Integrand size = 248, antiderivative size = 29 \[ \int \frac {3 x^3+e^{4+2 x} \left (x-4 x^2\right )+e^x \left (-x^2-2 x^3\right )}{2 e^{20+10 x}+2 e^{5 x} x^5-10 e^{4 x} x^6+20 e^{3 x} x^7-20 e^{2 x} x^8+10 e^x x^9-2 x^{10}+e^{16+8 x} \left (10 e^x x-10 x^2\right )+e^{12+6 x} \left (20 e^{2 x} x^2-40 e^x x^3+20 x^4\right )+e^{8+4 x} \left (20 e^{3 x} x^3-60 e^{2 x} x^4+60 e^x x^5-20 x^6\right )+e^{4+2 x} \left (10 e^{4 x} x^4-40 e^{3 x} x^5+60 e^{2 x} x^6-40 e^x x^7+10 x^8\right )} \, dx=2+\frac {1}{4 \left (e^x+\frac {e^{4+2 x}}{x}-x\right )^4 x^2} \] Output:
2+1/4/(exp(x)-x+exp(4+2*x)/x)^4/x^2
Time = 2.09 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int \frac {3 x^3+e^{4+2 x} \left (x-4 x^2\right )+e^x \left (-x^2-2 x^3\right )}{2 e^{20+10 x}+2 e^{5 x} x^5-10 e^{4 x} x^6+20 e^{3 x} x^7-20 e^{2 x} x^8+10 e^x x^9-2 x^{10}+e^{16+8 x} \left (10 e^x x-10 x^2\right )+e^{12+6 x} \left (20 e^{2 x} x^2-40 e^x x^3+20 x^4\right )+e^{8+4 x} \left (20 e^{3 x} x^3-60 e^{2 x} x^4+60 e^x x^5-20 x^6\right )+e^{4+2 x} \left (10 e^{4 x} x^4-40 e^{3 x} x^5+60 e^{2 x} x^6-40 e^x x^7+10 x^8\right )} \, dx=\frac {x^2}{4 \left (e^{4+2 x}+e^x x-x^2\right )^4} \] Input:
Integrate[(3*x^3 + E^(4 + 2*x)*(x - 4*x^2) + E^x*(-x^2 - 2*x^3))/(2*E^(20 + 10*x) + 2*E^(5*x)*x^5 - 10*E^(4*x)*x^6 + 20*E^(3*x)*x^7 - 20*E^(2*x)*x^8 + 10*E^x*x^9 - 2*x^10 + E^(16 + 8*x)*(10*E^x*x - 10*x^2) + E^(12 + 6*x)*( 20*E^(2*x)*x^2 - 40*E^x*x^3 + 20*x^4) + E^(8 + 4*x)*(20*E^(3*x)*x^3 - 60*E ^(2*x)*x^4 + 60*E^x*x^5 - 20*x^6) + E^(4 + 2*x)*(10*E^(4*x)*x^4 - 40*E^(3* x)*x^5 + 60*E^(2*x)*x^6 - 40*E^x*x^7 + 10*x^8)),x]
Output:
x^2/(4*(E^(4 + 2*x) + E^x*x - x^2)^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.
