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} \left (6 x^6-50 x^5+100 x^4+100 x^2+475\right )-e^{\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} \left (-2 x^8+24 x^7-80 x^6+50 x^5+300 x^3+1425 x\right )\right )}{\left (5-e^x x\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} \left (x^2+5\right )+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^8}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {24 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^7}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {80 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^6}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {21 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {50 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {4 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^5}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {315 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {60 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^4}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1575 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {45 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {300 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {19 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {2 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+3 x} x^3}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {675 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {500 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {285 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {30 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+2 x} x^2}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {3375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {1425 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}+\frac {150 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}+x} x}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {5625 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {2375 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {(x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}-\frac {250 e^{\frac {20 x^5}{\left (e^x x-5\right )^2}+\frac {2 (x-5)^2 x^4}{\left (e^x x-5\right )^2}}}{\left (e^x x-5\right )^3 \left (e^{\frac {10 x^5}{\left (e^x x-5\right )^2}} x^2+5 e^{\frac {10 x^5}{\left (e^x x-5\right )^2}}+e^{\frac {x^4 \left (x^2+25\right )}{\left (e^x x-5\right )^2}}\right )^2}\right )dx\)

Input:

Int[(-5625 - 2625*x^2 - 250*x^4 + E^((2*(25*x^4 - 10*x^5 + x^6))/(25 - 10* 
E^x*x + E^(2*x)*x^2))*(-250 + 150*E^x*x - 30*E^(2*x)*x^2 + 2*E^(3*x)*x^3) 
+ E^x*(3375*x + 1575*x^3 + 150*x^5) + E^(2*x)*(-675*x^2 - 315*x^4 - 30*x^6 
) + E^(3*x)*(45*x^3 + 21*x^5 + 2*x^7) + E^((25*x^4 - 10*x^5 + x^6)/(25 - 1 
0*E^x*x + E^(2*x)*x^2))*(-2375 - 500*x^2 - 500*x^4 + 250*x^5 - 30*x^6 + E^ 
(2*x)*(-285*x^2 - 60*x^4) + E^(3*x)*(19*x^3 + 4*x^5) + E^x*(1425*x + 300*x 
^3 + 50*x^5 - 80*x^6 + 24*x^7 - 2*x^8)))/(-3125 - 1250*x^2 - 125*x^4 + E^( 
(2*(25*x^4 - 10*x^5 + x^6))/(25 - 10*E^x*x + E^(2*x)*x^2))*(-125 + 75*E^x* 
x - 15*E^(2*x)*x^2 + E^(3*x)*x^3) + E^x*(1875*x + 750*x^3 + 75*x^5) + E^(2 
*x)*(-375*x^2 - 150*x^4 - 15*x^6) + E^(3*x)*(25*x^3 + 10*x^5 + x^7) + E^(( 
25*x^4 - 10*x^5 + x^6)/(25 - 10*E^x*x + E^(2*x)*x^2))*(-1250 - 250*x^2 + E 
^x*(750*x + 150*x^3) + E^(2*x)*(-150*x^2 - 30*x^4) + E^(3*x)*(10*x^3 + 2*x 
^5))),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 41.19 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.19

method	result	size
risch	\(2 x -\frac {x}{x^{2}+{\mathrm e}^{-\frac {x^{4} \left (-5+x \right )^{2}}{-{\mathrm e}^{2 x} x^{2}+10 \,{\mathrm e}^{x} x -25}}+5}\)	\(44\)
parallelrisch	\(\frac {37500 x^{3}+37500 \,{\mathrm e}^{\frac {x^{4} \left (x^{2}-10 x +25\right )}{{\mathrm e}^{2 x} x^{2}-10 \,{\mathrm e}^{x} x +25}} x +168750 x}{18750 x^{2}+18750 \,{\mathrm e}^{\frac {x^{4} \left (x^{2}-10 x +25\right )}{{\mathrm e}^{2 x} x^{2}-10 \,{\mathrm e}^{x} x +25}}+93750}\)	\(82\)

