Integrand size = 287, antiderivative size = 38 \[ \int \frac {-125 x^4-75 e^{x^2} x^4-15 e^{2 x^2} x^4-e^{3 x^2} x^4+\left (250 x^3+250 x^4+e^{3 x^2} \left (2 x^3+2 x^4\right )+e^{2 x^2} \left (30 x^3+30 x^4\right )+e^{x^2} \left (150 x^3+150 x^4\right )\right ) \log (1+x)+\left (625+625 x-9650 x^2-9650 x^3+e^{3 x^2} \left (-85 x^2-85 x^3\right )+e^{x^2} \left (125+125 x-5480 x^2-3680 x^3+1420 x^4-380 x^5\right )+e^{2 x^2} \left (-1235 x^2-835 x^3+320 x^4-80 x^5\right )\right ) \log ^2(1+x)}{\left (625 x^2+625 x^3+e^{3 x^2} \left (5 x^2+5 x^3\right )+e^{2 x^2} \left (75 x^2+75 x^3\right )+e^{x^2} \left (375 x^2+375 x^3\right )\right ) \log ^2(1+x)} \, dx=x \left (-1-\left (4-\frac {-5+x}{\left (5+e^{x^2}\right ) x}\right )^2+\frac {x}{5 \log (1+x)}\right ) \]
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 2.84 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.76 \[ \int \frac {-125 x^4-75 e^{x^2} x^4-15 e^{2 x^2} x^4-e^{3 x^2} x^4+\left (250 x^3+250 x^4+e^{3 x^2} \left (2 x^3+2 x^4\right )+e^{2 x^2} \left (30 x^3+30 x^4\right )+e^{x^2} \left (150 x^3+150 x^4\right )\right ) \log (1+x)+\left (625+625 x-9650 x^2-9650 x^3+e^{3 x^2} \left (-85 x^2-85 x^3\right )+e^{x^2} \left (125+125 x-5480 x^2-3680 x^3+1420 x^4-380 x^5\right )+e^{2 x^2} \left (-1235 x^2-835 x^3+320 x^4-80 x^5\right )\right ) \log ^2(1+x)}{\left (625 x^2+625 x^3+e^{3 x^2} \left (5 x^2+5 x^3\right )+e^{2 x^2} \left (75 x^2+75 x^3\right )+e^{x^2} \left (375 x^2+375 x^3\right )\right ) \log ^2(1+x)} \, dx=\frac {8 (-5+x)}{5+e^{x^2}}-\frac {(-5+x)^2}{\left (5+e^{x^2}\right )^2 x}-17 x-\frac {2}{5} \operatorname {ExpIntegralEi}(\log (1+x))+\frac {x^2}{5 \log (1+x)}+\frac {2 \operatorname {LogIntegral}(1+x)}{5} \]
Integrate[(-125*x^4 - 75*E^x^2*x^4 - 15*E^(2*x^2)*x^4 - E^(3*x^2)*x^4 + (2 50*x^3 + 250*x^4 + E^(3*x^2)*(2*x^3 + 2*x^4) + E^(2*x^2)*(30*x^3 + 30*x^4) + E^x^2*(150*x^3 + 150*x^4))*Log[1 + x] + (625 + 625*x - 9650*x^2 - 9650* x^3 + E^(3*x^2)*(-85*x^2 - 85*x^3) + E^x^2*(125 + 125*x - 5480*x^2 - 3680* x^3 + 1420*x^4 - 380*x^5) + E^(2*x^2)*(-1235*x^2 - 835*x^3 + 320*x^4 - 80* x^5))*Log[1 + x]^2)/((625*x^2 + 625*x^3 + E^(3*x^2)*(5*x^2 + 5*x^3) + E^(2 *x^2)*(75*x^2 + 75*x^3) + E^x^2*(375*x^2 + 375*x^3))*Log[1 + x]^2),x]
(8*(-5 + x))/(5 + E^x^2) - (-5 + x)^2/((5 + E^x^2)^2*x) - 17*x - (2*ExpInt egralEi[Log[1 + x]])/5 + x^2/(5*Log[1 + x]) + (2*LogIntegral[1 + x])/5
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.