| \(\displaystyle \int \frac {3 x^3+e^{2 x+4} \left (x-4 x^2\right )+e^x \left (-2 x^3-x^2\right )}{-2 x^{10}+10 e^x x^9-20 e^{2 x} x^8+20 e^{3 x} x^7-10 e^{4 x} x^6+2 e^{5 x} x^5+e^{8 x+16} \left (10 e^x x-10 x^2\right )+e^{6 x+12} \left (20 x^4-40 e^x x^3+20 e^{2 x} x^2\right )+e^{4 x+8} \left (-20 x^6+60 e^x x^5-60 e^{2 x} x^4+20 e^{3 x} x^3\right )+e^{2 x+4} \left (10 x^8-40 e^x x^7+60 e^{2 x} x^6-40 e^{3 x} x^5+10 e^{4 x} x^4\right )+2 e^{10 x+20}} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x \left (3 x^2-e^x (2 x+1) x-e^{2 x+4} (4 x-1)\right )}{2 \left (-x^2+e^x x+e^{2 x+4}\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{2} \int \frac {x \left (3 x^2-e^x (2 x+1) x+e^{2 x+4} (1-4 x)\right )}{\left (-x^2+e^x x+e^{2 x+4}\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{2} \int \left (\frac {2 \left (e^x-2 x\right ) (x-1) x^2}{\left (-x^2+e^x x+e^{2 x+4}\right )^5}-\frac {x (4 x-1)}{\left (x^2-e^x x-e^{2 x+4}\right )^4}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{2} \left (-2 \int \frac {e^x x^2}{\left (-x^2+e^x x+e^{2 x+4}\right )^5}dx+\int \frac {x}{\left (x^2-e^x x-e^{2 x+4}\right )^4}dx-4 \int \frac {x^2}{\left (x^2-e^x x-e^{2 x+4}\right )^4}dx+4 \int \frac {x^4}{\left (x^2-e^x x-e^{2 x+4}\right )^5}dx+2 \int \frac {e^x x^3}{\left (-x^2+e^x x+e^{2 x+4}\right )^5}dx-4 \int \frac {x^3}{\left (x^2-e^x x-e^{2 x+4}\right )^5}dx\right )\) |
Input:
Int[(3*x^3 + E^(4 + 2*x)*(x - 4*x^2) + E^x*(-x^2 - 2*x^3))/(2*E^(20 + 10*x ) + 2*E^(5*x)*x^5 - 10*E^(4*x)*x^6 + 20*E^(3*x)*x^7 - 20*E^(2*x)*x^8 + 10* E^x*x^9 - 2*x^10 + E^(16 + 8*x)*(10*E^x*x - 10*x^2) + E^(12 + 6*x)*(20*E^( 2*x)*x^2 - 40*E^x*x^3 + 20*x^4) + E^(8 + 4*x)*(20*E^(3*x)*x^3 - 60*E^(2*x) *x^4 + 60*E^x*x^5 - 20*x^6) + E^(4 + 2*x)*(10*E^(4*x)*x^4 - 40*E^(3*x)*x^5 + 60*E^(2*x)*x^6 - 40*E^x*x^7 + 10*x^8)),x]
Output:
$Aborted
Time = 2.65 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83
| method | result | size |
| risch | \(\frac {x^{2}}{4 \left ({\mathrm e}^{x} x -x^{2}+{\mathrm e}^{4+2 x}\right )^{4}}\) | \(24\) |
| parallelrisch | \(\frac {x^{2}}{4 x^{8}-16 x^{7} {\mathrm e}^{x}+24 \,{\mathrm e}^{2 x} x^{6}-16 \,{\mathrm e}^{3 x} x^{5}+4 x^{4} {\mathrm e}^{4 x}-16 x^{6} {\mathrm e}^{4+2 x}+48 \,{\mathrm e}^{x} {\mathrm e}^{4+2 x} x^{5}-48 \,{\mathrm e}^{2 x} {\mathrm e}^{4+2 x} x^{4}+16 \,{\mathrm e}^{3 x} {\mathrm e}^{4+2 x} x^{3}+24 x^{4} {\mathrm e}^{4 x +8}-48 x^{3} {\mathrm e}^{x} {\mathrm e}^{4 x +8}+24 \,{\mathrm e}^{4 x +8} x^{2} {\mathrm e}^{2 x}-16 \,{\mathrm e}^{12+6 x} x^{2}+16 x \,{\mathrm e}^{x} {\mathrm e}^{12+6 x}+4 \,{\mathrm e}^{8 x +16}}\) | \(178\) |
Input:
int(((-4*x^2+x)*exp(4+2*x)+(-2*x^3-x^2)*exp(x)+3*x^3)/(2*exp(4+2*x)^5+(10* exp(x)*x-10*x^2)*exp(4+2*x)^4+(20*exp(x)^2*x^2-40*exp(x)*x^3+20*x^4)*exp(4 +2*x)^3+(20*x^3*exp(x)^3-60*exp(x)^2*x^4+60*x^5*exp(x)-20*x^6)*exp(4+2*x)^ 2+(10*x^4*exp(x)^4-40*x^5*exp(x)^3+60*x^6*exp(x)^2-40*x^7*exp(x)+10*x^8)*e xp(4+2*x)+2*x^5*exp(x)^5-10*x^6*exp(x)^4+20*x^7*exp(x)^3-20*x^8*exp(x)^2+1 0*x^9*exp(x)-2*x^10),x,method=_RETURNVERBOSE)
Output:
1/4*x^2/(exp(x)*x-x^2+exp(4+2*x))^4
Leaf count of result is larger than twice the leaf count of optimal. 136 vs. \(2 (26) = 52\).
