Integrand size = 251, antiderivative size = 29 \[ \int \frac {1000+1000 x+e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )+e^{2 x^2} \left (-2 x^2-20 x^4\right )+\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)+\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)+\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)+\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)+\left (-4 x-60 x^2\right ) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx=\left (1+\frac {2+x}{x}+\frac {e^{x^2}}{5-\log (x)}+\log ^2(x)\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(85\) vs. \(2(29)=58\).
Time = 0.30 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.93 \[ \int \frac {1000+1000 x+e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )+e^{2 x^2} \left (-2 x^2-20 x^4\right )+\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)+\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)+\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)+\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)+\left (-4 x-60 x^2\right ) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx=-2 \left (5 e^{x^2}-\frac {2}{x^2}-\frac {4}{x}-\frac {e^{2 x^2}}{2 (-5+\log (x))^2}+\frac {e^{x^2} (2+27 x)}{x (-5+\log (x))}+e^{x^2} \log (x)-\frac {2 (1+x) \log ^2(x)}{x}-\frac {\log ^4(x)}{2}\right ) \]
Integrate[(1000 + 1000*x + E^x^2*(80*x - 20*x^2 - 200*x^3 - 200*x^4) + E^( 2*x^2)*(-2*x^2 - 20*x^4) + (-600 - 1600*x - 1000*x^2 + 4*E^(2*x^2)*x^4 + E ^x^2*(-36*x - 96*x^2 + 80*x^3 + 80*x^4))*Log[x] + (120 + 1220*x + 600*x^2 + E^x^2*(4*x + 30*x^2 - 8*x^3 - 108*x^4))*Log[x]^2 + (-8 - 428*x - 620*x^2 + E^x^2*(-2*x^2 + 40*x^4))*Log[x]^3 + (68*x + 308*x^2 - 4*E^x^2*x^4)*Log[ x]^4 + (-4*x - 60*x^2)*Log[x]^5 + 4*x^2*Log[x]^6)/(-125*x^3 + 75*x^3*Log[x ] - 15*x^3*Log[x]^2 + x^3*Log[x]^3),x]
-2*(5*E^x^2 - 2/x^2 - 4/x - E^(2*x^2)/(2*(-5 + Log[x])^2) + (E^x^2*(2 + 27 *x))/(x*(-5 + Log[x])) + E^x^2*Log[x] - (2*(1 + x)*Log[x]^2)/x - Log[x]^4/ 2)
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.
| \(\displaystyle \int \frac {4 x^2 \log ^6(x)+\left (-60 x^2-4 x\right ) \log ^5(x)+e^{2 x^2} \left (-20 x^4-2 x^2\right )+\left (308 x^2-4 e^{x^2} x^4+68 x\right ) \log ^4(x)+\left (-620 x^2+e^{x^2} \left (40 x^4-2 x^2\right )-428 x-8\right ) \log ^3(x)+e^{x^2} \left (-200 x^4-200 x^3-20 x^2+80 x\right )+\left (600 x^2+e^{x^2} \left (-108 x^4-8 x^3+30 x^2+4 x\right )+1220 x+120\right ) \log ^2(x)+\left (-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (80 x^4+80 x^3-96 x^2-36 x\right )-1600 x-600\right ) \log (x)+1000 x+1000}{-125 x^3+x^3 \log ^3(x)-15 x^3 \log ^2(x)+75 x^3 \log (x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-4 x^2 \log ^6(x)-\left (-60 x^2-4 x\right ) \log ^5(x)-e^{2 