Input:

int(((2*x^3*exp(x)^3-30*exp(x)^2*x^2+150*exp(x)*x-250)*exp((x^6-10*x^5+25* 
x^4)/(exp(x)^2*x^2-10*exp(x)*x+25))^2+((4*x^5+19*x^3)*exp(x)^3+(-60*x^4-28 
5*x^2)*exp(x)^2+(-2*x^8+24*x^7-80*x^6+50*x^5+300*x^3+1425*x)*exp(x)-30*x^6 
+250*x^5-500*x^4-500*x^2-2375)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2-10*ex 
p(x)*x+25))+(2*x^7+21*x^5+45*x^3)*exp(x)^3+(-30*x^6-315*x^4-675*x^2)*exp(x 
)^2+(150*x^5+1575*x^3+3375*x)*exp(x)-250*x^4-2625*x^2-5625)/((x^3*exp(x)^3 
-15*exp(x)^2*x^2+75*exp(x)*x-125)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2-10 
*exp(x)*x+25))^2+((2*x^5+10*x^3)*exp(x)^3+(-30*x^4-150*x^2)*exp(x)^2+(150* 
x^3+750*x)*exp(x)-250*x^2-1250)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2-10*e 
xp(x)*x+25))+(x^7+10*x^5+25*x^3)*exp(x)^3+(-15*x^6-150*x^4-375*x^2)*exp(x) 
^2+(75*x^5+750*x^3+1875*x)*exp(x)-125*x^4-1250*x^2-3125),x,method=_RETURNV 
ERBOSE)
 

Output:

2*x-x/(x^2+exp(-x^4*(-5+x)^2/(-exp(2*x)*x^2+10*exp(x)*x-25))+5)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 86 vs. \(2 (32) = 64\).

Time = 0.11 (sec) , antiderivative size = 86, normalized size of antiderivative = 2.32 \[ \int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3\right )+e^x \left (3375 x+1575 x^3+150 x^5\right )+e^{2 x} \left (-675 x^2-315 x^4-30 x^6\right )+e^{3 x} \left (45 x^3+21 x^5+2 x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} \left (-285 x^2-60 x^4\right )+e^{3 x} \left (19 x^3+4 x^5\right )+e^x \left (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8\right )\right )}{-3125-1250 x^2-125 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3\right )+e^x \left (1875 x+750 x^3+75 x^5\right )+e^{2 x} \left (-375 x^2-150 x^4-15 x^6\right )+e^{3 x} \left (25 x^3+10 x^5+x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-1250-250 x^2+e^x \left (750 x+150 x^3\right )+e^{2 x} \left (-150 x^2-30 x^4\right )+e^{3 x} \left (10 x^3+2 x^5\right )\right )} \, dx=\frac {2 \, x^{3} + 2 \, x e^{\left (\frac {x^{6} - 10 \, x^{5} + 25 \, x^{4}}{x^{2} e^{\left (2 \, x\right )} - 10 \, x e^{x} + 25}\right )} + 9 \, x}{x^{2} + e^{\left (\frac {x^{6} - 10 \, x^{5} + 25 \, x^{4}}{x^{2} e^{\left (2 \, x\right )} - 10 \, x e^{x} + 25}\right )} + 5} \] Input:

integrate(((2*x^3*exp(x)^3-30*exp(x)^2*x^2+150*exp(x)*x-250)*exp((x^6-10*x 
^5+25*x^4)/(exp(x)^2*x^2-10*exp(x)*x+25))^2+((4*x^5+19*x^3)*exp(x)^3+(-60* 
x^4-285*x^2)*exp(x)^2+(-2*x^8+24*x^7-80*x^6+50*x^5+300*x^3+1425*x)*exp(x)- 
30*x^6+250*x^5-500*x^4-500*x^2-2375)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2 
-10*exp(x)*x+25))+(2*x^7+21*x^5+45*x^3)*exp(x)^3+(-30*x^6-315*x^4-675*x^2) 
*exp(x)^2+(150*x^5+1575*x^3+3375*x)*exp(x)-250*x^4-2625*x^2-5625)/((x^3*ex 
p(x)^3-15*exp(x)^2*x^2+75*exp(x)*x-125)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2* 
x^2-10*exp(x)*x+25))^2+((2*x^5+10*x^3)*exp(x)^3+(-30*x^4-150*x^2)*exp(x)^2 
+(150*x^3+750*x)*exp(x)-250*x^2-1250)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^ 
2-10*exp(x)*x+25))+(x^7+10*x^5+25*x^3)*exp(x)^3+(-15*x^6-150*x^4-375*x^2)* 
exp(x)^2+(75*x^5+750*x^3+1875*x)*exp(x)-125*x^4-1250*x^2-3125),x, algorith 
m="fricas")
 

