Integrand size = 501, antiderivative size = 37 \[ \int \frac {120 x+116 x^2+36 x^3+58 x^4+54 x^5+18 x^6+2 x^7+e^{3 x} \left (4 x+2 x^4\right )+e^{2 x} \left (36 x+12 x^2+18 x^4+6 x^5\right )+e^x \left (112 x+76 x^2+12 x^3+54 x^4+36 x^5+6 x^6\right )+e^{4 x} \left (54 x^2+2 e^{3 x} x^2+54 x^3+18 x^4+2 x^5+e^{2 x} \left (18 x^2+6 x^3\right )+e^x \left (54 x^2+36 x^3+6 x^4\right )\right )+e^{2 x} \left (-60-180 x-130 x^2-146 x^3-112 x^4-36 x^5-4 x^6+e^{3 x} \left (-2-4 x-4 x^3\right )+e^{2 x} \left (-18-42 x-12 x^2-36 x^3-12 x^4\right )+e^x \left (-56-152 x-78 x^2-120 x^3-72 x^4-12 x^5\right )\right )}{27 x^4+e^{3 x} x^4+27 x^5+9 x^6+x^7+e^{2 x} \left (9 x^4+3 x^5\right )+e^x \left (27 x^4+18 x^5+3 x^6\right )+e^{4 x} \left (27 x^2+e^{3 x} x^2+27 x^3+9 x^4+x^5+e^{2 x} \left (9 x^2+3 x^3\right )+e^x \left (27 x^2+18 x^3+3 x^4\right )\right )+e^{2 x} \left (-54 x^3-2 e^{3 x} x^3-54 x^4-18 x^5-2 x^6+e^{2 x} \left (-18 x^3-6 x^4\right )+e^x \left (-54 x^3-36 x^4-6 x^5\right )\right )} \, dx=2 x+\frac {2}{\left (e^{2 x}-x\right ) \left (x+\frac {x}{-1-\left (3+e^x+x\right )^2}\right )} \] Output:
2/(x+x/(-1-(exp(x)+3+x)^2))/(exp(2*x)-x)+2*x
Leaf count is larger than twice the leaf count of optimal. \(99\) vs. \(2(37)=74\).
Time = 10.15 (sec) , antiderivative size = 99, normalized size of antiderivative = 2.68 \[ \int \frac {120 x+116 x^2+36 x^3+58 x^4+54 x^5+18 x^6+2 x^7+e^{3 x} \left (4 x+2 x^4\right )+e^{2 x} \left (36 x+12 x^2+18 x^4+6 x^5\right )+e^x \left (112 x+76 x^2+12 x^3+54 x^4+36 x^5+6 x^6\right )+e^{4 x} \left (54 x^2+2 e^{3 x} x^2+54 x^3+18 x^4+2 x^5+e^{2 x} \left (18 x^2+6 x^3\right )+e^x \left (54 x^2+36 x^3+6 x^4\right )\right )+e^{2 x} \left (-60-180 x-130 x^2-146 x^3-112 x^4-36 x^5-4 x^6+e^{3 x} \left (-2-4 x-4 x^3\right )+e^{2 x} \left (-18-42 x-12 x^2-36 x^3-12 x^4\right )+e^x \left (-56-152 x-78 x^2-120 x^3-72 x^4-12 x^5\right )\right )}{27 x^4+e^{3 x} x^4+27 x^5+9 x^6+x^7+e^{2 x} \left (9 x^4+3 x^5\right )+e^x \left (27 x^4+18 x^5+3 x^6\right )+e^{4 x} \left (27 x^2+e^{3 x} x^2+27 x^3+9 x^4+x^5+e^{2 x} \left (9 x^2+3 x^3\right )+e^x \left (27 x^2+18 x^3+3 x^4\right )\right )+e^{2 x} \left (-54 x^3-2 e^{3 x} x^3-54 x^4-18 x^5-2 x^6+e^{2 x} \left (-18 x^3-6 x^4\right )+e^x \left (-54 x^3-36 x^4-6 x^5\right )\right )} \, dx=\frac {2 \left (x^2+\frac {2 (3+x)}{\left (3+e^x+x\right ) \left (9+5 x+x^2\right )^2}+\frac {1}{\left (3+e^x+x\right )^2 \left (9+5 x+x^2\right )}+\frac {90+97 x+44 x^2+10 x^3+x^4-2 e^x (3+x)}{\left (e^{2 x}-x\right ) \left (9+5 x+x^2\right )^2}\right )}{x} \] Input:
Integrate[(120*x + 116*x^2 + 36*x^3 + 58*x^4 + 54*x^5 + 18*x^6 + 2*x^7 + E ^(3*x)*(4*x + 2*x^4) + E^(2*x)*(36*x + 12*x^2 + 18*x^4 + 6*x^5) + E^x*(112 *x + 76*x^2 + 12*x^3 + 54*x^4 + 36*x^5 + 6*x^6) + E^(4*x)*(54*x^2 + 2*E^(3 *x)*x^2 + 54*x^3 + 18*x^4 + 2*x^5 + E^(2*x)*(18*x^2 + 6*x^3) + E^x*(54*x^2 + 36*x^3 + 6*x^4)) + E^(2*x)*(-60 - 180*x - 130*x^2 - 146*x^3 - 112*x^4 - 36*x^5 - 4*x^6 + E^(3*x)*(-2 - 4*x - 4*x^3) + E^(2*x)*(-18 - 42*x - 12*x^ 2 - 36*x^3 - 12*x^4) + E^x*(-56 - 152*x - 78*x^2 - 120*x^3 - 72*x^4 - 12*x ^5)))/(27*x^4 + E^(3*x)*x^4 + 27*x^5 + 9*x^6 + x^7 + E^(2*x)*(9*x^4 + 3*x^ 5) + E^x*(27*x^4 + 18*x^5 + 3*x^6) + E^(4*x)*(27*x^2 + E^(3*x)*x^2 + 27*x^ 3 + 9*x^4 + x^5 + E^(2*x)*(9*x^2 + 3*x^3) + E^x*(27*x^2 + 18*x^3 + 3*x^4)) + E^(2*x)*(-54*x^3 - 2*E^(3*x)*x^3 - 54*x^4 - 18*x^5 - 2*x^6 + E^(2*x)*(- 18*x^3 - 6*x^4) + E^x*(-54*x^3 - 36*x^4 - 6*x^5))),x]
Output:
(2*(x^2 + (2*(3 + x))/((3 + E^x + x)*(9 + 5*x + x^2)^2) + 1/((3 + E^x + x) ^2*(9 + 5*x + x^2)) + (90 + 97*x + 44*x^2 + 10*x^3 + x^4 - 2*E^x*(3 + x))/ ((E^(2*x) - x)*(9 + 5*x + x^2)^2)))/x
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.
