Integrand size = 219, antiderivative size = 27 \[ \int \frac {2 e^{5 x^6} x-10 e^{4 x^6} x^2-242 x^6+220 e^2 x^6-50 e^4 x^6+e^{3 x^6} \left (100 x^3-240 x^9+e^2 \left (-40 x^3+120 x^9\right )\right )+e^{2 x^6} \left (-220 x^4+480 x^{10}+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{x^6} \left (770 x^5-2640 x^{11}+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (-680 x^5+2520 x^{11}\right )\right )}{e^{5 x^6}-5 e^{4 x^6} x+10 e^{3 x^6} x^2-10 e^{2 x^6} x^3+5 e^{x^6} x^4-x^5} \, dx=\left (x+\frac {5 \left (2-e^2\right ) x^3}{\left (-e^{x^6}+x\right )^2}\right )^2 \] Output:
(5*x^3/(x-exp(x^6))^2*(2-exp(2))+x)^2
Time = 10.07 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.70 \[ \int \frac {2 e^{5 x^6} x-10 e^{4 x^6} x^2-242 x^6+220 e^2 x^6-50 e^4 x^6+e^{3 x^6} \left (100 x^3-240 x^9+e^2 \left (-40 x^3+120 x^9\right )\right )+e^{2 x^6} \left (-220 x^4+480 x^{10}+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{x^6} \left (770 x^5-2640 x^{11}+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (-680 x^5+2520 x^{11}\right )\right )}{e^{5 x^6}-5 e^{4 x^6} x+10 e^{3 x^6} x^2-10 e^{2 x^6} x^3+5 e^{x^6} x^4-x^5} \, dx=\frac {x^2 \left (e^{2 x^6}-2 e^{x^6} x+11 x^2-5 e^2 x^2\right )^2}{\left (e^{x^6}-x\right )^4} \] Input:
Integrate[(2*E^(5*x^6)*x - 10*E^(4*x^6)*x^2 - 242*x^6 + 220*E^2*x^6 - 50*E ^4*x^6 + E^(3*x^6)*(100*x^3 - 240*x^9 + E^2*(-40*x^3 + 120*x^9)) + E^(2*x^ 6)*(-220*x^4 + 480*x^10 + E^2*(100*x^4 - 240*x^10)) + E^x^6*(770*x^5 - 264 0*x^11 + E^4*(150*x^5 - 600*x^11) + E^2*(-680*x^5 + 2520*x^11)))/(E^(5*x^6 ) - 5*E^(4*x^6)*x + 10*E^(3*x^6)*x^2 - 10*E^(2*x^6)*x^3 + 5*E^x^6*x^4 - x^ 5),x]
Output:
(x^2*(E^(2*x^6) - 2*E^x^6*x + 11*x^2 - 5*E^2*x^2)^2)/(E^x^6 - x)^4
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.
| \(\displaystyle \int \frac {-50 e^4 x^6+220 e^2 x^6-242 x^6+2 e^{5 x^6} x-10 e^{4 x^6} x^2+e^{x^6} \left (-2640 x^{11}+770 x^5+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (2520 x^{11}-680 x^5\right )\right )+e^{2 x^6} \left (480 x^{10}-220 x^4+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{3 x^6} \left (-240 x^9+100 x^3+e^2 \left (120 x^9-40 x^3\right )\right )}{-5 e^{4 x^6} x+e^{5 x^6}-x^5+5 e^{x^6} x^4-10 e^{2 x^6} x^3+10 e^{3 x^6} x^2} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (220 e^2-242\right ) x^6-50 e^4 x^6+2 e^{5 x^6} x-10 e^{4 x^6} x^2+e^{x^6} \left (-2640 x^{11}+770 x^5+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (2520 x^{11}-680 x^5\right )\right )+e^{2 x^6} \left (480 x^{10}-220 x^4+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{3 