Output:

(2*x^3 + 2*x*e^((x^6 - 10*x^5 + 25*x^4)/(x^2*e^(2*x) - 10*x*e^x + 25)) + 9 
*x)/(x^2 + e^((x^6 - 10*x^5 + 25*x^4)/(x^2*e^(2*x) - 10*x*e^x + 25)) + 5)
 

Sympy [A] (verification not implemented)

Time = 0.80 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.11 \[ \int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3\right )+e^x \left (3375 x+1575 x^3+150 x^5\right )+e^{2 x} \left (-675 x^2-315 x^4-30 x^6\right )+e^{3 x} \left (45 x^3+21 x^5+2 x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} \left (-285 x^2-60 x^4\right )+e^{3 x} \left (19 x^3+4 x^5\right )+e^x \left (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8\right )\right )}{-3125-1250 x^2-125 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3\right )+e^x \left (1875 x+750 x^3+75 x^5\right )+e^{2 x} \left (-375 x^2-150 x^4-15 x^6\right )+e^{3 x} \left (25 x^3+10 x^5+x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-1250-250 x^2+e^x \left (750 x+150 x^3\right )+e^{2 x} \left (-150 x^2-30 x^4\right )+e^{3 x} \left (10 x^3+2 x^5\right )\right )} \, dx=2 x - \frac {x}{x^{2} + e^{\frac {x^{6} - 10 x^{5} + 25 x^{4}}{x^{2} e^{2 x} - 10 x e^{x} + 25}} + 5} \] Input:

integrate(((2*x**3*exp(x)**3-30*exp(x)**2*x**2+150*exp(x)*x-250)*exp((x**6 
-10*x**5+25*x**4)/(exp(x)**2*x**2-10*exp(x)*x+25))**2+((4*x**5+19*x**3)*ex 
p(x)**3+(-60*x**4-285*x**2)*exp(x)**2+(-2*x**8+24*x**7-80*x**6+50*x**5+300 
*x**3+1425*x)*exp(x)-30*x**6+250*x**5-500*x**4-500*x**2-2375)*exp((x**6-10 
*x**5+25*x**4)/(exp(x)**2*x**2-10*exp(x)*x+25))+(2*x**7+21*x**5+45*x**3)*e 
xp(x)**3+(-30*x**6-315*x**4-675*x**2)*exp(x)**2+(150*x**5+1575*x**3+3375*x 
)*exp(x)-250*x**4-2625*x**2-5625)/((x**3*exp(x)**3-15*exp(x)**2*x**2+75*ex 
p(x)*x-125)*exp((x**6-10*x**5+25*x**4)/(exp(x)**2*x**2-10*exp(x)*x+25))**2 
+((2*x**5+10*x**3)*exp(x)**3+(-30*x**4-150*x**2)*exp(x)**2+(150*x**3+750*x 
)*exp(x)-250*x**2-1250)*exp((x**6-10*x**5+25*x**4)/(exp(x)**2*x**2-10*exp( 
x)*x+25))+(x**7+10*x**5+25*x**3)*exp(x)**3+(-15*x**6-150*x**4-375*x**2)*ex 
p(x)**2+(75*x**5+750*x**3+1875*x)*exp(x)-125*x**4-1250*x**2-3125),x)
 

Output:

2*x - x/(x**2 + exp((x**6 - 10*x**5 + 25*x**4)/(x**2*exp(2*x) - 10*x*exp(x 
) + 25)) + 5)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 474 vs. \(2 (32) = 64\).