| \(\displaystyle \int \frac {2 x^7+18 x^6+54 x^5+58 x^4+e^{3 x} \left (2 x^4+4 x\right )+36 x^3+116 x^2+e^{2 x} \left (6 x^5+18 x^4+12 x^2+36 x\right )+e^{4 x} \left (2 x^5+18 x^4+54 x^3+2 e^{3 x} x^2+54 x^2+e^{2 x} \left (6 x^3+18 x^2\right )+e^x \left (6 x^4+36 x^3+54 x^2\right )\right )+e^x \left (6 x^6+36 x^5+54 x^4+12 x^3+76 x^2+112 x\right )+e^{2 x} \left (-4 x^6-36 x^5-112 x^4-146 x^3+e^{3 x} \left (-4 x^3-4 x-2\right )-130 x^2+e^{2 x} \left (-12 x^4-36 x^3-12 x^2-42 x-18\right )+e^x \left (-12 x^5-72 x^4-120 x^3-78 x^2-152 x-56\right )-180 x-60\right )+120 x}{x^7+9 x^6+27 x^5+e^{3 x} x^4+27 x^4+e^{2 x} \left (3 x^5+9 x^4\right )+e^x \left (3 x^6+18 x^5+27 x^4\right )+e^{2 x} \left (-2 x^6-18 x^5-54 x^4-2 e^{3 x} x^3-54 x^3+e^{2 x} \left (-6 x^4-18 x^3\right )+e^x \left (-6 x^5-36 x^4-54 x^3\right )\right )+e^{4 x} \left (x^5+9 x^4+27 x^3+e^{3 x} x^2+27 x^2+e^{2 x} \left (3 x^3+9 x^2\right )+e^x \left (3 x^4+18 x^3+27 x^2\right )\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (e^{7 x} x^2+3 e^{6 x} (x+3) x^2+e^{5 x} \left (3 x^4+16 x^3+27 x^2-2 x-1\right )+e^x \left (3 x^5+18 x^4+27 x^3+6 x^2+38 x+56\right ) x+e^{4 x} \left (x^5+3 x^4+9 x^3+21 x^2-21 x-9\right )-e^{3 x} \left (6 x^5+35 x^4+60 x^3+39 x^2+74 x+28\right )+\left (x^6+9 x^5+27 x^4+29 x^3+18 x^2+58 x+60\right ) x-e^{2 x} \left (2 x^6+15 x^5+47 x^4+73 x^3+59 x^2+72 x+30\right )\right )}{\left (e^{2 x}-x\right )^2 x^2 \left (x+e^x+3\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {e^{7 x} x^2+3 e^{6 x} (x+3) x^2+e^x \left (3 x^5+18 x^4+27 x^3+6 x^2+38 x+56\right ) x+\left (x^6+9 x^5+27 x^4+29 x^3+18 x^2+58 x+60\right ) x-e^{5 x} \left (-3 x^4-16 x^3-27 x^2+2 x+1\right )-e^{4 x} \left (-x^5-3 x^4-9 x^3-21 x^2+21 x+9\right )-e^{3 x} \left (6 x^5+35 x^4+60 x^3+39 x^2+74 x+28\right )-e^{2 x} \left (2 x^6+15 x^5+47 x^4+73 x^3+59 x^2+72 x+30\right )}{\left (e^{2 x}-x\right )^2 x^2 \left (x+e^x+3\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 (x+2)}{x \left (x+e^x+3\right )^3 \left (x^2+5 x+9\right )}-\frac {3 x^2+16 x+9}{x^2 \left (x+e^x+3\right )^2 \left (x^2+5 x+9\right )^2}+\frac {(2 x-1) \left (-x^4-10 x^3-44 x^2+2 e^x x-97 x+6 e^x-90\right )}{\left (e^{2 x}-x\right )^2 x \left (x^2+5 x+9\right )^2}-\frac {2 \left (x^4+12 x^3+49 x^2+72 x+27\right )}{x^2 \left (x+e^x+3\right ) \left (x^2+5 x+9\right )^3}+\frac {-2 x^7-31 x^6-221 x^5+2 e^x x^4-919 x^4+24 e^x x^3-2370 x^3+98 e^x x^2-3670 x^2+144 e^x x-2970 x+54 e^x-810}{\left (e^{2 x}-x\right ) x^2 \left (x^2+5 x+9\right )^3}+1\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle 2 \int \left (\frac {2 (x+2)}{x \left (x+e^x+3\right )^3 \left (x^2+5 x+9\right )}-\frac {3 x^2+16 x+9}{x^2 \left (x+e^x+3\right )^2 \left (x^2+5 x+9\right )^2}+\frac {(2 x-1) \left (-x^4-10 x^3-44 x^2+2 e^x x-97 x+6 e^x-90\right )}{\left (e^{2 x}-x\right )^2 x \left (x^2+5 x+9\right )^2}-\frac {2 \left (x^4+12 x^3+49 x^2+72 x+27\right )}{x^2 \left (x+e^x+3\right ) \left (x^2+5 x+9\right )^3}+\frac {-2 x^7-31 x^6-221 x^5+2 e^x x^4-919 x^4+24 e^x x^3-2370 x^3+98 e^x x^2-3670 x^2+144 e^x x-2970 x+54 e^x-810}{\left (e^{2 x}-x\right ) x^2 \left (x^2+5 x+9\right )^3}+1\right )dx\) |