Time = 0.09 (sec) , antiderivative size = 136, normalized size of antiderivative = 4.69 \[ \int \frac {3 x^3+e^{4+2 x} \left (x-4 x^2\right )+e^x \left (-x^2-2 x^3\right )}{2 e^{20+10 x}+2 e^{5 x} x^5-10 e^{4 x} x^6+20 e^{3 x} x^7-20 e^{2 x} x^8+10 e^x x^9-2 x^{10}+e^{16+8 x} \left (10 e^x x-10 x^2\right )+e^{12+6 x} \left (20 e^{2 x} x^2-40 e^x x^3+20 x^4\right )+e^{8+4 x} \left (20 e^{3 x} x^3-60 e^{2 x} x^4+60 e^x x^5-20 x^6\right )+e^{4+2 x} \left (10 e^{4 x} x^4-40 e^{3 x} x^5+60 e^{2 x} x^6-40 e^x x^7+10 x^8\right )} \, dx=\frac {x^{2}}{4 \, {\left (x^{8} - 4 \, x^{7} e^{x} - 2 \, {\left (2 \, x^{2} e^{12} - 3 \, x^{2} e^{8}\right )} e^{\left (6 \, x\right )} - 4 \, {\left (3 \, x^{3} e^{8} - x^{3} e^{4}\right )} e^{\left (5 \, x\right )} + {\left (6 \, x^{4} e^{8} - 12 \, x^{4} e^{4} + x^{4}\right )} e^{\left (4 \, x\right )} + 4 \, {\left (3 \, x^{5} e^{4} - x^{5}\right )} e^{\left (3 \, x\right )} - 2 \, {\left (2 \, x^{6} e^{4} - 3 \, x^{6}\right )} e^{\left (2 \, x\right )} + 4 \, x e^{\left (7 \, x + 12\right )} + e^{\left (8 \, x + 16\right )}\right )}} \] Input:
integrate(((-4*x^2+x)*exp(4+2*x)+(-2*x^3-x^2)*exp(x)+3*x^3)/(2*exp(4+2*x)^ 5+(10*exp(x)*x-10*x^2)*exp(4+2*x)^4+(20*exp(x)^2*x^2-40*exp(x)*x^3+20*x^4) *exp(4+2*x)^3+(20*x^3*exp(x)^3-60*exp(x)^2*x^4+60*x^5*exp(x)-20*x^6)*exp(4 +2*x)^2+(10*x^4*exp(x)^4-40*x^5*exp(x)^3+60*x^6*exp(x)^2-40*x^7*exp(x)+10* x^8)*exp(4+2*x)+2*x^5*exp(x)^5-10*x^6*exp(x)^4+20*x^7*exp(x)^3-20*x^8*exp( x)^2+10*x^9*exp(x)-2*x^10),x, algorithm="fricas")
Output:
1/4*x^2/(x^8 - 4*x^7*e^x - 2*(2*x^2*e^12 - 3*x^2*e^8)*e^(6*x) - 4*(3*x^3*e ^8 - x^3*e^4)*e^(5*x) + (6*x^4*e^8 - 12*x^4*e^4 + x^4)*e^(4*x) + 4*(3*x^5* e^4 - x^5)*e^(3*x) - 2*(2*x^6*e^4 - 3*x^6)*e^(2*x) + 4*x*e^(7*x + 12) + e^ (8*x + 16))
Timed out. \[ \int \frac {3 x^3+e^{4+2 x} \left (x-4 x^2\right )+e^x \left (-x^2-2 x^3\right )}{2 e^{20+10 x}+2 e^{5 x} x^5-10 e^{4 x} x^6+20 e^{3 x} x^7-20 e^{2 x} x^8+10 e^x x^9-2 x^{10}+e^{16+8 x} \left (10 e^x x-10 x^2\right )+e^{12+6 x} \left (20 e^{2 x} x^2-40 e^x x^3+20 x^4\right )+e^{8+4 x} \left (20 e^{3 x} x^3-60 e^{2 x} x^4+60 e^x x^5-20 x^6\right )+e^{4+2 x} \left (10 e^{4 x} x^4-40 e^{3 x} x^5+60 e^{2 x} x^6-40 e^x x^7+10 x^8\right )} \, dx=\text {Timed out} \] Input:
integrate(((-4*x**2+x)*exp(4+2*x)+(-2*x**3-x**2)*exp(x)+3*x**3)/(2*exp(4+2 *x)**5+(10*exp(x)*x-10*x**2)*exp(4+2*x)**4+(20*exp(x)**2*x**2-40*exp(x)*x* *3+20*x**4)*exp(4+2*x)**3+(20*x**3*exp(x)**3-60*exp(x)**2*x**4+60*x**5*exp (x)-20*x**6)*exp(4+2*x)**2+(10*x**4*exp(x)**4-40*x**5*exp(x)**3+60*x**6*ex p(x)**2-40*x**7*exp(x)+10*x**8)*exp(4+2*x)+2*x**5*exp(x)**5-10*x**6*exp(x) **4+20*x**7*exp(x)**3-20*x**8*exp(x)**2+10*x**9*exp(x)-2*x**10),x)
Output:
Timed out
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (26) = 52\).