x^6} \left (-240 x^9+100 x^3+e^2 \left (120 x^9-40 x^3\right )\right )}{-5 e^{4 x^6} x+e^{5 x^6}-x^5+5 e^{x^6} x^4-10 e^{2 x^6} x^3+10 e^{3 x^6} x^2}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (-242+220 e^2-50 e^4\right ) x^6+2 e^{5 x^6} x-10 e^{4 x^6} x^2+e^{x^6} \left (-2640 x^{11}+770 x^5+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (2520 x^{11}-680 x^5\right )\right )+e^{2 x^6} \left (480 x^{10}-220 x^4+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{3 x^6} \left (-240 x^9+100 x^3+e^2 \left (120 x^9-40 x^3\right )\right )}{-5 e^{4 x^6} x+e^{5 x^6}-x^5+5 e^{x^6} x^4-10 e^{2 x^6} x^3+10 e^{3 x^6} x^2}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-242+220 e^2-50 e^4\right ) x^6+2 e^{5 x^6} x-10 e^{4 x^6} x^2+e^{x^6} \left (-2640 x^{11}+770 x^5+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (2520 x^{11}-680 x^5\right )\right )+e^{2 x^6} \left (480 x^{10}-220 x^4+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{3 x^6} \left (-240 x^9+100 x^3+e^2 \left (120 x^9-40 x^3\right )\right )}{\left (e^{x^6}-x\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {100 \left (e^2-2\right )^2 \left (6 x^6-1\right ) x^6}{\left (e^{x^6}-x\right )^5}-\frac {150 \left (e^2-2\right )^2 \left (4 x^6-1\right ) x^5}{\left (e^{x^6}-x\right )^4}+\frac {20 \left (e^2-2\right ) \left (6 x^6-1\right ) x^4}{\left (e^{x^6}-x\right )^3}+\frac {40 \left (e^2-2\right ) \left (3 x^6-1\right ) x^3}{\left (e^{x^6}-x\right )^2}+2 x\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 100 \left (2-e^2\right )^2 \int \frac {x^6}{\left (e^{x^6}-x\right )^5}dx-600 \left (2-e^2\right )^2 \int \frac {x^{12}}{\left (e^{x^6}-x\right )^5}dx-600 \left (2-e^2\right )^2 \int \frac {x^{11}}{\left (e^{x^6}-x\right )^4}dx-120 \left (2-e^2\right ) \int \frac {x^{10}}{\left (e^{x^6}-x\right )^3}dx-120 \left (2-e^2\right ) \int \frac {x^9}{\left (e^{x^6}-x\right )^2}dx+150 \left (2-e^2\right )^2 \int \frac {x^5}{\left (e^{x^6}-x\right )^4}dx+20 \left (2-e^2\right ) \int \frac {x^4}{\left (e^{x^6}-x\right )^3}dx+40 \left (2-e^2\right ) \int \frac {x^3}{\left (e^{x^6}-x\right )^2}dx+x^2\) |
Input:
Int[(2*E^(5*x^6)*x - 10*E^(4*x^6)*x^2 - 242*x^6 + 220*E^2*x^6 - 50*E^4*x^6 + E^(3*x^6)*(100*x^3 - 240*x^9 + E^2*(-40*x^3 + 120*x^9)) + E^(2*x^6)*(-2 20*x^4 + 480*x^10 + E^2*(100*x^4 - 240*x^10)) + E^x^6*(770*x^5 - 2640*x^11 + E^4*(150*x^5 - 600*x^11) + E^2*(-680*x^5 + 2520*x^11)))/(E^(5*x^6) - 5* E^(4*x^6)*x + 10*E^(3*x^6)*x^2 - 10*E^(2*x^6)*x^3 + 5*E^x^6*x^4 - x^5),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(75\) vs. \(2(25)=50\).