Input:
Int[(120*x + 116*x^2 + 36*x^3 + 58*x^4 + 54*x^5 + 18*x^6 + 2*x^7 + E^(3*x) *(4*x + 2*x^4) + E^(2*x)*(36*x + 12*x^2 + 18*x^4 + 6*x^5) + E^x*(112*x + 7 6*x^2 + 12*x^3 + 54*x^4 + 36*x^5 + 6*x^6) + E^(4*x)*(54*x^2 + 2*E^(3*x)*x^ 2 + 54*x^3 + 18*x^4 + 2*x^5 + E^(2*x)*(18*x^2 + 6*x^3) + E^x*(54*x^2 + 36* x^3 + 6*x^4)) + E^(2*x)*(-60 - 180*x - 130*x^2 - 146*x^3 - 112*x^4 - 36*x^ 5 - 4*x^6 + E^(3*x)*(-2 - 4*x - 4*x^3) + E^(2*x)*(-18 - 42*x - 12*x^2 - 36 *x^3 - 12*x^4) + E^x*(-56 - 152*x - 78*x^2 - 120*x^3 - 72*x^4 - 12*x^5)))/ (27*x^4 + E^(3*x)*x^4 + 27*x^5 + 9*x^6 + x^7 + E^(2*x)*(9*x^4 + 3*x^5) + E ^x*(27*x^4 + 18*x^5 + 3*x^6) + E^(4*x)*(27*x^2 + E^(3*x)*x^2 + 27*x^3 + 9* x^4 + x^5 + E^(2*x)*(9*x^2 + 3*x^3) + E^x*(27*x^2 + 18*x^3 + 3*x^4)) + E^( 2*x)*(-54*x^3 - 2*E^(3*x)*x^3 - 54*x^4 - 18*x^5 - 2*x^6 + E^(2*x)*(-18*x^3 - 6*x^4) + E^x*(-54*x^3 - 36*x^4 - 6*x^5))),x]
Output:
$Aborted
Time = 201.68 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.30
| method | result | size |
| risch | \(2 x -\frac {2 \left (x^{2}+2 \,{\mathrm e}^{x} x +{\mathrm e}^{2 x}+6 x +6 \,{\mathrm e}^{x}+10\right )}{x \left (x -{\mathrm e}^{2 x}\right ) \left ({\mathrm e}^{x}+3+x \right )^{2}}\) | \(48\) |
| parallelrisch | \(\frac {-20-12 x -10 \,{\mathrm e}^{2 x} x^{3}-2 \left ({\mathrm e}^{2 x}\right )^{2} x^{2}-18 \,{\mathrm e}^{2 x} x^{2}+4 \,{\mathrm e}^{x} x^{4}+12 \,{\mathrm e}^{x} x^{3}-2 x^{4} {\mathrm e}^{2 x}-2 \,{\mathrm e}^{2 x}-4 \,{\mathrm e}^{x} x -2 x^{2}+18 x^{3}+12 x^{4}+2 x^{5}-12 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{x} {\mathrm e}^{2 x} x^{3}-12 \,{\mathrm e}^{x} {\mathrm e}^{2 x} x^{2}}{x \left (x^{3}+2 \,{\mathrm e}^{x} x^{2}-{\mathrm e}^{2 x} x^{2}-5 x \,{\mathrm e}^{2 x}-2 \,{\mathrm e}^{x} {\mathrm e}^{2 x} x -\left ({\mathrm e}^{2 x}\right )^{2}+6 x^{2}+6 \,{\mathrm e}^{x} x -6 \,{\mathrm e}^{x} {\mathrm e}^{2 x}+9 x -9 \,{\mathrm e}^{2 x}\right )}\) | \(211\) |
Input:
int(((2*x^2*exp(x)^3+(6*x^3+18*x^2)*exp(x)^2+(6*x^4+36*x^3+54*x^2)*exp(x)+ 2*x^5+18*x^4+54*x^3+54*x^2)*exp(2*x)^2+((-4*x^3-4*x-2)*exp(x)^3+(-12*x^4-3 6*x^3-12*x^2-42*x-18)*exp(x)^2+(-12*x^5-72*x^4-120*x^3-78*x^2-152*x-56)*ex p(x)-4*x^6-36*x^5-112*x^4-146*x^3-130*x^2-180*x-60)*exp(2*x)+(2*x^4+4*x)*e xp(x)^3+(6*x^5+18*x^4+12*x^2+36*x)*exp(x)^2+(6*x^6+36*x^5+54*x^4+12*x^3+76 *x^2+112*x)*exp(x)+2*x^7+18*x^6+54*x^5+58*x^4+36*x^3+116*x^2+120*x)/((x^2* exp(x)^3+(3*x^3+9*x^2)*exp(x)^2+(3*x^4+18*x^3+27*x^2)*exp(x)+x^5+9*x^4+27* x^3+27*x^2)*exp(2*x)^2+(-2*x^3*exp(x)^3+(-6*x^4-18*x^3)*exp(x)^2+(-6*x^5-3 6*x^4-54*x^3)*exp(x)-2*x^6-18*x^5-54*x^4-54*x^3)*exp(2*x)+x^4*exp(x)^3+(3* x^5+9*x^4)*exp(x)^2+(3*x^6+18*x^5+27*x^4)*exp(x)+x^7+9*x^6+27*x^5+27*x^4), x,method=_RETURNVERBOSE)
Output:
2*x-2/x*(x^2+2*exp(x)*x+exp(2*x)+6*x+6*exp(x)+10)/(x-exp(2*x))/(exp(x)+3+x )^2
Leaf count of result is larger than twice the leaf count of optimal. 154 vs. \(2 (34) = 68\).