x^2} \left (-20 x^4-2 x^2\right )-\left (308 x^2-4 e^{x^2} x^4+68 x\right ) \log ^4(x)-\left (-620 x^2+e^{x^2} \left (40 x^4-2 x^2\right )-428 x-8\right ) \log ^3(x)-e^{x^2} \left (-200 x^4-200 x^3-20 x^2+80 x\right )-\left (600 x^2+e^{x^2} \left (-108 x^4-8 x^3+30 x^2+4 x\right )+1220 x+120\right ) \log ^2(x)-\left (-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (80 x^4+80 x^3-96 x^2-36 x\right )-1600 x-600\right ) \log (x)-1000 x-1000}{x^3 (5-\log (x))^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {8 \log ^3(x)}{x^3 (\log (x)-5)^3}+\frac {120 \log ^2(x)}{x^3 (\log (x)-5)^3}-\frac {600 \log (x)}{x^3 (\log (x)-5)^3}+\frac {1000}{x^3 (\log (x)-5)^3}-\frac {4 (15 x+1) \log ^5(x)}{x^2 (\log (x)-5)^3}+\frac {68 \log ^4(x)}{x^2 (\log (x)-5)^3}-\frac {428 \log ^3(x)}{x^2 (\log (x)-5)^3}+\frac {1220 \log ^2(x)}{x^2 (\log (x)-5)^3}-\frac {1600 \log (x)}{x^2 (\log (x)-5)^3}+\frac {2 e^{2 x^2} \left (-10 x^2+2 x^2 \log (x)-1\right )}{x (\log (x)-5)^3}+\frac {1000}{x^2 (\log (x)-5)^3}-\frac {2 e^{x^2} \left (-20 x^3+2 x^3 \log ^3(x)-10 x^3 \log ^2(x)+4 x^3 \log (x)-20 x^2+4 x^2 \log (x)-2 x+x \log ^2(x)-10 x \log (x)-2 \log (x)+8\right )}{x^2 (\log (x)-5)^2}+\frac {4 \log ^6(x)}{x (\log (x)-5)^3}+\frac {308 \log ^4(x)}{x (\log (x)-5)^3}-\frac {620 \log ^3(x)}{x (\log (x)-5)^3}+\frac {600 \log ^2(x)}{x (\log (x)-5)^3}-\frac {1000 \log (x)}{x (\log (x)-5)^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -8 \int \frac {\log ^3(x)}{x^3 (\log (x)-5)^3}dx+120 \int \frac {\log ^2(x)}{x^3 (\log (x)-5)^3}dx+68 \int \frac {\log ^4(x)}{x^2 (\log (x)-5)^3}dx-428 \int \frac {\log ^3(x)}{x^2 (\log (x)-5)^3}dx+1220 \int \frac {\log ^2(x)}{x^2 (\log (x)-5)^3}dx-\frac {800 \log (x) \operatorname {ExpIntegralEi}(5-\log (x))}{e^5}-\frac {1200 \log (x) \operatorname {ExpIntegralEi}(2 (5-\log (x)))}{e^{10}}+\frac {3350 \operatorname {ExpIntegralEi}(5-\log (x))}{e^5}+\frac {2600 \operatorname {ExpIntegralEi}(2 (5-\log (x)))}{e^{10}}+\frac {600 (11-2 \log (x)) \operatorname {ExpIntegralEi}(2 (5-\log (x)))}{e^{10}}-\frac {800 (5-\log (x)) \operatorname {ExpIntegralEi}(5-\log (x))}{e^5}-\frac {2400 (5-\log (x)) \operatorname {ExpIntegralEi}(2 (5-\log (x)))}{e^{10}}+\frac {1200}{x^2}+\frac {600 \log (x)}{x^2 (5-\log (x))}+\frac {300 \log (x)}{x^2 (5-\log (x))^2}+\frac {e^{2 x^2} \left (5 x^2-x^2 \log (x)\right )}{x^2 (5-\log (x))^3}-\frac {300 (11-2 \log (x))}{x^2 (5-\log (x))}-\frac {1000}{x^2 (5-\log (x))}-\frac {500}{x^2 (5-\log (x))^2}+\frac {2 e^{x^2} \left (10 x^3+x^3 \left (-\log ^3(x)\right )+5 x^3 \log ^2(x)-2 x^3 \log (x)+10 x^2-2 x^2 \log (x)\right )}{x^3 (5-\log (x))^2}+\frac {1468}{x}+\log ^4(x)+\frac {4 \log ^2(x)}{x}+\frac {100 \log ^2(x)}{(5-\log (x))^2}+4 \log ^2(x)+\frac {68 \log (x)}{x}+\frac {800 \log (x)}{x (5-\log (x))}+\frac {800 \log (x)}{x (5-\log (x))^2}-\frac {7550}{x (5-\log (x))}+\frac {1000}{5-\log (x)}+\frac {5750}{x (5-\log (x))^2}-\frac {2500}{(5-\log (x))^2}\) |