Time = 2.27 (sec) , antiderivative size = 474, normalized size of antiderivative = 12.81 \[ \int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3\right )+e^x \left (3375 x+1575 x^3+150 x^5\right )+e^{2 x} \left (-675 x^2-315 x^4-30 x^6\right )+e^{3 x} \left (45 x^3+21 x^5+2 x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} \left (-285 x^2-60 x^4\right )+e^{3 x} \left (19 x^3+4 x^5\right )+e^x \left (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8\right )\right )}{-3125-1250 x^2-125 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3\right )+e^x \left (1875 x+750 x^3+75 x^5\right )+e^{2 x} \left (-375 x^2-150 x^4-15 x^6\right )+e^{3 x} \left (25 x^3+10 x^5+x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-1250-250 x^2+e^x \left (750 x+150 x^3\right )+e^{2 x} \left (-150 x^2-30 x^4\right )+e^{3 x} \left (10 x^3+2 x^5\right )\right )} \, dx =\text {Too large to display} \] Input:

integrate(((2*x^3*exp(x)^3-30*exp(x)^2*x^2+150*exp(x)*x-250)*exp((x^6-10*x 
^5+25*x^4)/(exp(x)^2*x^2-10*exp(x)*x+25))^2+((4*x^5+19*x^3)*exp(x)^3+(-60* 
x^4-285*x^2)*exp(x)^2+(-2*x^8+24*x^7-80*x^6+50*x^5+300*x^3+1425*x)*exp(x)- 
30*x^6+250*x^5-500*x^4-500*x^2-2375)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2 
-10*exp(x)*x+25))+(2*x^7+21*x^5+45*x^3)*exp(x)^3+(-30*x^6-315*x^4-675*x^2) 
*exp(x)^2+(150*x^5+1575*x^3+3375*x)*exp(x)-250*x^4-2625*x^2-5625)/((x^3*ex 
p(x)^3-15*exp(x)^2*x^2+75*exp(x)*x-125)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2* 
x^2-10*exp(x)*x+25))^2+((2*x^5+10*x^3)*exp(x)^3+(-30*x^4-150*x^2)*exp(x)^2 
+(150*x^3+750*x)*exp(x)-250*x^2-1250)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^ 
2-10*exp(x)*x+25))+(x^7+10*x^5+25*x^3)*exp(x)^3+(-15*x^6-150*x^4-375*x^2)* 
exp(x)^2+(75*x^5+750*x^3+1875*x)*exp(x)-125*x^4-1250*x^2-3125),x, algorith 
m="maxima")
 

Output:

(2*x*e^(x^4*e^(-2*x) + 10*x^3*e^(-3*x) + 25*x^2*e^(-2*x) + 75*x^2*e^(-4*x) 
 + 250*x*e^(-3*x) + 500*x*e^(-5*x) + 15625/(x^2*e^(8*x) - 10*x*e^(7*x) + 2 
5*e^(6*x)) + 15625/(x^2*e^(6*x) - 10*x*e^(5*x) + 25*e^(4*x)) + 18750/(x*e^ 
(7*x) - 5*e^(6*x)) + 12500/(x*e^(5*x) - 5*e^(4*x)) + 1875*e^(-4*x) + 3125* 
e^(-6*x)) + (2*x^3 + 9*x)*e^(10*x^3*e^(-2*x) + 100*x^2*e^(-3*x) + 750*x*e^ 
(-4*x) + 31250/(x^2*e^(7*x) - 10*x*e^(6*x) + 25*e^(5*x)) + 31250/(x*e^(6*x 
) - 5*e^(5*x)) + 5000*e^(-5*x)))/((x^2 + 5)*e^(10*x^3*e^(-2*x) + 100*x^2*e 
^(-3*x) + 750*x*e^(-4*x) + 31250/(x^2*e^(7*x) - 10*x*e^(6*x) + 25*e^(5*x)) 
 + 31250/(x*e^(6*x) - 5*e^(5*x)) + 5000*e^(-5*x)) + e^(x^4*e^(-2*x) + 10*x 
^3*e^(-3*x) + 25*x^2*e^(-2*x) + 75*x^2*e^(-4*x) + 250*x*e^(-3*x) + 500*x*e 
^(-5*x) + 15625/(x^2*e^(8*x) - 10*x*e^(7*x) + 25*e^(6*x)) + 15625/(x^2*e^( 
6*x) - 10*x*e^(5*x) + 25*e^(4*x)) + 18750/(x*e^(7*x) - 5*e^(6*x)) + 12500/ 
(x*e^(5*x) - 5*e^(4*x)) + 1875*e^(-4*x) + 3125*e^(-6*x)))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 86 vs. \(2 (32) = 64\).