Time = 0.10 (sec) , antiderivative size = 154, normalized size of antiderivative = 4.16 \[ \int \frac {120 x+116 x^2+36 x^3+58 x^4+54 x^5+18 x^6+2 x^7+e^{3 x} \left (4 x+2 x^4\right )+e^{2 x} \left (36 x+12 x^2+18 x^4+6 x^5\right )+e^x \left (112 x+76 x^2+12 x^3+54 x^4+36 x^5+6 x^6\right )+e^{4 x} \left (54 x^2+2 e^{3 x} x^2+54 x^3+18 x^4+2 x^5+e^{2 x} \left (18 x^2+6 x^3\right )+e^x \left (54 x^2+36 x^3+6 x^4\right )\right )+e^{2 x} \left (-60-180 x-130 x^2-146 x^3-112 x^4-36 x^5-4 x^6+e^{3 x} \left (-2-4 x-4 x^3\right )+e^{2 x} \left (-18-42 x-12 x^2-36 x^3-12 x^4\right )+e^x \left (-56-152 x-78 x^2-120 x^3-72 x^4-12 x^5\right )\right )}{27 x^4+e^{3 x} x^4+27 x^5+9 x^6+x^7+e^{2 x} \left (9 x^4+3 x^5\right )+e^x \left (27 x^4+18 x^5+3 x^6\right )+e^{4 x} \left (27 x^2+e^{3 x} x^2+27 x^3+9 x^4+x^5+e^{2 x} \left (9 x^2+3 x^3\right )+e^x \left (27 x^2+18 x^3+3 x^4\right )\right )+e^{2 x} \left (-54 x^3-2 e^{3 x} x^3-54 x^4-18 x^5-2 x^6+e^{2 x} \left (-18 x^3-6 x^4\right )+e^x \left (-54 x^3-36 x^4-6 x^5\right )\right )} \, dx=\frac {2 \, {\left (x^{5} + 6 \, x^{4} + 9 \, x^{3} - x^{2} e^{\left (4 \, x\right )} - x^{2} - 2 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{\left (3 \, x\right )} - {\left (x^{4} + 5 \, x^{3} + 9 \, x^{2} + 1\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{4} + 3 \, x^{3} - x - 3\right )} e^{x} - 6 \, x - 10\right )}}{x^{4} + 6 \, x^{3} + 9 \, x^{2} - x e^{\left (4 \, x\right )} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{\left (3 \, x\right )} - {\left (x^{3} + 5 \, x^{2} + 9 \, x\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{x}} \] Input:
integrate(((2*x^2*exp(x)^3+(6*x^3+18*x^2)*exp(x)^2+(6*x^4+36*x^3+54*x^2)*e xp(x)+2*x^5+18*x^4+54*x^3+54*x^2)*exp(2*x)^2+((-4*x^3-4*x-2)*exp(x)^3+(-12 *x^4-36*x^3-12*x^2-42*x-18)*exp(x)^2+(-12*x^5-72*x^4-120*x^3-78*x^2-152*x- 56)*exp(x)-4*x^6-36*x^5-112*x^4-146*x^3-130*x^2-180*x-60)*exp(2*x)+(2*x^4+ 4*x)*exp(x)^3+(6*x^5+18*x^4+12*x^2+36*x)*exp(x)^2+(6*x^6+36*x^5+54*x^4+12* x^3+76*x^2+112*x)*exp(x)+2*x^7+18*x^6+54*x^5+58*x^4+36*x^3+116*x^2+120*x)/ ((x^2*exp(x)^3+(3*x^3+9*x^2)*exp(x)^2+(3*x^4+18*x^3+27*x^2)*exp(x)+x^5+9*x ^4+27*x^3+27*x^2)*exp(2*x)^2+(-2*x^3*exp(x)^3+(-6*x^4-18*x^3)*exp(x)^2+(-6 *x^5-36*x^4-54*x^3)*exp(x)-2*x^6-18*x^5-54*x^4-54*x^3)*exp(2*x)+x^4*exp(x) ^3+(3*x^5+9*x^4)*exp(x)^2+(3*x^6+18*x^5+27*x^4)*exp(x)+x^7+9*x^6+27*x^5+27 *x^4),x, algorithm="fricas")
Output:
2*(x^5 + 6*x^4 + 9*x^3 - x^2*e^(4*x) - x^2 - 2*(x^3 + 3*x^2)*e^(3*x) - (x^ 4 + 5*x^3 + 9*x^2 + 1)*e^(2*x) + 2*(x^4 + 3*x^3 - x - 3)*e^x - 6*x - 10)/( x^4 + 6*x^3 + 9*x^2 - x*e^(4*x) - 2*(x^2 + 3*x)*e^(3*x) - (x^3 + 5*x^2 + 9 *x)*e^(2*x) + 2*(x^3 + 3*x^2)*e^x)
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (26) = 52\).
Time = 0.27 (sec) , antiderivative size = 94, normalized size of antiderivative = 2.54 \[ \int \frac {120 x+116 x^2+36 x^3+58 x^4+54 x^5+18 x^6+2 x^7+e^{3 x} \left (4 x+2 x^4\right )+e^{2 x} \left (36 x+12 x^2+18 x^4+6 x^5\right )+e^x \left (112 x+76 x^2+12 x^3+54 x^4+36 x^5+6 x^6\right )+e^{4 x} \left (54 x^2+2 e^{3 x} x^2+54 x^3+18 x^4+2 x^5+e^{2 x} \left (18 x^2+6 x^3\right )+e^x \left (54 x^2+36 x^3+6 x^4\right )\right )+e^{2 x} \left (-60-180 x-130 x^2-146 x^3-112 x^4-36 x^5-4 x^6+e^{3 x} \left (-2-4 x-4 x^3\right )+e^{2 x} \left (-18-42 x-12 x^2-36 x^3-12 x^4\right )+e^x \left (-56-152 x-78 x^2-120 x^3-72 x^4-12 x^5\right )\right )}{27 x^4+e^{3 x} x^4+27 x^5+9 x^6+x^7+e^{2 x} \left (9 x^4+3 x^5\right )+e^x \left (27 x^4+18 x^5+3 x^6\right )+e^{4 x} \left (27 x^2+e^{3 x} x^2+27 x^3+9 x^4+x^5+e^{2 x} \left (9 x^2+3 x^3\right )+e^x \left (27 x^2+18 x^3+3 x^4\right )\right )+e^{2 x} \left (-54 x^3-2 e^{3 x} x^3-54 x^4-18 x^5-2 x^6+e^{2 x} \left (-18 x^3-6 x^4\right )+e^x \left (-54 x^3-36 x^4-6 x^5\right )\right )} \, dx=2 x + \frac {2 x^{2} + 12 x + \left (4 x + 12\right ) e^{x} + 2 e^{2 x} + 20}{- x^{4} - 6 x^{3} - 9 x^{2} + x e^{4 x} + \left (2 x^{2} + 6 x\right ) e^{3 x} + \left (- 2 x^{3} - 6 x^{2}\right ) e^{x} + \left (x^{3} + 5 x^{2} + 9 x\right ) e^{2 x}} \] Input:
integrate(((2*x**2*exp(x)**3+(6*x**3+18*x**2)*exp(x)**2+(6*x**4+36*x**3+54 *x**2)*exp(x)+2*x**5+18*x**4+54*x**3+54*x**2)*exp(2*x)**2+((-4*x**3-4*x-2) *exp(x)**3+(-12*x**4-36*x**3-12*x**2-42*x-18)*exp(x)**2+(-12*x**5-72*x**4- 120*x**3-78*x**2-152*x-56)*exp(x)-4*x**6-36*x**5-112*x**4-146*x**3-130*x** 2-180*x-60)*exp(2*x)+(2*x**4+4*x)*exp(x)**3+(6*x**5+18*x**4+12*x**2+36*x)* exp(x)**2+(6*x**6+36*x**5+54*x**4+12*x**3+76*x**2+112*x)*exp(x)+2*x**7+18* x**6+54*x**5+58*x**4+36*x**3+116*x**2+120*x)/((x**2*exp(x)**3+(3*x**3+9*x* *2)*exp(x)**2+(3*x**4+18*x**3+27*x**2)*exp(x)+x**5+9*x**4+27*x**3+27*x**2) *exp(2*x)**2+(-2*x**3*exp(x)**3+(-6*x**4-18*x**3)*exp(x)**2+(-6*x**5-36*x* *4-54*x**3)*exp(x)-2*x**6-18*x**5-54*x**4-54*x**3)*exp(2*x)+x**4*exp(x)**3 +(3*x**5+9*x**4)*exp(x)**2+(3*x**6+18*x**5+27*x**4)*exp(x)+x**7+9*x**6+27* x**5+27*x**4),x)
Output:
2*x + (2*x**2 + 12*x + (4*x + 12)*exp(x) + 2*exp(2*x) + 20)/(-x**4 - 6*x** 3 - 9*x**2 + x*exp(4*x) + (2*x**2 + 6*x)*exp(3*x) + (-2*x**3 - 6*x**2)*exp (x) + (x**3 + 5*x**2 + 9*x)*exp(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 154 vs. \(2 (34) = 68\).