Time = 0.45 (sec) , antiderivative size = 117, normalized size of antiderivative = 4.03 \[ \int \frac {3 x^3+e^{4+2 x} \left (x-4 x^2\right )+e^x \left (-x^2-2 x^3\right )}{2 e^{20+10 x}+2 e^{5 x} x^5-10 e^{4 x} x^6+20 e^{3 x} x^7-20 e^{2 x} x^8+10 e^x x^9-2 x^{10}+e^{16+8 x} \left (10 e^x x-10 x^2\right )+e^{12+6 x} \left (20 e^{2 x} x^2-40 e^x x^3+20 x^4\right )+e^{8+4 x} \left (20 e^{3 x} x^3-60 e^{2 x} x^4+60 e^x x^5-20 x^6\right )+e^{4+2 x} \left (10 e^{4 x} x^4-40 e^{3 x} x^5+60 e^{2 x} x^6-40 e^x x^7+10 x^8\right )} \, dx=\frac {x^{2}}{4 \, {\left (x^{8} - 2 \, x^{6} {\left (2 \, e^{4} - 3\right )} e^{\left (2 \, x\right )} - 4 \, x^{7} e^{x} + 4 \, x^{5} {\left (3 \, e^{4} - 1\right )} e^{\left (3 \, x\right )} + x^{4} {\left (6 \, e^{8} - 12 \, e^{4} + 1\right )} e^{\left (4 \, x\right )} - 4 \, x^{3} {\left (3 \, e^{8} - e^{4}\right )} e^{\left (5 \, x\right )} - 2 \, x^{2} {\left (2 \, e^{12} - 3 \, e^{8}\right )} e^{\left (6 \, x\right )} + 4 \, x e^{\left (7 \, x + 12\right )} + e^{\left (8 \, x + 16\right )}\right )}} \] Input:
integrate(((-4*x^2+x)*exp(4+2*x)+(-2*x^3-x^2)*exp(x)+3*x^3)/(2*exp(4+2*x)^ 5+(10*exp(x)*x-10*x^2)*exp(4+2*x)^4+(20*exp(x)^2*x^2-40*exp(x)*x^3+20*x^4) *exp(4+2*x)^3+(20*x^3*exp(x)^3-60*exp(x)^2*x^4+60*x^5*exp(x)-20*x^6)*exp(4 +2*x)^2+(10*x^4*exp(x)^4-40*x^5*exp(x)^3+60*x^6*exp(x)^2-40*x^7*exp(x)+10* x^8)*exp(4+2*x)+2*x^5*exp(x)^5-10*x^6*exp(x)^4+20*x^7*exp(x)^3-20*x^8*exp( x)^2+10*x^9*exp(x)-2*x^10),x, algorithm="maxima")
Output:
1/4*x^2/(x^8 - 2*x^6*(2*e^4 - 3)*e^(2*x) - 4*x^7*e^x + 4*x^5*(3*e^4 - 1)*e ^(3*x) + x^4*(6*e^8 - 12*e^4 + 1)*e^(4*x) - 4*x^3*(3*e^8 - e^4)*e^(5*x) - 2*x^2*(2*e^12 - 3*e^8)*e^(6*x) + 4*x*e^(7*x + 12) + e^(8*x + 16))
Leaf count of result is larger than twice the leaf count of optimal. 147 vs. \(2 (26) = 52\).