Time = 4.86 (sec) , antiderivative size = 86, normalized size of antiderivative = 2.32 \[ \int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3\right )+e^x \left (3375 x+1575 x^3+150 x^5\right )+e^{2 x} \left (-675 x^2-315 x^4-30 x^6\right )+e^{3 x} \left (45 x^3+21 x^5+2 x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} \left (-285 x^2-60 x^4\right )+e^{3 x} \left (19 x^3+4 x^5\right )+e^x \left (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8\right )\right )}{-3125-1250 x^2-125 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3\right )+e^x \left (1875 x+750 x^3+75 x^5\right )+e^{2 x} \left (-375 x^2-150 x^4-15 x^6\right )+e^{3 x} \left (25 x^3+10 x^5+x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-1250-250 x^2+e^x \left (750 x+150 x^3\right )+e^{2 x} \left (-150 x^2-30 x^4\right )+e^{3 x} \left (10 x^3+2 x^5\right )\right )} \, dx=\frac {2 \, x^{3} + 2 \, x e^{\left (\frac {x^{6} - 10 \, x^{5} + 25 \, x^{4}}{x^{2} e^{\left (2 \, x\right )} - 10 \, x e^{x} + 25}\right )} + 9 \, x}{x^{2} + e^{\left (\frac {x^{6} - 10 \, x^{5} + 25 \, x^{4}}{x^{2} e^{\left (2 \, x\right )} - 10 \, x e^{x} + 25}\right )} + 5} \] Input:

integrate(((2*x^3*exp(x)^3-30*exp(x)^2*x^2+150*exp(x)*x-250)*exp((x^6-10*x 
^5+25*x^4)/(exp(x)^2*x^2-10*exp(x)*x+25))^2+((4*x^5+19*x^3)*exp(x)^3+(-60* 
x^4-285*x^2)*exp(x)^2+(-2*x^8+24*x^7-80*x^6+50*x^5+300*x^3+1425*x)*exp(x)- 
30*x^6+250*x^5-500*x^4-500*x^2-2375)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2 
-10*exp(x)*x+25))+(2*x^7+21*x^5+45*x^3)*exp(x)^3+(-30*x^6-315*x^4-675*x^2) 
*exp(x)^2+(150*x^5+1575*x^3+3375*x)*exp(x)-250*x^4-2625*x^2-5625)/((x^3*ex 
p(x)^3-15*exp(x)^2*x^2+75*exp(x)*x-125)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2* 
x^2-10*exp(x)*x+25))^2+((2*x^5+10*x^3)*exp(x)^3+(-30*x^4-150*x^2)*exp(x)^2 
+(150*x^3+750*x)*exp(x)-250*x^2-1250)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^ 
2-10*exp(x)*x+25))+(x^7+10*x^5+25*x^3)*exp(x)^3+(-15*x^6-150*x^4-375*x^2)* 
exp(x)^2+(75*x^5+750*x^3+1875*x)*exp(x)-125*x^4-1250*x^2-3125),x, algorith 
m="giac")
 

Output:

(2*x^3 + 2*x*e^((x^6 - 10*x^5 + 25*x^4)/(x^2*e^(2*x) - 10*x*e^x + 25)) + 9 
*x)/(x^2 + e^((x^6 - 10*x^5 + 25*x^4)/(x^2*e^(2*x) - 10*x*e^x + 25)) + 5)
 

Mupad [B] (verification not implemented)