Int[(1000 + 1000*x + E^x^2*(80*x - 20*x^2 - 200*x^3 - 200*x^4) + E^(2*x^2) *(-2*x^2 - 20*x^4) + (-600 - 1600*x - 1000*x^2 + 4*E^(2*x^2)*x^4 + E^x^2*( -36*x - 96*x^2 + 80*x^3 + 80*x^4))*Log[x] + (120 + 1220*x + 600*x^2 + E^x^ 2*(4*x + 30*x^2 - 8*x^3 - 108*x^4))*Log[x]^2 + (-8 - 428*x - 620*x^2 + E^x ^2*(-2*x^2 + 40*x^4))*Log[x]^3 + (68*x + 308*x^2 - 4*E^x^2*x^4)*Log[x]^4 + (-4*x - 60*x^2)*Log[x]^5 + 4*x^2*Log[x]^6)/(-125*x^3 + 75*x^3*Log[x] - 15 *x^3*Log[x]^2 + x^3*Log[x]^3),x]
3.7.10.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(78\) vs. \(2(28)=56\).
Time = 3.30 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.72
| method | result | size |
| risch | \(\ln \left (x \right )^{4}+\frac {4 \left (1+x \right ) \ln \left (x \right )^{2}}{x}-2 \,{\mathrm e}^{x^{2}} \ln \left (x \right )-\frac {2 \left (5 x^{2} {\mathrm e}^{x^{2}}-4 x -2\right )}{x^{2}}+\frac {{\mathrm e}^{x^{2}} \left ({\mathrm e}^{x^{2}} x -54 x \ln \left (x \right )+270 x -4 \ln \left (x \right )+20\right )}{\left (\ln \left (x \right )-5\right )^{2} x}\) | \(79\) |
| parallelrisch | \(\frac {1000+2000 x -40 x \,{\mathrm e}^{x^{2}} \ln \left (x \right )+10 \,{\mathrm e}^{2 x^{2}} x^{2}+40 x \ln \left (x \right )^{4}+200 \,{\mathrm e}^{x^{2}} x +1080 x \ln \left (x \right )^{2}-800 x \ln \left (x \right )+10 x^{2} \ln \left (x \right )^{6}-100 x^{2} \ln \left (x \right )^{5}-400 x^{2} \ln \left (x \right )^{3}-400 x \ln \left (x \right )^{3}+1000 x^{2} \ln \left (x \right )^{2}+290 x^{2} \ln \left (x \right )^{4}-40 x^{2} {\mathrm e}^{x^{2}} \ln \left (x \right )+40 \ln \left (x \right )^{2}-400 \ln \left (x \right )+200 x^{2} {\mathrm e}^{x^{2}}-20 \ln \left (x \right )^{3} {\mathrm e}^{x^{2}} x^{2}+100 \ln \left (x \right )^{2} {\mathrm e}^{x^{2}} x^{2}}{10 x^{2} \left (\ln \left (x \right )^{2}-10 \ln \left (x \right )+25\right )}\) | \(177\) |
int((4*x^2*ln(x)^6+(-60*x^2-4*x)*ln(x)^5+(-4*x^4*exp(x^2)+308*x^2+68*x)*ln (x)^4+((40*x^4-2*x^2)*exp(x^2)-620*x^2-428*x-8)*ln(x)^3+((-108*x^4-8*x^3+3 0*x^2+4*x)*exp(x^2)+600*x^2+1220*x+120)*ln(x)^2+(4*x^4*exp(x^2)^2+(80*x^4+ 80*x^3-96*x^2-36*x)*exp(x^2)-1000*x^2-1600*x-600)*ln(x)+(-20*x^4-2*x^2)*ex p(x^2)^2+(-200*x^4-200*x^3-20*x^2+80*x)*exp(x^2)+1000*x+1000)/(x^3*ln(x)^3 -15*x^3*ln(x)^2+75*x^3*ln(x)-125*x^3),x,method=_RETURNVERBOSE)
ln(x)^4+4*(1+x)/x*ln(x)^2-2*exp(x^2)*ln(x)-2*(5*x^2*exp(x^2)-4*x-2)/x^2+ex p(x^2)*(exp(x^2)*x-54*x*ln(x)+270*x-4*ln(x)+20)/(ln(x)-5)^2/x
Leaf count of result is larger than twice the leaf count of optimal. 148 vs. \(2 (27) = 54\).