Time = 1.05 (sec) , antiderivative size = 147, normalized size of antiderivative = 5.07 \[ \int \frac {3 x^3+e^{4+2 x} \left (x-4 x^2\right )+e^x \left (-x^2-2 x^3\right )}{2 e^{20+10 x}+2 e^{5 x} x^5-10 e^{4 x} x^6+20 e^{3 x} x^7-20 e^{2 x} x^8+10 e^x x^9-2 x^{10}+e^{16+8 x} \left (10 e^x x-10 x^2\right )+e^{12+6 x} \left (20 e^{2 x} x^2-40 e^x x^3+20 x^4\right )+e^{8+4 x} \left (20 e^{3 x} x^3-60 e^{2 x} x^4+60 e^x x^5-20 x^6\right )+e^{4+2 x} \left (10 e^{4 x} x^4-40 e^{3 x} x^5+60 e^{2 x} x^6-40 e^x x^7+10 x^8\right )} \, dx=\frac {x^{2}}{2 \, {\left (x^{8} - 4 \, x^{7} e^{x} + 6 \, x^{6} e^{\left (2 \, x\right )} - 4 \, x^{6} e^{\left (2 \, x + 4\right )} - 4 \, x^{5} e^{\left (3 \, x\right )} + 12 \, x^{5} e^{\left (3 \, x + 4\right )} + x^{4} e^{\left (4 \, x\right )} + 6 \, x^{4} e^{\left (4 \, x + 8\right )} - 12 \, x^{4} e^{\left (4 \, x + 4\right )} - 12 \, x^{3} e^{\left (5 \, x + 8\right )} + 4 \, x^{3} e^{\left (5 \, x + 4\right )} - 4 \, x^{2} e^{\left (6 \, x + 12\right )} + 6 \, x^{2} e^{\left (6 \, x + 8\right )} + 4 \, x e^{\left (7 \, x + 12\right )} + e^{\left (8 \, x + 16\right )}\right )}} \] Input:
integrate(((-4*x^2+x)*exp(4+2*x)+(-2*x^3-x^2)*exp(x)+3*x^3)/(2*exp(4+2*x)^ 5+(10*exp(x)*x-10*x^2)*exp(4+2*x)^4+(20*exp(x)^2*x^2-40*exp(x)*x^3+20*x^4) *exp(4+2*x)^3+(20*x^3*exp(x)^3-60*exp(x)^2*x^4+60*x^5*exp(x)-20*x^6)*exp(4 +2*x)^2+(10*x^4*exp(x)^4-40*x^5*exp(x)^3+60*x^6*exp(x)^2-40*x^7*exp(x)+10* x^8)*exp(4+2*x)+2*x^5*exp(x)^5-10*x^6*exp(x)^4+20*x^7*exp(x)^3-20*x^8*exp( x)^2+10*x^9*exp(x)-2*x^10),x, algorithm="giac")
Output:
1/2*x^2/(x^8 - 4*x^7*e^x + 6*x^6*e^(2*x) - 4*x^6*e^(2*x + 4) - 4*x^5*e^(3* x) + 12*x^5*e^(3*x + 4) + x^4*e^(4*x) + 6*x^4*e^(4*x + 8) - 12*x^4*e^(4*x + 4) - 12*x^3*e^(5*x + 8) + 4*x^3*e^(5*x + 4) - 4*x^2*e^(6*x + 12) + 6*x^2 *e^(6*x + 8) + 4*x*e^(7*x + 12) + e^(8*x + 16))