Time = 5.16 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.24 \[ \int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3\right )+e^x \left (3375 x+1575 x^3+150 x^5\right )+e^{2 x} \left (-675 x^2-315 x^4-30 x^6\right )+e^{3 x} \left (45 x^3+21 x^5+2 x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} \left (-285 x^2-60 x^4\right )+e^{3 x} \left (19 x^3+4 x^5\right )+e^x \left (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8\right )\right )}{-3125-1250 x^2-125 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3\right )+e^x \left (1875 x+750 x^3+75 x^5\right )+e^{2 x} \left (-375 x^2-150 x^4-15 x^6\right )+e^{3 x} \left (25 x^3+10 x^5+x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-1250-250 x^2+e^x \left (750 x+150 x^3\right )+e^{2 x} \left (-150 x^2-30 x^4\right )+e^{3 x} \left (10 x^3+2 x^5\right )\right )} \, dx=2\,x-\frac {x}{x^2+{\mathrm {e}}^{\frac {x^6}{x^2\,{\mathrm {e}}^{2\,x}-10\,x\,{\mathrm {e}}^x+25}}\,{\mathrm {e}}^{-\frac {10\,x^5}{x^2\,{\mathrm {e}}^{2\,x}-10\,x\,{\mathrm {e}}^x+25}}\,{\mathrm {e}}^{\frac {25\,x^4}{x^2\,{\mathrm {e}}^{2\,x}-10\,x\,{\mathrm {e}}^x+25}}+5} \] Input:

int((exp((25*x^4 - 10*x^5 + x^6)/(x^2*exp(2*x) - 10*x*exp(x) + 25))*(exp(2 
*x)*(285*x^2 + 60*x^4) - exp(3*x)*(19*x^3 + 4*x^5) - exp(x)*(1425*x + 300* 
x^3 + 50*x^5 - 80*x^6 + 24*x^7 - 2*x^8) + 500*x^2 + 500*x^4 - 250*x^5 + 30 
*x^6 + 2375) - exp(3*x)*(45*x^3 + 21*x^5 + 2*x^7) + exp(2*x)*(675*x^2 + 31 
5*x^4 + 30*x^6) + exp((2*(25*x^4 - 10*x^5 + x^6))/(x^2*exp(2*x) - 10*x*exp 
(x) + 25))*(30*x^2*exp(2*x) - 2*x^3*exp(3*x) - 150*x*exp(x) + 250) + 2625* 
x^2 + 250*x^4 - exp(x)*(3375*x + 1575*x^3 + 150*x^5) + 5625)/(exp(2*x)*(37 
5*x^2 + 150*x^4 + 15*x^6) - exp(3*x)*(25*x^3 + 10*x^5 + x^7) + exp((2*(25* 
x^4 - 10*x^5 + x^6))/(x^2*exp(2*x) - 10*x*exp(x) + 25))*(15*x^2*exp(2*x) - 
 x^3*exp(3*x) - 75*x*exp(x) + 125) + exp((25*x^4 - 10*x^5 + x^6)/(x^2*exp( 
2*x) - 10*x*exp(x) + 25))*(exp(2*x)*(150*x^2 + 30*x^4) - exp(3*x)*(10*x^3 
+ 2*x^5) - exp(x)*(750*x + 150*x^3) + 250*x^2 + 1250) + 1250*x^2 + 125*x^4 
 - exp(x)*(1875*x + 750*x^3 + 75*x^5) + 3125),x)
 

Output:

2*x - x/(x^2 + exp(x^6/(x^2*exp(2*x) - 10*x*exp(x) + 25))*exp(-(10*x^5)/(x 
^2*exp(2*x) - 10*x*exp(x) + 25))*exp((25*x^4)/(x^2*exp(2*x) - 10*x*exp(x) 
+ 25)) + 5)
 