Time = 0.26 (sec) , antiderivative size = 148, normalized size of antiderivative = 5.10 \[ \int \frac {1000+1000 x+e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )+e^{2 x^2} \left (-2 x^2-20 x^4\right )+\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)+\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)+\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)+\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)+\left (-4 x-60 x^2\right ) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx=\frac {x^{2} \log \left (x\right )^{6} - 10 \, x^{2} \log \left (x\right )^{5} + {\left (29 \, x^{2} + 4 \, x\right )} \log \left (x\right )^{4} - 2 \, {\left (x^{2} e^{\left (x^{2}\right )} + 20 \, x^{2} + 20 \, x\right )} \log \left (x\right )^{3} + x^{2} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (5 \, x^{2} e^{\left (x^{2}\right )} + 50 \, x^{2} + 54 \, x + 2\right )} \log \left (x\right )^{2} + 20 \, {\left (x^{2} + x\right )} e^{\left (x^{2}\right )} - 4 \, {\left ({\left (x^{2} + x\right )} e^{\left (x^{2}\right )} + 20 \, x + 10\right )} \log \left (x\right ) + 200 \, x + 100}{x^{2} \log \left (x\right )^{2} - 10 \, x^{2} \log \left (x\right ) + 25 \, x^{2}} \]
integrate((4*x^2*log(x)^6+(-60*x^2-4*x)*log(x)^5+(-4*x^4*exp(x^2)+308*x^2+ 68*x)*log(x)^4+((40*x^4-2*x^2)*exp(x^2)-620*x^2-428*x-8)*log(x)^3+((-108*x ^4-8*x^3+30*x^2+4*x)*exp(x^2)+600*x^2+1220*x+120)*log(x)^2+(4*x^4*exp(x^2) ^2+(80*x^4+80*x^3-96*x^2-36*x)*exp(x^2)-1000*x^2-1600*x-600)*log(x)+(-20*x ^4-2*x^2)*exp(x^2)^2+(-200*x^4-200*x^3-20*x^2+80*x)*exp(x^2)+1000*x+1000)/ (x^3*log(x)^3-15*x^3*log(x)^2+75*x^3*log(x)-125*x^3),x, algorithm=\
(x^2*log(x)^6 - 10*x^2*log(x)^5 + (29*x^2 + 4*x)*log(x)^4 - 2*(x^2*e^(x^2) + 20*x^2 + 20*x)*log(x)^3 + x^2*e^(2*x^2) + 2*(5*x^2*e^(x^2) + 50*x^2 + 5 4*x + 2)*log(x)^2 + 20*(x^2 + x)*e^(x^2) - 4*((x^2 + x)*e^(x^2) + 20*x + 1 0)*log(x) + 200*x + 100)/(x^2*log(x)^2 - 10*x^2*log(x) + 25*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 121 vs. \(2 (22) = 44\).