Timed out. \[ \int \frac {3 x^3+e^{4+2 x} \left (x-4 x^2\right )+e^x \left (-x^2-2 x^3\right )}{2 e^{20+10 x}+2 e^{5 x} x^5-10 e^{4 x} x^6+20 e^{3 x} x^7-20 e^{2 x} x^8+10 e^x x^9-2 x^{10}+e^{16+8 x} \left (10 e^x x-10 x^2\right )+e^{12+6 x} \left (20 e^{2 x} x^2-40 e^x x^3+20 x^4\right )+e^{8+4 x} \left (20 e^{3 x} x^3-60 e^{2 x} x^4+60 e^x x^5-20 x^6\right )+e^{4+2 x} \left (10 e^{4 x} x^4-40 e^{3 x} x^5+60 e^{2 x} x^6-40 e^x x^7+10 x^8\right )} \, dx=\int \frac {{\mathrm {e}}^{2\,x+4}\,\left (x-4\,x^2\right )-{\mathrm {e}}^x\,\left (2\,x^3+x^2\right )+3\,x^3}{2\,{\mathrm {e}}^{10\,x+20}+{\mathrm {e}}^{2\,x+4}\,\left (10\,x^4\,{\mathrm {e}}^{4\,x}-40\,x^7\,{\mathrm {e}}^x-40\,x^5\,{\mathrm {e}}^{3\,x}+60\,x^6\,{\mathrm {e}}^{2\,x}+10\,x^8\right )+10\,x^9\,{\mathrm {e}}^x+{\mathrm {e}}^{6\,x+12}\,\left (20\,x^2\,{\mathrm {e}}^{2\,x}-40\,x^3\,{\mathrm {e}}^x+20\,x^4\right )+{\mathrm {e}}^{8\,x+16}\,\left (10\,x\,{\mathrm {e}}^x-10\,x^2\right )+2\,x^5\,{\mathrm {e}}^{5\,x}-10\,x^6\,{\mathrm {e}}^{4\,x}+20\,x^7\,{\mathrm {e}}^{3\,x}-20\,x^8\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^{4\,x+8}\,\left (60\,x^5\,{\mathrm {e}}^x+20\,x^3\,{\mathrm {e}}^{3\,x}-60\,x^4\,{\mathrm {e}}^{2\,x}-20\,x^6\right )-2\,x^{10}} \,d x \] Input:
int((exp(2*x + 4)*(x - 4*x^2) - exp(x)*(x^2 + 2*x^3) + 3*x^3)/(2*exp(10*x + 20) + exp(2*x + 4)*(10*x^4*exp(4*x) - 40*x^7*exp(x) - 40*x^5*exp(3*x) + 60*x^6*exp(2*x) + 10*x^8) + 10*x^9*exp(x) + exp(6*x + 12)*(20*x^2*exp(2*x) - 40*x^3*exp(x) + 20*x^4) + exp(8*x + 16)*(10*x*exp(x) - 10*x^2) + 2*x^5* exp(5*x) - 10*x^6*exp(4*x) + 20*x^7*exp(3*x) - 20*x^8*exp(2*x) + exp(4*x + 8)*(60*x^5*exp(x) + 20*x^3*exp(3*x) - 60*x^4*exp(2*x) - 20*x^6) - 2*x^10) ,x)
Output:
int((exp(2*x + 4)*(x - 4*x^2) - exp(x)*(x^2 + 2*x^3) + 3*x^3)/(2*exp(10*x + 20) + exp(2*x + 4)*(10*x^4*exp(4*x) - 40*x^7*exp(x) - 40*x^5*exp(3*x) + 60*x^6*exp(2*x) + 10*x^8) + 10*x^9*exp(x) + exp(6*x + 12)*(20*x^2*exp(2*x) - 40*x^3*exp(x) + 20*x^4) + exp(8*x + 16)*(10*x*exp(x) - 10*x^2) + 2*x^5* exp(5*x) - 10*x^6*exp(4*x) + 20*x^7*exp(3*x) - 20*x^8*exp(2*x) + exp(4*x + 8)*(60*x^5*exp(x) + 20*x^3*exp(3*x) - 60*x^4*exp(2*x) - 20*x^6) - 2*x^10) , x)
\[ \int \frac {3 x^3+e^{4+2 x} \left (x-4 x^2\right )+e^x \left (-x^2-2 x^3\right )}{2 e^{20+10 x}+2 e^{5 x} x^5-10 e^{4 x} x^6+20 e^{3 x} x^7-20 e^{2 x} x^8+10 e^x x^9-2 x^{10}+e^{16+8 x} \left (10 e^x x-10 x^2\right )+e^{12+6 x} \left (20 e^{2 x} x^2-40 e^x x^3+20 x^4\right )+e^{8+4 x} \left (20 e^{3 x} x^3-60 e^{2 x} x^4+60 e^x x^5-20 x^6\right )+e^{4+2 x} \left (10 e^{4 x} x^4-40 e^{3 x} x^5+60 e^{2 x} x^6-40 e^x x^7+10 x^8\right )} \, dx =\text {Too large to display} \] Input:
int(((-4*x^2+x)*exp(4+2*x)+(-2*x^3-x^2)*exp(x)+3*x^3)/(2*exp(4+2*x)^5+(10* exp(x)*x-10*x^2)*exp(4+2*x)^4+(20*exp(x)^2*x^2-40*exp(x)*x^3+20*x^4)*exp(4 +2*x)^3+(20*x^3*exp(x)^3-60*exp(x)^2*x^4+60*x^5*exp(x)-20*x^6)*exp(4+2*x)^ 2+(10*x^4*exp(x)^4-40*x^5*exp(x)^3+60*x^6*exp(x)^2-40*x^7*exp(x)+10*x^8)*e xp(4+2*x)+2*x^5*exp(x)^5-10*x^6*exp(x)^4+20*x^7*exp(x)^3-20*x^8*exp(x)^2+1 0*x^9*exp(x)-2*x^10),x)
Output:
(3*int(x**3/(e**(10*x)*e**20 + 5*e**(9*x)*e**16*x - 5*e**(8*x)*e**16*x**2 + 10*e**(8*x)*e**12*x**2 - 20*e**(7*x)*e**12*x**3 + 10*e**(7*x)*e**8*x**3 + 10*e**(6*x)*e**12*x**4 - 30*e**(6*x)*e**8*x**4 + 5*e**(6*x)*e**4*x**4 + 30*e**(5*x)*e**8*x**5 - 20*e**(5*x)*e**4*x**5 + e**(5*x)*x**5 - 10*e**(4*x )*e**8*x**6 + 30*e**(4*x)*e**4*x**6 - 5*e**(4*x)*x**6 - 20*e**(3*x)*e**4*x **7 + 10*e**(3*x)*x**7 + 5*e**(2*x)*e**4*x**8 - 10*e**(2*x)*x**8 + 5*e**x* x**9 - x**10),x) - 4*int((e**(2*x)*x**2)/(e**(10*x)*e**20 + 5*e**(9*x)*e** 16*x - 5*e**(8*x)*e**16*x**2 + 10*e**(8*x)*e**12*x**2 - 20*e**(7*x)*e**12* x**3 + 10*e**(7*x)*e**8*x**3 + 10*e**(6*x)*e**12*x**4 - 30*e**(6*x)*e**8*x **4 + 5*e**(6*x)*e**4*x**4 + 30*e**(5*x)*e**8*x**5 - 20*e**(5*x)*e**4*x**5 + e**(5*x)*x**5 - 10*e**(4*x)*e**8*x**6 + 30*e**(4*x)*e**4*x**6 - 5*e**(4 *x)*x**6 - 20*e**(3*x)*e**4*x**7 + 10*e**(3*x)*x**7 + 5*e**(2*x)*e**4*x**8 - 10*e**(2*x)*x**8 + 5*e**x*x**9 - x**10),x)*e**4 + int((e**(2*x)*x)/(e** (10*x)*e**20 + 5*e**(9*x)*e**16*x - 5*e**(8*x)*e**16*x**2 + 10*e**(8*x)*e* *12*x**2 - 20*e**(7*x)*e**12*x**3 + 10*e**(7*x)*e**8*x**3 + 10*e**(6*x)*e* *12*x**4 - 30*e**(6*x)*e**8*x**4 + 5*e**(6*x)*e**4*x**4 + 30*e**(5*x)*e**8 *x**5 - 20*e**(5*x)*e**4*x**5 + e**(5*x)*x**5 - 10*e**(4*x)*e**8*x**6 + 30 *e**(4*x)*e**4*x**6 - 5*e**(4*x)*x**6 - 20*e**(3*x)*e**4*x**7 + 10*e**(3*x )*x**7 + 5*e**(2*x)*e**4*x**8 - 10*e**(2*x)*x**8 + 5*e**x*x**9 - x**10),x) *e**4 - 2*int((e**x*x**3)/(e**(10*x)*e**20 + 5*e**(9*x)*e**16*x - 5*e**...