\(\displaystyle \int \frac {-125 x^4-75 e^{x^2} x^4-15 e^{2 x^2} x^4-e^{3 x^2} x^4+\left (250 x^4+250 x^3+e^{3 x^2} \left (2 x^4+2 x^3\right )+e^{2 x^2} \left (30 x^4+30 x^3\right )+e^{x^2} \left (150 x^4+150 x^3\right )\right ) \log (x+1)+\left (-9650 x^3-9650 x^2+e^{3 x^2} \left (-85 x^3-85 x^2\right )+e^{x^2} \left (-380 x^5+1420 x^4-3680 x^3-5480 x^2+125 x+125\right )+e^{2 x^2} \left (-80 x^5+320 x^4-835 x^3-1235 x^2\right )+625 x+625\right ) \log ^2(x+1)}{\left (625 x^3+625 x^2+e^{3 x^2} \left (5 x^3+5 x^2\right )+e^{2 x^2} \left (75 x^3+75 x^2\right )+e^{x^2} \left (375 x^3+375 x^2\right )\right ) \log ^2(x+1)} \, dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \left (-\frac {x^2}{5 (x+1) \log ^2(x+1)}+\frac {-17 e^{3 x^2} x^2-e^{2 x^2} \left (16 x^2-80 x+247\right ) x^2-1930 x^2+e^{x^2} \left (-76 x^4+360 x^3-1096 x^2+25\right )+125}{\left (e^{x^2}+5\right )^3 x^2}+\frac {2 x}{5 \log (x+1)}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -500 \int \frac {1}{\left (5+e^{x^2}\right )^3}dx+99 \int \frac {1}{\left (5+e^{x^2}\right )^2}dx+8 \int \frac {1}{5+e^{x^2}}dx+25 \int \frac {1}{\left (5+e^{x^2}\right )^2 x^2}dx-20 \int \frac {x^2}{\left (5+e^{x^2}\right )^3}dx+84 \int \frac {x^2}{\left (5+e^{x^2}\right )^2}dx-16 \int \frac {x^2}{5+e^{x^2}}dx-\frac {40}{e^{x^2}+5}+\frac {10}{\left (e^{x^2}+5\right )^2}-17 x+\frac {(x+1)^2}{5 \log (x+1)}-\frac {2 (x+1)}{5 \log (x+1)}+\frac {1}{5 \log (x+1)}\) |
Int[(-125*x^4 - 75*E^x^2*x^4 - 15*E^(2*x^2)*x^4 - E^(3*x^2)*x^4 + (250*x^3 + 250*x^4 + E^(3*x^2)*(2*x^3 + 2*x^4) + E^(2*x^2)*(30*x^3 + 30*x^4) + E^x ^2*(150*x^3 + 150*x^4))*Log[1 + x] + (625 + 625*x - 9650*x^2 - 9650*x^3 + E^(3*x^2)*(-85*x^2 - 85*x^3) + E^x^2*(125 + 125*x - 5480*x^2 - 3680*x^3 + 1420*x^4 - 380*x^5) + E^(2*x^2)*(-1235*x^2 - 835*x^3 + 320*x^4 - 80*x^5))* Log[1 + x]^2)/((625*x^2 + 625*x^3 + E^(3*x^2)*(5*x^2 + 5*x^3) + E^(2*x^2)* (75*x^2 + 75*x^3) + E^x^2*(375*x^2 + 375*x^3))*Log[1 + x]^2),x]
3.23.62.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 1.25 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.66
method | result | size |
risch | \(-\frac {17 \,{\mathrm e}^{2 x^{2}} x^{2}+162 x^{2} {\mathrm e}^{x^{2}}+386 x^{2}+40 \,{\mathrm e}^{x^{2}} x +190 x +25}{x \left (5+{\mathrm e}^{x^{2}}\right )^{2}}+\frac {x^{2}}{5 \ln \left (1+x \right )}\) | \(63\) |
parallelrisch | \(-\frac {-20 \,{\mathrm e}^{2 x^{2}} x^{3}+1700 \ln \left (1+x \right ) {\mathrm e}^{2 x^{2}} x^{2}-200 x^{3} {\mathrm e}^{x^{2}}+16200 \ln \left (1+x \right ) {\mathrm e}^{x^{2}} x^{2}-3640 \ln \left (1+x \right ) x \,{\mathrm e}^{2 x^{2}}-500 x^{3}+38600 x^{2} \ln \left (1+x \right )-32400 \ln \left (1+x \right ) {\mathrm e}^{x^{2}} x -72000 x \ln \left (1+x \right )+2500 \ln \left (1+x \right )}{100 \ln \left (1+x \right ) \left ({\mathrm e}^{2 x^{2}}+10 \,{\mathrm e}^{x^{2}}+25\right ) x}\) | \(128\) |