Time = 2.38 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.81
| method | result | size |
| risch | \(x^{2}+\frac {5 x^{4} \left (5 x^{2} {\mathrm e}^{4}-22 x^{2} {\mathrm e}^{2}+4 \,{\mathrm e}^{2} x \,{\mathrm e}^{x^{6}}-2 \,{\mathrm e}^{2} {\mathrm e}^{2 x^{6}}+24 x^{2}-8 x \,{\mathrm e}^{x^{6}}+4 \,{\mathrm e}^{2 x^{6}}\right )}{\left (x -{\mathrm e}^{x^{6}}\right )^{4}}\) | \(76\) |
| parallelrisch | \(\frac {25 x^{6} {\mathrm e}^{4}-110 x^{6} {\mathrm e}^{2}+20 \,{\mathrm e}^{x^{6}} {\mathrm e}^{2} x^{5}-10 \,{\mathrm e}^{2 x^{6}} {\mathrm e}^{2} x^{4}+121 x^{6}-44 x^{5} {\mathrm e}^{x^{6}}+26 \,{\mathrm e}^{2 x^{6}} x^{4}-4 \,{\mathrm e}^{3 x^{6}} x^{3}+x^{2} {\mathrm e}^{4 x^{6}}}{x^{4}-4 x^{3} {\mathrm e}^{x^{6}}+6 x^{2} {\mathrm e}^{2 x^{6}}-4 x \,{\mathrm e}^{3 x^{6}}+{\mathrm e}^{4 x^{6}}}\) | \(130\) |
Input:
int((2*x*exp(x^6)^5-10*x^2*exp(x^6)^4+((120*x^9-40*x^3)*exp(2)-240*x^9+100 *x^3)*exp(x^6)^3+((-240*x^10+100*x^4)*exp(2)+480*x^10-220*x^4)*exp(x^6)^2+ ((-600*x^11+150*x^5)*exp(2)^2+(2520*x^11-680*x^5)*exp(2)-2640*x^11+770*x^5 )*exp(x^6)-50*x^6*exp(2)^2+220*x^6*exp(2)-242*x^6)/(exp(x^6)^5-5*x*exp(x^6 )^4+10*x^2*exp(x^6)^3-10*x^3*exp(x^6)^2+5*x^4*exp(x^6)-x^5),x,method=_RETU RNVERBOSE)
Output:
x^2+5*x^4*(5*x^2*exp(2)^2-22*x^2*exp(2)+4*exp(2)*x*exp(x^6)-2*exp(2)*exp(x ^6)^2+24*x^2-8*x*exp(x^6)+4*exp(x^6)^2)/(x-exp(x^6))^4
Leaf count of result is larger than twice the leaf count of optimal. 123 vs. \(2 (25) = 50\).
Time = 0.13 (sec) , antiderivative size = 123, normalized size of antiderivative = 4.56 \[ \int \frac {2 e^{5 x^6} x-10 e^{4 x^6} x^2-242 x^6+220 e^2 x^6-50 e^4 x^6+e^{3 x^6} \left (100 x^3-240 x^9+e^2 \left (-40 x^3+120 x^9\right )\right )+e^{2 x^6} \left (-220 x^4+480 x^{10}+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{x^6} \left (770 x^5-2640 x^{11}+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (-680 x^5+2520 x^{11}\right )\right )}{e^{5 x^6}-5 e^{4 x^6} x+10 e^{3 x^6} x^2-10 e^{2 x^6} x^3+5 e^{x^6} x^4-x^5} \, dx=\frac {25 \, x^{6} e^{4} - 110 \, x^{6} e^{2} + 121 \, x^{6} - 4 \, x^{3} e^{\left (3 \, x^{6}\right )} + x^{2} e^{\left (4 \, x^{6}\right )} - 2 \, {\left (5 \, x^{4} e^{2} - 13 \, x^{4}\right )} e^{\left (2 \, x^{6}\right )} + 4 \, {\left (5 \, x^{5} e^{2} - 11 \, x^{5}\right )} e^{\left (x^{6}\right )}}{x^{4} - 4 \, x^{3} e^{\left (x^{6}\right )} + 6 \, x^{2} e^{\left (2 \, x^{6}\right )} - 4 \, x e^{\left (3 \, x^{6}\right )} + e^{\left (4 \, x^{6}\right )}} \] Input:
integrate((2*x*exp(x^6)^5-10*x^2*exp(x^6)^4+((120*x^9-40*x^3)*exp(2)-240*x ^9+100*x^3)*exp(x^6)^3+((-240*x^10+100*x^4)*exp(2)+480*x^10-220*x^4)*exp(x ^6)^2+((-600*x^11+150*x^5)*exp(2)^2+(2520*x^11-680*x^5)*exp(2)-2640*x^11+7 70*x^5)*exp(x^6)-50*x^6*exp(2)^2+220*x^6*exp(2)-242*x^6)/(exp(x^6)^5-5*x*e xp(x^6)^4+10*x^2*exp(x^6)^3-10*x^3*exp(x^6)^2+5*x^4*exp(x^6)-x^5),x, algor ithm="fricas")
Output:
(25*x^6*e^4 - 110*x^6*e^2 + 121*x^6 - 4*x^3*e^(3*x^6) + x^2*e^(4*x^6) - 2* (5*x^4*e^2 - 13*x^4)*e^(2*x^6) + 4*(5*x^5*e^2 - 11*x^5)*e^(x^6))/(x^4 - 4* x^3*e^(x^6) + 6*x^2*e^(2*x^6) - 4*x*e^(3*x^6) + e^(4*x^6))
Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (20) = 40\).