Time = 0.28 (sec) , antiderivative size = 121, normalized size of antiderivative = 4.17 \[ \int \frac {1000+1000 x+e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )+e^{2 x^2} \left (-2 x^2-20 x^4\right )+\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)+\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)+\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)+\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)+\left (-4 x-60 x^2\right ) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx=\frac {\left (x \log {\left (x \right )} - 5 x\right ) e^{2 x^{2}} + \left (- 2 x \log {\left (x \right )}^{4} + 20 x \log {\left (x \right )}^{3} - 54 x \log {\left (x \right )}^{2} + 40 x \log {\left (x \right )} - 100 x - 4 \log {\left (x \right )}^{2} + 40 \log {\left (x \right )} - 100\right ) e^{x^{2}}}{x \log {\left (x \right )}^{3} - 15 x \log {\left (x \right )}^{2} + 75 x \log {\left (x \right )} - 125 x} + \log {\left (x \right )}^{4} + \frac {\left (4 x + 4\right ) \log {\left (x \right )}^{2}}{x} - \frac {- 8 x - 4}{x^{2}} \]
integrate((4*x**2*ln(x)**6+(-60*x**2-4*x)*ln(x)**5+(-4*x**4*exp(x**2)+308* x**2+68*x)*ln(x)**4+((40*x**4-2*x**2)*exp(x**2)-620*x**2-428*x-8)*ln(x)**3 +((-108*x**4-8*x**3+30*x**2+4*x)*exp(x**2)+600*x**2+1220*x+120)*ln(x)**2+( 4*x**4*exp(x**2)**2+(80*x**4+80*x**3-96*x**2-36*x)*exp(x**2)-1000*x**2-160 0*x-600)*ln(x)+(-20*x**4-2*x**2)*exp(x**2)**2+(-200*x**4-200*x**3-20*x**2+ 80*x)*exp(x**2)+1000*x+1000)/(x**3*ln(x)**3-15*x**3*ln(x)**2+75*x**3*ln(x) -125*x**3),x)
((x*log(x) - 5*x)*exp(2*x**2) + (-2*x*log(x)**4 + 20*x*log(x)**3 - 54*x*lo g(x)**2 + 40*x*log(x) - 100*x - 4*log(x)**2 + 40*log(x) - 100)*exp(x**2))/ (x*log(x)**3 - 15*x*log(x)**2 + 75*x*log(x) - 125*x) + log(x)**4 + (4*x + 4)*log(x)**2/x - (-8*x - 4)/x**2
Leaf count of result is larger than twice the leaf count of optimal. 147 vs. \(2 (27) = 54\).
Time = 0.26 (sec) , antiderivative size = 147, normalized size of antiderivative = 5.07 \[ \int \frac {1000+1000 x+e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )+e^{2 x^2} \left (-2 x^2-20 x^4\right )+\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)+\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)+\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)+\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)+\left (-4 x-60 x^2\right ) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx=\frac {x^{2} \log \left (x\right )^{6} - 10 \, x^{2} \log \left (x\right )^{5} + {\left (29 \, x^{2} + 4 \, x\right )} \log \left (x\right )^{4} - 40 \, {\left (x^{2} + x\right )} \log \left (x\right )^{3} + x^{2} e^{\left (2 \, x^{2}\right )} + 4 \, {\left (25 \, x^{2} + 27 \, x + 1\right )} \log \left (x\right )^{2} - 2 \, {\left (x^{2} \log \left (x\right )^{3} - 5 \, x^{2} \log \left (x\right )^{2} - 10 \, x^{2} + 2 \, {\left (x^{2} + x\right )} \log \left (x\right ) - 10 \, x\right )} e^{\left (x^{2}\right )} - 40 \, {\left (2 \, x + 1\right )} \log \left (x\right ) + 200 \, x + 100}{x^{2} \log \left (x\right )^{2} - 10 \, x^{2} \log \left (x\right ) + 25 \, x^{2}} \]
integrate((4*x^2*log(x)^6+(-60*x^2-4*x)*log(x)^5+(-4*x^4*exp(x^2)+308*x^2+ 68*x)*log(x)^4+((40*x^4-2*x^2)*exp(x^2)-620*x^2-428*x-8)*log(x)^3+((-108*x ^4-8*x^3+30*x^2+4*x)*exp(x^2)+600*x^2+1220*x+120)*log(x)^2+(4*x^4*exp(x^2) ^2+(80*x^4+80*x^3-96*x^2-36*x)*exp(x^2)-1000*x^2-1600*x-600)*log(x)+(-20*x ^4-2*x^2)*exp(x^2)^2+(-200*x^4-200*x^3-20*x^2+80*x)*exp(x^2)+1000*x+1000)/ (x^3*log(x)^3-15*x^3*log(x)^2+75*x^3*log(x)-125*x^3),x, algorithm=\
(x^2*log(x)^6 - 10*x^2*log(x)^5 + (29*x^2 + 4*x)*log(x)^4 - 40*(x^2 + x)*l og(x)^3 + x^2*e^(2*x^2) + 4*(25*x^2 + 27*x + 1)*log(x)^2 - 2*(x^2*log(x)^3 - 5*x^2*log(x)^2 - 10*x^2 + 2*(x^2 + x)*log(x) - 10*x)*e^(x^2) - 40*(2*x + 1)*log(x) + 200*x + 100)/(x^2*log(x)^2 - 10*x^2*log(x) + 25*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 181 vs. \(2 (27) = 54\).