Reduce [B] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 187, normalized size of antiderivative = 5.05 \[ \int \frac {-5625-2625 x^2-250 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-250+150 e^x x-30 e^{2 x} x^2+2 e^{3 x} x^3\right )+e^x \left (3375 x+1575 x^3+150 x^5\right )+e^{2 x} \left (-675 x^2-315 x^4-30 x^6\right )+e^{3 x} \left (45 x^3+21 x^5+2 x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-2375-500 x^2-500 x^4+250 x^5-30 x^6+e^{2 x} \left (-285 x^2-60 x^4\right )+e^{3 x} \left (19 x^3+4 x^5\right )+e^x \left (1425 x+300 x^3+50 x^5-80 x^6+24 x^7-2 x^8\right )\right )}{-3125-1250 x^2-125 x^4+e^{\frac {2 \left (25 x^4-10 x^5+x^6\right )}{25-10 e^x x+e^{2 x} x^2}} \left (-125+75 e^x x-15 e^{2 x} x^2+e^{3 x} x^3\right )+e^x \left (1875 x+750 x^3+75 x^5\right )+e^{2 x} \left (-375 x^2-150 x^4-15 x^6\right )+e^{3 x} \left (25 x^3+10 x^5+x^7\right )+e^{\frac {25 x^4-10 x^5+x^6}{25-10 e^x x+e^{2 x} x^2}} \left (-1250-250 x^2+e^x \left (750 x+150 x^3\right )+e^{2 x} \left (-150 x^2-30 x^4\right )+e^{3 x} \left (10 x^3+2 x^5\right )\right )} \, dx=\frac {x \left (2 e^{\frac {x^{6}+25 x^{4}}{e^{2 x} x^{2}-10 e^{x} x +25}}+2 e^{\frac {10 x^{5}}{e^{2 x} x^{2}-10 e^{x} x +25}} x^{2}+9 e^{\frac {10 x^{5}}{e^{2 x} x^{2}-10 e^{x} x +25}}\right )}{e^{\frac {x^{6}+25 x^{4}}{e^{2 x} x^{2}-10 e^{x} x +25}}+e^{\frac {10 x^{5}}{e^{2 x} x^{2}-10 e^{x} x +25}} x^{2}+5 e^{\frac {10 x^{5}}{e^{2 x} x^{2}-10 e^{x} x +25}}} \] Input:

int(((2*x^3*exp(x)^3-30*exp(x)^2*x^2+150*exp(x)*x-250)*exp((x^6-10*x^5+25* 
x^4)/(exp(x)^2*x^2-10*exp(x)*x+25))^2+((4*x^5+19*x^3)*exp(x)^3+(-60*x^4-28 
5*x^2)*exp(x)^2+(-2*x^8+24*x^7-80*x^6+50*x^5+300*x^3+1425*x)*exp(x)-30*x^6 
+250*x^5-500*x^4-500*x^2-2375)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2-10*ex 
p(x)*x+25))+(2*x^7+21*x^5+45*x^3)*exp(x)^3+(-30*x^6-315*x^4-675*x^2)*exp(x 
)^2+(150*x^5+1575*x^3+3375*x)*exp(x)-250*x^4-2625*x^2-5625)/((x^3*exp(x)^3 
-15*exp(x)^2*x^2+75*exp(x)*x-125)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2-10 
*exp(x)*x+25))^2+((2*x^5+10*x^3)*exp(x)^3+(-30*x^4-150*x^2)*exp(x)^2+(150* 
x^3+750*x)*exp(x)-250*x^2-1250)*exp((x^6-10*x^5+25*x^4)/(exp(x)^2*x^2-10*e 
xp(x)*x+25))+(x^7+10*x^5+25*x^3)*exp(x)^3+(-15*x^6-150*x^4-375*x^2)*exp(x) 
^2+(75*x^5+750*x^3+1875*x)*exp(x)-125*x^4-1250*x^2-3125),x)
 

Output:

(x*(2*e**((x**6 + 25*x**4)/(e**(2*x)*x**2 - 10*e**x*x + 25)) + 2*e**((10*x 
**5)/(e**(2*x)*x**2 - 10*e**x*x + 25))*x**2 + 9*e**((10*x**5)/(e**(2*x)*x* 
*2 - 10*e**x*x + 25))))/(e**((x**6 + 25*x**4)/(e**(2*x)*x**2 - 10*e**x*x + 
 25)) + e**((10*x**5)/(e**(2*x)*x**2 - 10*e**x*x + 25))*x**2 + 5*e**((10*x 
**5)/(e**(2*x)*x**2 - 10*e**x*x + 25)))