Time = 0.13 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.89 \[ \int \frac {2 e^{5 x^6} x-10 e^{4 x^6} x^2-242 x^6+220 e^2 x^6-50 e^4 x^6+e^{3 x^6} \left (100 x^3-240 x^9+e^2 \left (-40 x^3+120 x^9\right )\right )+e^{2 x^6} \left (-220 x^4+480 x^{10}+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{x^6} \left (770 x^5-2640 x^{11}+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (-680 x^5+2520 x^{11}\right )\right )}{e^{5 x^6}-5 e^{4 x^6} x+10 e^{3 x^6} x^2-10 e^{2 x^6} x^3+5 e^{x^6} x^4-x^5} \, dx=x^{2} + \frac {- 110 x^{6} e^{2} + 120 x^{6} + 25 x^{6} e^{4} + \left (- 40 x^{5} + 20 x^{5} e^{2}\right ) e^{x^{6}} + \left (- 10 x^{4} e^{2} + 20 x^{4}\right ) e^{2 x^{6}}}{x^{4} - 4 x^{3} e^{x^{6}} + 6 x^{2} e^{2 x^{6}} - 4 x e^{3 x^{6}} + e^{4 x^{6}}} \] Input:
integrate((2*x*exp(x**6)**5-10*x**2*exp(x**6)**4+((120*x**9-40*x**3)*exp(2 )-240*x**9+100*x**3)*exp(x**6)**3+((-240*x**10+100*x**4)*exp(2)+480*x**10- 220*x**4)*exp(x**6)**2+((-600*x**11+150*x**5)*exp(2)**2+(2520*x**11-680*x* *5)*exp(2)-2640*x**11+770*x**5)*exp(x**6)-50*x**6*exp(2)**2+220*x**6*exp(2 )-242*x**6)/(exp(x**6)**5-5*x*exp(x**6)**4+10*x**2*exp(x**6)**3-10*x**3*ex p(x**6)**2+5*x**4*exp(x**6)-x**5),x)
Output:
x**2 + (-110*x**6*exp(2) + 120*x**6 + 25*x**6*exp(4) + (-40*x**5 + 20*x**5 *exp(2))*exp(x**6) + (-10*x**4*exp(2) + 20*x**4)*exp(2*x**6))/(x**4 - 4*x* *3*exp(x**6) + 6*x**2*exp(2*x**6) - 4*x*exp(3*x**6) + exp(4*x**6))
Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (25) = 50\).
Time = 0.10 (sec) , antiderivative size = 110, normalized size of antiderivative = 4.07 \[ \int \frac {2 e^{5 x^6} x-10 e^{4 x^6} x^2-242 x^6+220 e^2 x^6-50 e^4 x^6+e^{3 x^6} \left (100 x^3-240 x^9+e^2 \left (-40 x^3+120 x^9\right )\right )+e^{2 x^6} \left (-220 x^4+480 x^{10}+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{x^6} \left (770 x^5-2640 x^{11}+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (-680 x^5+2520 x^{11}\right )\right )}{e^{5 x^6}-5 e^{4 x^6} x+10 e^{3 x^6} x^2-10 e^{2 x^6} x^3+5 e^{x^6} x^4-x^5} \, dx=\frac {x^{6} {\left (25 \, e^{4} - 110 \, e^{2} + 121\right )} + 4 \, x^{5} {\left (5 \, e^{2} - 11\right )} e^{\left (x^{6}\right )} - 2 \, x^{4} {\left (5 \, e^{2} - 13\right )} e^{\left (2 \, x^{6}\right )} - 4 \, x^{3} e^{\left (3 \, x^{6}\right )} + x^{2} e^{\left (4 \, x^{6}\right )}}{x^{4} - 4 \, x^{3} e^{\left (x^{6}\right )} + 6 \, x^{2} e^{\left (2 \, x^{6}\right )} - 4 \, x e^{\left (3 \, x^{6}\right )} + e^{\left (4 \, x^{6}\right )}} \] Input:
integrate((2*x*exp(x^6)^5-10*x^2*exp(x^6)^4+((120*x^9-40*x^3)*exp(2)-240*x ^9+100*x^3)*exp(x^6)^3+((-240*x^10+100*x^4)*exp(2)+480*x^10-220*x^4)*exp(x ^6)^2+((-600*x^11+150*x^5)*exp(2)^2+(2520*x^11-680*x^5)*exp(2)-2640*x^11+7 70*x^5)*exp(x^6)-50*x^6*exp(2)^2+220*x^6*exp(2)-242*x^6)/(exp(x^6)^5-5*x*e xp(x^6)^4+10*x^2*exp(x^6)^3-10*x^3*exp(x^6)^2+5*x^4*exp(x^6)-x^5),x, algor ithm="maxima")
Output:
(x^6*(25*e^4 - 110*e^2 + 121) + 4*x^5*(5*e^2 - 11)*e^(x^6) - 2*x^4*(5*e^2 - 13)*e^(2*x^6) - 4*x^3*e^(3*x^6) + x^2*e^(4*x^6))/(x^4 - 4*x^3*e^(x^6) + 6*x^2*e^(2*x^6) - 4*x*e^(3*x^6) + e^(4*x^6))
Leaf count of result is larger than twice the leaf count of optimal. 127 vs. \(2 (25) = 50\).