Time = 0.30 (sec) , antiderivative size = 181, normalized size of antiderivative = 6.24 \[ \int \frac {1000+1000 x+e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )+e^{2 x^2} \left (-2 x^2-20 x^4\right )+\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)+\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)+\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)+\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)+\left (-4 x-60 x^2\right ) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx=\frac {x^{2} \log \left (x\right )^{6} - 10 \, x^{2} \log \left (x\right )^{5} - 2 \, x^{2} e^{\left (x^{2}\right )} \log \left (x\right )^{3} + 29 \, x^{2} \log \left (x\right )^{4} + 10 \, x^{2} e^{\left (x^{2}\right )} \log \left (x\right )^{2} - 40 \, x^{2} \log \left (x\right )^{3} + 4 \, x \log \left (x\right )^{4} - 4 \, x^{2} e^{\left (x^{2}\right )} \log \left (x\right ) + 100 \, x^{2} \log \left (x\right )^{2} - 40 \, x \log \left (x\right )^{3} + x^{2} e^{\left (2 \, x^{2}\right )} + 20 \, x^{2} e^{\left (x^{2}\right )} - 4 \, x e^{\left (x^{2}\right )} \log \left (x\right ) + 108 \, x \log \left (x\right )^{2} + 20 \, x e^{\left (x^{2}\right )} - 80 \, x \log \left (x\right ) + 4 \, \log \left (x\right )^{2} + 200 \, x - 40 \, \log \left (x\right ) + 100}{x^{2} \log \left (x\right )^{2} - 10 \, x^{2} \log \left (x\right ) + 25 \, x^{2}} \]
integrate((4*x^2*log(x)^6+(-60*x^2-4*x)*log(x)^5+(-4*x^4*exp(x^2)+308*x^2+ 68*x)*log(x)^4+((40*x^4-2*x^2)*exp(x^2)-620*x^2-428*x-8)*log(x)^3+((-108*x ^4-8*x^3+30*x^2+4*x)*exp(x^2)+600*x^2+1220*x+120)*log(x)^2+(4*x^4*exp(x^2) ^2+(80*x^4+80*x^3-96*x^2-36*x)*exp(x^2)-1000*x^2-1600*x-600)*log(x)+(-20*x ^4-2*x^2)*exp(x^2)^2+(-200*x^4-200*x^3-20*x^2+80*x)*exp(x^2)+1000*x+1000)/ (x^3*log(x)^3-15*x^3*log(x)^2+75*x^3*log(x)-125*x^3),x, algorithm=\
(x^2*log(x)^6 - 10*x^2*log(x)^5 - 2*x^2*e^(x^2)*log(x)^3 + 29*x^2*log(x)^4 + 10*x^2*e^(x^2)*log(x)^2 - 40*x^2*log(x)^3 + 4*x*log(x)^4 - 4*x^2*e^(x^2 )*log(x) + 100*x^2*log(x)^2 - 40*x*log(x)^3 + x^2*e^(2*x^2) + 20*x^2*e^(x^ 2) - 4*x*e^(x^2)*log(x) + 108*x*log(x)^2 + 20*x*e^(x^2) - 80*x*log(x) + 4* log(x)^2 + 200*x - 40*log(x) + 100)/(x^2*log(x)^2 - 10*x^2*log(x) + 25*x^2 )