int((((-85*x^3-85*x^2)*exp(x^2)^3+(-80*x^5+320*x^4-835*x^3-1235*x^2)*exp(x ^2)^2+(-380*x^5+1420*x^4-3680*x^3-5480*x^2+125*x+125)*exp(x^2)-9650*x^3-96 50*x^2+625*x+625)*ln(1+x)^2+((2*x^4+2*x^3)*exp(x^2)^3+(30*x^4+30*x^3)*exp( x^2)^2+(150*x^4+150*x^3)*exp(x^2)+250*x^4+250*x^3)*ln(1+x)-x^4*exp(x^2)^3- 15*x^4*exp(x^2)^2-75*x^4*exp(x^2)-125*x^4)/((5*x^3+5*x^2)*exp(x^2)^3+(75*x ^3+75*x^2)*exp(x^2)^2+(375*x^3+375*x^2)*exp(x^2)+625*x^3+625*x^2)/ln(1+x)^ 2,x,method=_RETURNVERBOSE)
-(17*x^2*exp(x^2)^2+162*x^2*exp(x^2)+386*x^2+40*exp(x^2)*x+190*x+25)/x/(5+ exp(x^2))^2+1/5*x^2/ln(1+x)
Leaf count of result is larger than twice the leaf count of optimal. 96 vs. \(2 (35) = 70\).
Time = 0.26 (sec) , antiderivative size = 96, normalized size of antiderivative = 2.53 \[ \int \frac {-125 x^4-75 e^{x^2} x^4-15 e^{2 x^2} x^4-e^{3 x^2} x^4+\left (250 x^3+250 x^4+e^{3 x^2} \left (2 x^3+2 x^4\right )+e^{2 x^2} \left (30 x^3+30 x^4\right )+e^{x^2} \left (150 x^3+150 x^4\right )\right ) \log (1+x)+\left (625+625 x-9650 x^2-9650 x^3+e^{3 x^2} \left (-85 x^2-85 x^3\right )+e^{x^2} \left (125+125 x-5480 x^2-3680 x^3+1420 x^4-380 x^5\right )+e^{2 x^2} \left (-1235 x^2-835 x^3+320 x^4-80 x^5\right )\right ) \log ^2(1+x)}{\left (625 x^2+625 x^3+e^{3 x^2} \left (5 x^2+5 x^3\right )+e^{2 x^2} \left (75 x^2+75 x^3\right )+e^{x^2} \left (375 x^2+375 x^3\right )\right ) \log ^2(1+x)} \, dx=\frac {x^{3} e^{\left (2 \, x^{2}\right )} + 10 \, x^{3} e^{\left (x^{2}\right )} + 25 \, x^{3} - 5 \, {\left (17 \, x^{2} e^{\left (2 \, x^{2}\right )} + 386 \, x^{2} + 2 \, {\left (81 \, x^{2} + 20 \, x\right )} e^{\left (x^{2}\right )} + 190 \, x + 25\right )} \log \left (x + 1\right )}{5 \, {\left (x e^{\left (2 \, x^{2}\right )} + 10 \, x e^{\left (x^{2}\right )} + 25 \, x\right )} \log \left (x + 1\right )} \]
integrate((((-85*x^3-85*x^2)*exp(x^2)^3+(-80*x^5+320*x^4-835*x^3-1235*x^2) *exp(x^2)^2+(-380*x^5+1420*x^4-3680*x^3-5480*x^2+125*x+125)*exp(x^2)-9650* x^3-9650*x^2+625*x+625)*log(1+x)^2+((2*x^4+2*x^3)*exp(x^2)^3+(30*x^4+30*x^ 3)*exp(x^2)^2+(150*x^4+150*x^3)*exp(x^2)+250*x^4+250*x^3)*log(1+x)-x^4*exp (x^2)^3-15*x^4*exp(x^2)^2-75*x^4*exp(x^2)-125*x^4)/((5*x^3+5*x^2)*exp(x^2) ^3+(75*x^3+75*x^2)*exp(x^2)^2+(375*x^3+375*x^2)*exp(x^2)+625*x^3+625*x^2)/ log(1+x)^2,x, algorithm=\
1/5*(x^3*e^(2*x^2) + 10*x^3*e^(x^2) + 25*x^3 - 5*(17*x^2*e^(2*x^2) + 386*x ^2 + 2*(81*x^2 + 20*x)*e^(x^2) + 190*x + 25)*log(x + 1))/((x*e^(2*x^2) + 1 0*x*e^(x^2) + 25*x)*log(x + 1))
Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (26) = 52\).