Time = 0.35 (sec) , antiderivative size = 154, normalized size of antiderivative = 4.16 \[ \int \frac {120 x+116 x^2+36 x^3+58 x^4+54 x^5+18 x^6+2 x^7+e^{3 x} \left (4 x+2 x^4\right )+e^{2 x} \left (36 x+12 x^2+18 x^4+6 x^5\right )+e^x \left (112 x+76 x^2+12 x^3+54 x^4+36 x^5+6 x^6\right )+e^{4 x} \left (54 x^2+2 e^{3 x} x^2+54 x^3+18 x^4+2 x^5+e^{2 x} \left (18 x^2+6 x^3\right )+e^x \left (54 x^2+36 x^3+6 x^4\right )\right )+e^{2 x} \left (-60-180 x-130 x^2-146 x^3-112 x^4-36 x^5-4 x^6+e^{3 x} \left (-2-4 x-4 x^3\right )+e^{2 x} \left (-18-42 x-12 x^2-36 x^3-12 x^4\right )+e^x \left (-56-152 x-78 x^2-120 x^3-72 x^4-12 x^5\right )\right )}{27 x^4+e^{3 x} x^4+27 x^5+9 x^6+x^7+e^{2 x} \left (9 x^4+3 x^5\right )+e^x \left (27 x^4+18 x^5+3 x^6\right )+e^{4 x} \left (27 x^2+e^{3 x} x^2+27 x^3+9 x^4+x^5+e^{2 x} \left (9 x^2+3 x^3\right )+e^x \left (27 x^2+18 x^3+3 x^4\right )\right )+e^{2 x} \left (-54 x^3-2 e^{3 x} x^3-54 x^4-18 x^5-2 x^6+e^{2 x} \left (-18 x^3-6 x^4\right )+e^x \left (-54 x^3-36 x^4-6 x^5\right )\right )} \, dx=\frac {2 \, {\left (x^{5} + 6 \, x^{4} + 9 \, x^{3} - x^{2} e^{\left (4 \, x\right )} - x^{2} - 2 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{\left (3 \, x\right )} - {\left (x^{4} + 5 \, x^{3} + 9 \, x^{2} + 1\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{4} + 3 \, x^{3} - x - 3\right )} e^{x} - 6 \, x - 10\right )}}{x^{4} + 6 \, x^{3} + 9 \, x^{2} - x e^{\left (4 \, x\right )} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{\left (3 \, x\right )} - {\left (x^{3} + 5 \, x^{2} + 9 \, x\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{x}} \] Input:
integrate(((2*x^2*exp(x)^3+(6*x^3+18*x^2)*exp(x)^2+(6*x^4+36*x^3+54*x^2)*e xp(x)+2*x^5+18*x^4+54*x^3+54*x^2)*exp(2*x)^2+((-4*x^3-4*x-2)*exp(x)^3+(-12 *x^4-36*x^3-12*x^2-42*x-18)*exp(x)^2+(-12*x^5-72*x^4-120*x^3-78*x^2-152*x- 56)*exp(x)-4*x^6-36*x^5-112*x^4-146*x^3-130*x^2-180*x-60)*exp(2*x)+(2*x^4+ 4*x)*exp(x)^3+(6*x^5+18*x^4+12*x^2+36*x)*exp(x)^2+(6*x^6+36*x^5+54*x^4+12* x^3+76*x^2+112*x)*exp(x)+2*x^7+18*x^6+54*x^5+58*x^4+36*x^3+116*x^2+120*x)/ ((x^2*exp(x)^3+(3*x^3+9*x^2)*exp(x)^2+(3*x^4+18*x^3+27*x^2)*exp(x)+x^5+9*x ^4+27*x^3+27*x^2)*exp(2*x)^2+(-2*x^3*exp(x)^3+(-6*x^4-18*x^3)*exp(x)^2+(-6 *x^5-36*x^4-54*x^3)*exp(x)-2*x^6-18*x^5-54*x^4-54*x^3)*exp(2*x)+x^4*exp(x) ^3+(3*x^5+9*x^4)*exp(x)^2+(3*x^6+18*x^5+27*x^4)*exp(x)+x^7+9*x^6+27*x^5+27 *x^4),x, algorithm="maxima")
Output:
2*(x^5 + 6*x^4 + 9*x^3 - x^2*e^(4*x) - x^2 - 2*(x^3 + 3*x^2)*e^(3*x) - (x^ 4 + 5*x^3 + 9*x^2 + 1)*e^(2*x) + 2*(x^4 + 3*x^3 - x - 3)*e^x - 6*x - 10)/( x^4 + 6*x^3 + 9*x^2 - x*e^(4*x) - 2*(x^2 + 3*x)*e^(3*x) - (x^3 + 5*x^2 + 9 *x)*e^(2*x) + 2*(x^3 + 3*x^2)*e^x)
Leaf count of result is larger than twice the leaf count of optimal. 525 vs. \(2 (34) = 68\).