Timed out. \[ \int \frac {1000+1000 x+e^{x^2} \left (80 x-20 x^2-200 x^3-200 x^4\right )+e^{2 x^2} \left (-2 x^2-20 x^4\right )+\left (-600-1600 x-1000 x^2+4 e^{2 x^2} x^4+e^{x^2} \left (-36 x-96 x^2+80 x^3+80 x^4\right )\right ) \log (x)+\left (120+1220 x+600 x^2+e^{x^2} \left (4 x+30 x^2-8 x^3-108 x^4\right )\right ) \log ^2(x)+\left (-8-428 x-620 x^2+e^{x^2} \left (-2 x^2+40 x^4\right )\right ) \log ^3(x)+\left (68 x+308 x^2-4 e^{x^2} x^4\right ) \log ^4(x)+\left (-4 x-60 x^2\right ) \log ^5(x)+4 x^2 \log ^6(x)}{-125 x^3+75 x^3 \log (x)-15 x^3 \log ^2(x)+x^3 \log ^3(x)} \, dx=-\int -\frac {1000\,x-{\ln \left (x\right )}^5\,\left (60\,x^2+4\,x\right )-{\mathrm {e}}^{x^2}\,\left (200\,x^4+200\,x^3+20\,x^2-80\,x\right )-{\ln \left (x\right )}^3\,\left (428\,x+{\mathrm {e}}^{x^2}\,\left (2\,x^2-40\,x^4\right )+620\,x^2+8\right )+4\,x^2\,{\ln \left (x\right )}^6+{\ln \left (x\right )}^4\,\left (68\,x-4\,x^4\,{\mathrm {e}}^{x^2}+308\,x^2\right )+{\ln \left (x\right )}^2\,\left (1220\,x+{\mathrm {e}}^{x^2}\,\left (-108\,x^4-8\,x^3+30\,x^2+4\,x\right )+600\,x^2+120\right )-{\mathrm {e}}^{2\,x^2}\,\left (20\,x^4+2\,x^2\right )-\ln \left (x\right )\,\left (1600\,x+{\mathrm {e}}^{x^2}\,\left (-80\,x^4-80\,x^3+96\,x^2+36\,x\right )-4\,x^4\,{\mathrm {e}}^{2\,x^2}+1000\,x^2+600\right )+1000}{x^3\,{\ln \left (x\right )}^3-15\,x^3\,{\ln \left (x\right )}^2+75\,x^3\,\ln \left (x\right )-125\,x^3} \,d x \]
int((1000*x - log(x)^5*(4*x + 60*x^2) - exp(x^2)*(20*x^2 - 80*x + 200*x^3 + 200*x^4) - log(x)^3*(428*x + exp(x^2)*(2*x^2 - 40*x^4) + 620*x^2 + 8) + 4*x^2*log(x)^6 + log(x)^4*(68*x - 4*x^4*exp(x^2) + 308*x^2) + log(x)^2*(12 20*x + exp(x^2)*(4*x + 30*x^2 - 8*x^3 - 108*x^4) + 600*x^2 + 120) - exp(2* x^2)*(2*x^2 + 20*x^4) - log(x)*(1600*x + exp(x^2)*(36*x + 96*x^2 - 80*x^3 - 80*x^4) - 4*x^4*exp(2*x^2) + 1000*x^2 + 600) + 1000)/(75*x^3*log(x) - 15 *x^3*log(x)^2 + x^3*log(x)^3 - 125*x^3),x)
-int(-(1000*x - log(x)^5*(4*x + 60*x^2) - exp(x^2)*(20*x^2 - 80*x + 200*x^ 3 + 200*x^4) - log(x)^3*(428*x + exp(x^2)*(2*x^2 - 40*x^4) + 620*x^2 + 8) + 4*x^2*log(x)^6 + log(x)^4*(68*x - 4*x^4*exp(x^2) + 308*x^2) + log(x)^2*( 1220*x + exp(x^2)*(4*x + 30*x^2 - 8*x^3 - 108*x^4) + 600*x^2 + 120) - exp( 2*x^2)*(2*x^2 + 20*x^4) - log(x)*(1600*x + exp(x^2)*(36*x + 96*x^2 - 80*x^ 3 - 80*x^4) - 4*x^4*exp(2*x^2) + 1000*x^2 + 600) + 1000)/(75*x^3*log(x) - 15*x^3*log(x)^2 + x^3*log(x)^3 - 125*x^3), x)