Time = 0.15 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.47 \[ \int \frac {-125 x^4-75 e^{x^2} x^4-15 e^{2 x^2} x^4-e^{3 x^2} x^4+\left (250 x^3+250 x^4+e^{3 x^2} \left (2 x^3+2 x^4\right )+e^{2 x^2} \left (30 x^3+30 x^4\right )+e^{x^2} \left (150 x^3+150 x^4\right )\right ) \log (1+x)+\left (625+625 x-9650 x^2-9650 x^3+e^{3 x^2} \left (-85 x^2-85 x^3\right )+e^{x^2} \left (125+125 x-5480 x^2-3680 x^3+1420 x^4-380 x^5\right )+e^{2 x^2} \left (-1235 x^2-835 x^3+320 x^4-80 x^5\right )\right ) \log ^2(1+x)}{\left (625 x^2+625 x^3+e^{3 x^2} \left (5 x^2+5 x^3\right )+e^{2 x^2} \left (75 x^2+75 x^3\right )+e^{x^2} \left (375 x^2+375 x^3\right )\right ) \log ^2(1+x)} \, dx=\frac {x^{2}}{5 \log {\left (x + 1 \right )}} - 17 x + \frac {39 x^{2} - 190 x + \left (8 x^{2} - 40 x\right ) e^{x^{2}} - 25}{x e^{2 x^{2}} + 10 x e^{x^{2}} + 25 x} \]
integrate((((-85*x**3-85*x**2)*exp(x**2)**3+(-80*x**5+320*x**4-835*x**3-12 35*x**2)*exp(x**2)**2+(-380*x**5+1420*x**4-3680*x**3-5480*x**2+125*x+125)* exp(x**2)-9650*x**3-9650*x**2+625*x+625)*ln(1+x)**2+((2*x**4+2*x**3)*exp(x **2)**3+(30*x**4+30*x**3)*exp(x**2)**2+(150*x**4+150*x**3)*exp(x**2)+250*x **4+250*x**3)*ln(1+x)-x**4*exp(x**2)**3-15*x**4*exp(x**2)**2-75*x**4*exp(x **2)-125*x**4)/((5*x**3+5*x**2)*exp(x**2)**3+(75*x**3+75*x**2)*exp(x**2)** 2+(375*x**3+375*x**2)*exp(x**2)+625*x**3+625*x**2)/ln(1+x)**2,x)
x**2/(5*log(x + 1)) - 17*x + (39*x**2 - 190*x + (8*x**2 - 40*x)*exp(x**2) - 25)/(x*exp(2*x**2) + 10*x*exp(x**2) + 25*x)
Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (35) = 70\).