Time = 0.50 (sec) , antiderivative size = 525, normalized size of antiderivative = 14.19 \[ \int \frac {120 x+116 x^2+36 x^3+58 x^4+54 x^5+18 x^6+2 x^7+e^{3 x} \left (4 x+2 x^4\right )+e^{2 x} \left (36 x+12 x^2+18 x^4+6 x^5\right )+e^x \left (112 x+76 x^2+12 x^3+54 x^4+36 x^5+6 x^6\right )+e^{4 x} \left (54 x^2+2 e^{3 x} x^2+54 x^3+18 x^4+2 x^5+e^{2 x} \left (18 x^2+6 x^3\right )+e^x \left (54 x^2+36 x^3+6 x^4\right )\right )+e^{2 x} \left (-60-180 x-130 x^2-146 x^3-112 x^4-36 x^5-4 x^6+e^{3 x} \left (-2-4 x-4 x^3\right )+e^{2 x} \left (-18-42 x-12 x^2-36 x^3-12 x^4\right )+e^x \left (-56-152 x-78 x^2-120 x^3-72 x^4-12 x^5\right )\right )}{27 x^4+e^{3 x} x^4+27 x^5+9 x^6+x^7+e^{2 x} \left (9 x^4+3 x^5\right )+e^x \left (27 x^4+18 x^5+3 x^6\right )+e^{4 x} \left (27 x^2+e^{3 x} x^2+27 x^3+9 x^4+x^5+e^{2 x} \left (9 x^2+3 x^3\right )+e^x \left (27 x^2+18 x^3+3 x^4\right )\right )+e^{2 x} \left (-54 x^3-2 e^{3 x} x^3-54 x^4-18 x^5-2 x^6+e^{2 x} \left (-18 x^3-6 x^4\right )+e^x \left (-54 x^3-36 x^4-6 x^5\right )\right )} \, dx =\text {Too large to display} \] Input:
integrate(((2*x^2*exp(x)^3+(6*x^3+18*x^2)*exp(x)^2+(6*x^4+36*x^3+54*x^2)*e xp(x)+2*x^5+18*x^4+54*x^3+54*x^2)*exp(2*x)^2+((-4*x^3-4*x-2)*exp(x)^3+(-12 *x^4-36*x^3-12*x^2-42*x-18)*exp(x)^2+(-12*x^5-72*x^4-120*x^3-78*x^2-152*x- 56)*exp(x)-4*x^6-36*x^5-112*x^4-146*x^3-130*x^2-180*x-60)*exp(2*x)+(2*x^4+ 4*x)*exp(x)^3+(6*x^5+18*x^4+12*x^2+36*x)*exp(x)^2+(6*x^6+36*x^5+54*x^4+12* x^3+76*x^2+112*x)*exp(x)+2*x^7+18*x^6+54*x^5+58*x^4+36*x^3+116*x^2+120*x)/ ((x^2*exp(x)^3+(3*x^3+9*x^2)*exp(x)^2+(3*x^4+18*x^3+27*x^2)*exp(x)+x^5+9*x ^4+27*x^3+27*x^2)*exp(2*x)^2+(-2*x^3*exp(x)^3+(-6*x^4-18*x^3)*exp(x)^2+(-6 *x^5-36*x^4-54*x^3)*exp(x)-2*x^6-18*x^5-54*x^4-54*x^3)*exp(2*x)+x^4*exp(x) ^3+(3*x^5+9*x^4)*exp(x)^2+(3*x^6+18*x^5+27*x^4)*exp(x)+x^7+9*x^6+27*x^5+27 *x^4),x, algorithm="giac")
Output:
2*(x^9 - x^8*e^(2*x) + 2*x^8*e^x + 16*x^8 - 2*x^7*e^(3*x) - 15*x^7*e^(2*x) + 26*x^7*e^x + 112*x^7 - x^6*e^(4*x) - 26*x^6*e^(3*x) - 102*x^6*e^(2*x) + 146*x^6*e^x + 436*x^6 - 10*x^5*e^(4*x) - 146*x^5*e^(3*x) - 395*x^5*e^(2*x ) + 434*x^5*e^x + 976*x^5 - 43*x^4*e^(4*x) - 438*x^4*e^(3*x) - 920*x^4*e^( 2*x) + 650*x^4*e^x + 1070*x^4 - 90*x^3*e^(4*x) - 702*x^3*e^(3*x) - 1235*x^ 3*e^(2*x) + 194*x^3*e^x - 170*x^3 - 81*x^2*e^(4*x) - 486*x^2*e^(3*x) - 812 *x^2*e^(2*x) - 878*x^2*e^x - 2119*x^2 + 2*x*e^(3*x) - 163*x*e^(2*x) - 1410 *x*e^x - 2799*x + 6*e^(3*x) - 135*e^(2*x) - 972*e^x - 1620)/(x^8 - x^7*e^( 2*x) + 2*x^7*e^x + 16*x^7 - 2*x^6*e^(3*x) - 15*x^6*e^(2*x) + 26*x^6*e^x + 112*x^6 - x^5*e^(4*x) - 26*x^5*e^(3*x) - 102*x^5*e^(2*x) + 146*x^5*e^x + 4 38*x^5 - 10*x^4*e^(4*x) - 146*x^4*e^(3*x) - 395*x^4*e^(2*x) + 438*x^4*e^x + 1008*x^4 - 43*x^3*e^(4*x) - 438*x^3*e^(3*x) - 918*x^3*e^(2*x) + 702*x^3* e^x + 1296*x^3 - 90*x^2*e^(4*x) - 702*x^2*e^(3*x) - 1215*x^2*e^(2*x) + 486 *x^2*e^x + 729*x^2 - 81*x*e^(4*x) - 486*x*e^(3*x) - 729*x*e^(2*x))