Time = 0.18 (sec) , antiderivative size = 127, normalized size of antiderivative = 4.70 \[ \int \frac {2 e^{5 x^6} x-10 e^{4 x^6} x^2-242 x^6+220 e^2 x^6-50 e^4 x^6+e^{3 x^6} \left (100 x^3-240 x^9+e^2 \left (-40 x^3+120 x^9\right )\right )+e^{2 x^6} \left (-220 x^4+480 x^{10}+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{x^6} \left (770 x^5-2640 x^{11}+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (-680 x^5+2520 x^{11}\right )\right )}{e^{5 x^6}-5 e^{4 x^6} x+10 e^{3 x^6} x^2-10 e^{2 x^6} x^3+5 e^{x^6} x^4-x^5} \, dx=\frac {25 \, x^{6} e^{4} - 110 \, x^{6} e^{2} + 121 \, x^{6} + 20 \, x^{5} e^{\left (x^{6} + 2\right )} - 44 \, x^{5} e^{\left (x^{6}\right )} + 26 \, x^{4} e^{\left (2 \, x^{6}\right )} - 10 \, x^{4} e^{\left (2 \, x^{6} + 2\right )} - 4 \, x^{3} e^{\left (3 \, x^{6}\right )} + x^{2} e^{\left (4 \, x^{6}\right )}}{x^{4} - 4 \, x^{3} e^{\left (x^{6}\right )} + 6 \, x^{2} e^{\left (2 \, x^{6}\right )} - 4 \, x e^{\left (3 \, x^{6}\right )} + e^{\left (4 \, x^{6}\right )}} \] Input:
integrate((2*x*exp(x^6)^5-10*x^2*exp(x^6)^4+((120*x^9-40*x^3)*exp(2)-240*x ^9+100*x^3)*exp(x^6)^3+((-240*x^10+100*x^4)*exp(2)+480*x^10-220*x^4)*exp(x ^6)^2+((-600*x^11+150*x^5)*exp(2)^2+(2520*x^11-680*x^5)*exp(2)-2640*x^11+7 70*x^5)*exp(x^6)-50*x^6*exp(2)^2+220*x^6*exp(2)-242*x^6)/(exp(x^6)^5-5*x*e xp(x^6)^4+10*x^2*exp(x^6)^3-10*x^3*exp(x^6)^2+5*x^4*exp(x^6)-x^5),x, algor ithm="giac")
Output:
(25*x^6*e^4 - 110*x^6*e^2 + 121*x^6 + 20*x^5*e^(x^6 + 2) - 44*x^5*e^(x^6) + 26*x^4*e^(2*x^6) - 10*x^4*e^(2*x^6 + 2) - 4*x^3*e^(3*x^6) + x^2*e^(4*x^6 ))/(x^4 - 4*x^3*e^(x^6) + 6*x^2*e^(2*x^6) - 4*x*e^(3*x^6) + e^(4*x^6))
Time = 3.22 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.56 \[ \int \frac {2 e^{5 x^6} x-10 e^{4 x^6} x^2-242 x^6+220 e^2 x^6-50 e^4 x^6+e^{3 x^6} \left (100 x^3-240 x^9+e^2 \left (-40 x^3+120 x^9\right )\right )+e^{2 x^6} \left (-220 x^4+480 x^{10}+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{x^6} \left (770 x^5-2640 x^{11}+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (-680 x^5+2520 x^{11}\right )\right )}{e^{5 x^6}-5 e^{4 x^6} x+10 e^{3 x^6} x^2-10 e^{2 x^6} x^3+5 e^{x^6} x^4-x^5} \, dx=\frac {x^2\,{\left ({\mathrm {e}}^{2\,x^6}-2\,x\,{\mathrm {e}}^{x^6}-5\,x^2\,{\mathrm {e}}^2+11\,x^2\right )}^2}{{\left (x-{\mathrm {e}}^{x^6}\right )}^4} \] Input:
int(-(exp(3*x^6)*(exp(2)*(40*x^3 - 120*x^9) - 100*x^3 + 240*x^9) - exp(2*x ^6)*(exp(2)*(100*x^4 - 240*x^10) - 220*x^4 + 480*x^10) - 2*x*exp(5*x^6) - exp(x^6)*(exp(4)*(150*x^5 - 600*x^11) - exp(2)*(680*x^5 - 2520*x^11) + 770 *x^5 - 2640*x^11) - 220*x^6*exp(2) + 50*x^6*exp(4) + 10*x^2*exp(4*x^6) + 2 42*x^6)/(exp(5*x^6) - 5*x*exp(4*x^6) + 5*x^4*exp(x^6) + 10*x^2*exp(3*x^6) - 10*x^3*exp(2*x^6) - x^5),x)
Output:
(x^2*(exp(2*x^6) - 2*x*exp(x^6) - 5*x^2*exp(2) + 11*x^2)^2)/(x - exp(x^6)) ^4
Time = 0.17 (sec) , antiderivative size = 138, normalized size of antiderivative = 5.11 \[ \int \frac {2 e^{5 x^6} x-10 e^{4 x^6} x^2-242 x^6+220 e^2 x^6-50 e^4 x^6+e^{3 x^6} \left (100 x^3-240 x^9+e^2 \left (-40 x^3+120 x^9\right )\right )+e^{2 x^6} \left (-220 x^4+480 x^{10}+e^2 \left (100 x^4-240 x^{10}\right )\right )+e^{x^6} \left (770 x^5-2640 x^{11}+e^4 \left (150 x^5-600 x^{11}\right )+e^2 \left (-680 x^5+2520 x^{11}\right )\right )}{e^{5 x^6}-5 e^{4 x^6} x+10 e^{3 x^6} x^2-10 e^{2 x^6} x^3+5 e^{x^6} x^4-x^5} \, dx=\frac {x^{2} \left (e^{4 x^{6}}-4 e^{3 x^{6}} x -10 e^{2 x^{6}} e^{2} x^{2}+26 e^{2 x^{6}} x^{2}+20 e^{x^{6}} e^{2} x^{3}-44 e^{x^{6}} x^{3}+25 e^{4} x^{4}-110 e^{2} x^{4}+121 x^{4}\right )}{e^{4 x^{6}}-4 e^{3 x^{6}} x +6 e^{2 x^{6}} x^{2}-4 e^{x^{6}} x^{3}+x^{4}} \] Input:
int((2*x*exp(x^6)^5-10*x^2*exp(x^6)^4+((120*x^9-40*x^3)*exp(2)-240*x^9+100 *x^3)*exp(x^6)^3+((-240*x^10+100*x^4)*exp(2)+480*x^10-220*x^4)*exp(x^6)^2+ ((-600*x^11+150*x^5)*exp(2)^2+(2520*x^11-680*x^5)*exp(2)-2640*x^11+770*x^5 )*exp(x^6)-50*x^6*exp(2)^2+220*x^6*exp(2)-242*x^6)/(exp(x^6)^5-5*x*exp(x^6 )^4+10*x^2*exp(x^6)^3-10*x^3*exp(x^6)^2+5*x^4*exp(x^6)-x^5),x)
Output:
(x**2*(e**(4*x**6) - 4*e**(3*x**6)*x - 10*e**(2*x**6)*e**2*x**2 + 26*e**(2 *x**6)*x**2 + 20*e**(x**6)*e**2*x**3 - 44*e**(x**6)*x**3 + 25*e**4*x**4 - 110*e**2*x**4 + 121*x**4))/(e**(4*x**6) - 4*e**(3*x**6)*x + 6*e**(2*x**6)* x**2 - 4*e**(x**6)*x**3 + x**4)