Time = 0.26 (sec) , antiderivative size = 102, normalized size of antiderivative = 2.68 \[ \int \frac {-125 x^4-75 e^{x^2} x^4-15 e^{2 x^2} x^4-e^{3 x^2} x^4+\left (250 x^3+250 x^4+e^{3 x^2} \left (2 x^3+2 x^4\right )+e^{2 x^2} \left (30 x^3+30 x^4\right )+e^{x^2} \left (150 x^3+150 x^4\right )\right ) \log (1+x)+\left (625+625 x-9650 x^2-9650 x^3+e^{3 x^2} \left (-85 x^2-85 x^3\right )+e^{x^2} \left (125+125 x-5480 x^2-3680 x^3+1420 x^4-380 x^5\right )+e^{2 x^2} \left (-1235 x^2-835 x^3+320 x^4-80 x^5\right )\right ) \log ^2(1+x)}{\left (625 x^2+625 x^3+e^{3 x^2} \left (5 x^2+5 x^3\right )+e^{2 x^2} \left (75 x^2+75 x^3\right )+e^{x^2} \left (375 x^2+375 x^3\right )\right ) \log ^2(1+x)} \, dx=\frac {25 \, x^{3} + {\left (x^{3} - 85 \, x^{2} \log \left (x + 1\right )\right )} e^{\left (2 \, x^{2}\right )} + 10 \, {\left (x^{3} - {\left (81 \, x^{2} + 20 \, x\right )} \log \left (x + 1\right )\right )} e^{\left (x^{2}\right )} - 5 \, {\left (386 \, x^{2} + 190 \, x + 25\right )} \log \left (x + 1\right )}{5 \, {\left (x e^{\left (2 \, x^{2}\right )} \log \left (x + 1\right ) + 10 \, x e^{\left (x^{2}\right )} \log \left (x + 1\right ) + 25 \, x \log \left (x + 1\right )\right )}} \]
integrate((((-85*x^3-85*x^2)*exp(x^2)^3+(-80*x^5+320*x^4-835*x^3-1235*x^2) *exp(x^2)^2+(-380*x^5+1420*x^4-3680*x^3-5480*x^2+125*x+125)*exp(x^2)-9650* x^3-9650*x^2+625*x+625)*log(1+x)^2+((2*x^4+2*x^3)*exp(x^2)^3+(30*x^4+30*x^ 3)*exp(x^2)^2+(150*x^4+150*x^3)*exp(x^2)+250*x^4+250*x^3)*log(1+x)-x^4*exp (x^2)^3-15*x^4*exp(x^2)^2-75*x^4*exp(x^2)-125*x^4)/((5*x^3+5*x^2)*exp(x^2) ^3+(75*x^3+75*x^2)*exp(x^2)^2+(375*x^3+375*x^2)*exp(x^2)+625*x^3+625*x^2)/ log(1+x)^2,x, algorithm=\
1/5*(25*x^3 + (x^3 - 85*x^2*log(x + 1))*e^(2*x^2) + 10*(x^3 - (81*x^2 + 20 *x)*log(x + 1))*e^(x^2) - 5*(386*x^2 + 190*x + 25)*log(x + 1))/(x*e^(2*x^2 )*log(x + 1) + 10*x*e^(x^2)*log(x + 1) + 25*x*log(x + 1))
Leaf count of result is larger than twice the leaf count of optimal. 121 vs. \(2 (35) = 70\).
Time = 0.38 (sec) , antiderivative size = 121, normalized size of antiderivative = 3.18 \[ \int \frac {-125 x^4-75 e^{x^2} x^4-15 e^{2 x^2} x^4-e^{3 x^2} x^4+\left (250 x^3+250 x^4+e^{3 x^2} \left (2 x^3+2 x^4\right )+e^{2 x^2} \left (30 x^3+30 x^4\right )+e^{x^2} \left (150 x^3+150 x^4\right )\right ) \log (1+x)+\left (625+625 x-9650 x^2-9650 x^3+e^{3 x^2} \left (-85 x^2-85 x^3\right )+e^{x^2} \left (125+125 x-5480 x^2-3680 x^3+1420 x^4-380 x^5\right )+e^{2 x^2} \left (-1235 x^2-835 x^3+320 x^4-80 x^5\right )\right ) \log ^2(1+x)}{\left (625 x^2+625 x^3+e^{3 x^2} \left (5 x^2+5 x^3\right )+e^{2 x^2} \left (75 x^2+75 x^3\right )+e^{x^2} \left (375 x^2+375 x^3\right )\right ) \log ^2(1+x)} \, dx=\frac {x^{3} e^{\left (2 \, x^{2}\right )} + 10 \, x^{3} e^{\left (x^{2}\right )} - 85 \, x^{2} e^{\left (2 \, x^{2}\right )} \log \left (x + 1\right ) - 810 \, x^{2} e^{\left (x^{2}\right )} \log \left (x + 1\right ) + 25 \, x^{3} - 1930 \, x^{2} \log \left (x + 1\right ) - 200 \, x e^{\left (x^{2}\right )} \log \left (x + 1\right ) - 950 \, x \log \left (x + 1\right ) - 125 \, \log \left (x + 1\right )}{5 \, {\left (x e^{\left (2 \, x^{2}\right )} \log \left (x + 1\right ) + 10 \, x e^{\left (x^{2}\right )} \log \left (x + 1\right ) + 25 \, x \log \left (x + 1\right )\right )}} \]
integrate((((-85*x^3-85*x^2)*exp(x^2)^3+(-80*x^5+320*x^4-835*x^3-1235*x^2) *exp(x^2)^2+(-380*x^5+1420*x^4-3680*x^3-5480*x^2+125*x+125)*exp(x^2)-9650* x^3-9650*x^2+625*x+625)*log(1+x)^2+((2*x^4+2*x^3)*exp(x^2)^3+(30*x^4+30*x^ 3)*exp(x^2)^2+(150*x^4+150*x^3)*exp(x^2)+250*x^4+250*x^3)*log(1+x)-x^4*exp (x^2)^3-15*x^4*exp(x^2)^2-75*x^4*exp(x^2)-125*x^4)/((5*x^3+5*x^2)*exp(x^2) ^3+(75*x^3+75*x^2)*exp(x^2)^2+(375*x^3+375*x^2)*exp(x^2)+625*x^3+625*x^2)/ log(1+x)^2,x, algorithm=\
1/5*(x^3*e^(2*x^2) + 10*x^3*e^(x^2) - 85*x^2*e^(2*x^2)*log(x + 1) - 810*x^ 2*e^(x^2)*log(x + 1) + 25*x^3 - 1930*x^2*log(x + 1) - 200*x*e^(x^2)*log(x + 1) - 950*x*log(x + 1) - 125*log(x + 1))/(x*e^(2*x^2)*log(x + 1) + 10*x*e ^(x^2)*log(x + 1) + 25*x*log(x + 1))
Time = 14.28 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.34 \[ \int \frac {-125 x^4-75 e^{x^2} x^4-15 e^{2 x^2} x^4-e^{3 x^2} x^4+\left (250 x^3+250 x^4+e^{3 x^2} \left (2 x^3+2 x^4\right )+e^{2 x^2} \left (30 x^3+30 x^4\right )+e^{x^2} \left (150 x^3+150 x^4\right )\right ) \log (1+x)+\left (625+625 x-9650 x^2-9650 x^3+e^{3 x^2} \left (-85 x^2-85 x^3\right )+e^{x^2} \left (125+125 x-5480 x^2-3680 x^3+1420 x^4-380 x^5\right )+e^{2 x^2} \left (-1235 x^2-835 x^3+320 x^4-80 x^5\right )\right ) \log ^2(1+x)}{\left (625 x^2+625 x^3+e^{3 x^2} \left (5 x^2+5 x^3\right )+e^{2 x^2} \left (75 x^2+75 x^3\right )+e^{x^2} \left (375 x^2+375 x^3\right )\right ) \log ^2(1+x)} \, dx=\frac {\frac {x^2}{5}-\frac {2\,x\,\ln \left (x+1\right )\,\left (x+1\right )}{5}}{\ln \left (x+1\right )}-\frac {83\,x}{5}+\frac {2\,x^2}{5}-\frac {8\,\left (5\,x-x^2\right )}{x\,\left ({\mathrm {e}}^{x^2}+5\right )}-\frac {x^4-10\,x^3+25\,x^2}{x^3\,\left (10\,{\mathrm {e}}^{x^2}+{\mathrm {e}}^{2\,x^2}+25\right )} \]
int(-(log(x + 1)^2*(exp(2*x^2)*(1235*x^2 + 835*x^3 - 320*x^4 + 80*x^5) - 6 25*x - exp(x^2)*(125*x - 5480*x^2 - 3680*x^3 + 1420*x^4 - 380*x^5 + 125) + exp(3*x^2)*(85*x^2 + 85*x^3) + 9650*x^2 + 9650*x^3 - 625) - log(x + 1)*(e xp(x^2)*(150*x^3 + 150*x^4) + exp(3*x^2)*(2*x^3 + 2*x^4) + exp(2*x^2)*(30* x^3 + 30*x^4) + 250*x^3 + 250*x^4) + 75*x^4*exp(x^2) + 15*x^4*exp(2*x^2) + x^4*exp(3*x^2) + 125*x^4)/(log(x + 1)^2*(exp(x^2)*(375*x^2 + 375*x^3) + e xp(3*x^2)*(5*x^2 + 5*x^3) + exp(2*x^2)*(75*x^2 + 75*x^3) + 625*x^2 + 625*x ^3)),x)