Timed out. \[ \int \frac {120 x+116 x^2+36 x^3+58 x^4+54 x^5+18 x^6+2 x^7+e^{3 x} \left (4 x+2 x^4\right )+e^{2 x} \left (36 x+12 x^2+18 x^4+6 x^5\right )+e^x \left (112 x+76 x^2+12 x^3+54 x^4+36 x^5+6 x^6\right )+e^{4 x} \left (54 x^2+2 e^{3 x} x^2+54 x^3+18 x^4+2 x^5+e^{2 x} \left (18 x^2+6 x^3\right )+e^x \left (54 x^2+36 x^3+6 x^4\right )\right )+e^{2 x} \left (-60-180 x-130 x^2-146 x^3-112 x^4-36 x^5-4 x^6+e^{3 x} \left (-2-4 x-4 x^3\right )+e^{2 x} \left (-18-42 x-12 x^2-36 x^3-12 x^4\right )+e^x \left (-56-152 x-78 x^2-120 x^3-72 x^4-12 x^5\right )\right )}{27 x^4+e^{3 x} x^4+27 x^5+9 x^6+x^7+e^{2 x} \left (9 x^4+3 x^5\right )+e^x \left (27 x^4+18 x^5+3 x^6\right )+e^{4 x} \left (27 x^2+e^{3 x} x^2+27 x^3+9 x^4+x^5+e^{2 x} \left (9 x^2+3 x^3\right )+e^x \left (27 x^2+18 x^3+3 x^4\right )\right )+e^{2 x} \left (-54 x^3-2 e^{3 x} x^3-54 x^4-18 x^5-2 x^6+e^{2 x} \left (-18 x^3-6 x^4\right )+e^x \left (-54 x^3-36 x^4-6 x^5\right )\right )} \, dx=\int \frac {120\,x+{\mathrm {e}}^{3\,x}\,\left (2\,x^4+4\,x\right )+{\mathrm {e}}^{2\,x}\,\left (6\,x^5+18\,x^4+12\,x^2+36\,x\right )+{\mathrm {e}}^x\,\left (6\,x^6+36\,x^5+54\,x^4+12\,x^3+76\,x^2+112\,x\right )-{\mathrm {e}}^{2\,x}\,\left (180\,x+{\mathrm {e}}^{3\,x}\,\left (4\,x^3+4\,x+2\right )+{\mathrm {e}}^x\,\left (12\,x^5+72\,x^4+120\,x^3+78\,x^2+152\,x+56\right )+{\mathrm {e}}^{2\,x}\,\left (12\,x^4+36\,x^3+12\,x^2+42\,x+18\right )+130\,x^2+146\,x^3+112\,x^4+36\,x^5+4\,x^6+60\right )+116\,x^2+36\,x^3+58\,x^4+54\,x^5+18\,x^6+2\,x^7+{\mathrm {e}}^{4\,x}\,\left ({\mathrm {e}}^x\,\left (6\,x^4+36\,x^3+54\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (6\,x^3+18\,x^2\right )+2\,x^2\,{\mathrm {e}}^{3\,x}+54\,x^2+54\,x^3+18\,x^4+2\,x^5\right )}{{\mathrm {e}}^x\,\left (3\,x^6+18\,x^5+27\,x^4\right )+{\mathrm {e}}^{2\,x}\,\left (3\,x^5+9\,x^4\right )+x^4\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{4\,x}\,\left ({\mathrm {e}}^x\,\left (3\,x^4+18\,x^3+27\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (3\,x^3+9\,x^2\right )+x^2\,{\mathrm {e}}^{3\,x}+27\,x^2+27\,x^3+9\,x^4+x^5\right )+27\,x^4+27\,x^5+9\,x^6+x^7-{\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^x\,\left (6\,x^5+36\,x^4+54\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (6\,x^4+18\,x^3\right )+2\,x^3\,{\mathrm {e}}^{3\,x}+54\,x^3+54\,x^4+18\,x^5+2\,x^6\right )} \,d x \] Input:
int((120*x + exp(3*x)*(4*x + 2*x^4) + exp(2*x)*(36*x + 12*x^2 + 18*x^4 + 6 *x^5) + exp(x)*(112*x + 76*x^2 + 12*x^3 + 54*x^4 + 36*x^5 + 6*x^6) - exp(2 *x)*(180*x + exp(3*x)*(4*x + 4*x^3 + 2) + exp(x)*(152*x + 78*x^2 + 120*x^3 + 72*x^4 + 12*x^5 + 56) + exp(2*x)*(42*x + 12*x^2 + 36*x^3 + 12*x^4 + 18) + 130*x^2 + 146*x^3 + 112*x^4 + 36*x^5 + 4*x^6 + 60) + 116*x^2 + 36*x^3 + 58*x^4 + 54*x^5 + 18*x^6 + 2*x^7 + exp(4*x)*(exp(x)*(54*x^2 + 36*x^3 + 6* x^4) + exp(2*x)*(18*x^2 + 6*x^3) + 2*x^2*exp(3*x) + 54*x^2 + 54*x^3 + 18*x ^4 + 2*x^5))/(exp(x)*(27*x^4 + 18*x^5 + 3*x^6) + exp(2*x)*(9*x^4 + 3*x^5) + x^4*exp(3*x) + exp(4*x)*(exp(x)*(27*x^2 + 18*x^3 + 3*x^4) + exp(2*x)*(9* x^2 + 3*x^3) + x^2*exp(3*x) + 27*x^2 + 27*x^3 + 9*x^4 + x^5) + 27*x^4 + 27 *x^5 + 9*x^6 + x^7 - exp(2*x)*(exp(x)*(54*x^3 + 36*x^4 + 6*x^5) + exp(2*x) *(18*x^3 + 6*x^4) + 2*x^3*exp(3*x) + 54*x^3 + 54*x^4 + 18*x^5 + 2*x^6)),x)
Output:
int((120*x + exp(3*x)*(4*x + 2*x^4) + exp(2*x)*(36*x + 12*x^2 + 18*x^4 + 6 *x^5) + exp(x)*(112*x + 76*x^2 + 12*x^3 + 54*x^4 + 36*x^5 + 6*x^6) - exp(2 *x)*(180*x + exp(3*x)*(4*x + 4*x^3 + 2) + exp(x)*(152*x + 78*x^2 + 120*x^3 + 72*x^4 + 12*x^5 + 56) + exp(2*x)*(42*x + 12*x^2 + 36*x^3 + 12*x^4 + 18) + 130*x^2 + 146*x^3 + 112*x^4 + 36*x^5 + 4*x^6 + 60) + 116*x^2 + 36*x^3 + 58*x^4 + 54*x^5 + 18*x^6 + 2*x^7 + exp(4*x)*(exp(x)*(54*x^2 + 36*x^3 + 6* x^4) + exp(2*x)*(18*x^2 + 6*x^3) + 2*x^2*exp(3*x) + 54*x^2 + 54*x^3 + 18*x ^4 + 2*x^5))/(exp(x)*(27*x^4 + 18*x^5 + 3*x^6) + exp(2*x)*(9*x^4 + 3*x^5) + x^4*exp(3*x) + exp(4*x)*(exp(x)*(27*x^2 + 18*x^3 + 3*x^4) + exp(2*x)*(9* x^2 + 3*x^3) + x^2*exp(3*x) + 27*x^2 + 27*x^3 + 9*x^4 + x^5) + 27*x^4 + 27 *x^5 + 9*x^6 + x^7 - exp(2*x)*(exp(x)*(54*x^3 + 36*x^4 + 6*x^5) + exp(2*x) *(18*x^3 + 6*x^4) + 2*x^3*exp(3*x) + 54*x^3 + 54*x^4 + 18*x^5 + 2*x^6)), x )
Time = 0.26 (sec) , antiderivative size = 192, normalized size of antiderivative = 5.19 \[ \int \frac {120 x+116 x^2+36 x^3+58 x^4+54 x^5+18 x^6+2 x^7+e^{3 x} \left (4 x+2 x^4\right )+e^{2 x} \left (36 x+12 x^2+18 x^4+6 x^5\right )+e^x \left (112 x+76 x^2+12 x^3+54 x^4+36 x^5+6 x^6\right )+e^{4 x} \left (54 x^2+2 e^{3 x} x^2+54 x^3+18 x^4+2 x^5+e^{2 x} \left (18 x^2+6 x^3\right )+e^x \left (54 x^2+36 x^3+6 x^4\right )\right )+e^{2 x} \left (-60-180 x-130 x^2-146 x^3-112 x^4-36 x^5-4 x^6+e^{3 x} \left (-2-4 x-4 x^3\right )+e^{2 x} \left (-18-42 x-12 x^2-36 x^3-12 x^4\right )+e^x \left (-56-152 x-78 x^2-120 x^3-72 x^4-12 x^5\right )\right )}{27 x^4+e^{3 x} x^4+27 x^5+9 x^6+x^7+e^{2 x} \left (9 x^4+3 x^5\right )+e^x \left (27 x^4+18 x^5+3 x^6\right )+e^{4 x} \left (27 x^2+e^{3 x} x^2+27 x^3+9 x^4+x^5+e^{2 x} \left (9 x^2+3 x^3\right )+e^x \left (27 x^2+18 x^3+3 x^4\right )\right )+e^{2 x} \left (-54 x^3-2 e^{3 x} x^3-54 x^4-18 x^5-2 x^6+e^{2 x} \left (-18 x^3-6 x^4\right )+e^x \left (-54 x^3-36 x^4-6 x^5\right )\right )} \, dx=\frac {2 e^{4 x} x^{2}+4 e^{3 x} x^{3}+12 e^{3 x} x^{2}+2 e^{2 x} x^{4}+10 e^{2 x} x^{3}+18 e^{2 x} x^{2}+2 e^{2 x}-4 e^{x} x^{4}-12 e^{x} x^{3}+4 e^{x} x +12 e^{x}-2 x^{5}-12 x^{4}-18 x^{3}+2 x^{2}+12 x +20}{x \left (e^{4 x}+2 e^{3 x} x +6 e^{3 x}+e^{2 x} x^{2}+5 e^{2 x} x +9 e^{2 x}-2 e^{x} x^{2}-6 e^{x} x -x^{3}-6 x^{2}-9 x \right )} \] Input:
int(((2*x^2*exp(x)^3+(6*x^3+18*x^2)*exp(x)^2+(6*x^4+36*x^3+54*x^2)*exp(x)+ 2*x^5+18*x^4+54*x^3+54*x^2)*exp(2*x)^2+((-4*x^3-4*x-2)*exp(x)^3+(-12*x^4-3 6*x^3-12*x^2-42*x-18)*exp(x)^2+(-12*x^5-72*x^4-120*x^3-78*x^2-152*x-56)*ex p(x)-4*x^6-36*x^5-112*x^4-146*x^3-130*x^2-180*x-60)*exp(2*x)+(2*x^4+4*x)*e xp(x)^3+(6*x^5+18*x^4+12*x^2+36*x)*exp(x)^2+(6*x^6+36*x^5+54*x^4+12*x^3+76 *x^2+112*x)*exp(x)+2*x^7+18*x^6+54*x^5+58*x^4+36*x^3+116*x^2+120*x)/((x^2* exp(x)^3+(3*x^3+9*x^2)*exp(x)^2+(3*x^4+18*x^3+27*x^2)*exp(x)+x^5+9*x^4+27* x^3+27*x^2)*exp(2*x)^2+(-2*x^3*exp(x)^3+(-6*x^4-18*x^3)*exp(x)^2+(-6*x^5-3 6*x^4-54*x^3)*exp(x)-2*x^6-18*x^5-54*x^4-54*x^3)*exp(2*x)+x^4*exp(x)^3+(3* x^5+9*x^4)*exp(x)^2+(3*x^6+18*x^5+27*x^4)*exp(x)+x^7+9*x^6+27*x^5+27*x^4), x)
Output:
(2*(e**(4*x)*x**2 + 2*e**(3*x)*x**3 + 6*e**(3*x)*x**2 + e**(2*x)*x**4 + 5* e**(2*x)*x**3 + 9*e**(2*x)*x**2 + e**(2*x) - 2*e**x*x**4 - 6*e**x*x**3 + 2 *e**x*x + 6*e**x - x**5 - 6*x**4 - 9*x**3 + x**2 + 6*x + 10))/(x*(e**(4*x) + 2*e**(3*x)*x + 6*e**(3*x) + e**(2*x)*x**2 + 5*e**(2*x)*x + 9*e**(2*x) - 2*e**x*x**2 - 6*e**x*x - x**3 - 6*x**2 - 9*x))