\(\int \frac {e^x (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 (-64 x^4+32 x^5))+e^{2 x} (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 (-8 x+8 x^2+128 x^5-64 x^6))+e^{3 x} (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} (8 x^3+24 x^6)+e^5 (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7))+e^{4 x} (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} (-8 x^4-8 x^7)+e^5 (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8))+e^{5 x} (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} (x^2+2 x^5+x^8)+e^5 (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9))}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 (-64 x^4+32 x^5)+e^x (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 (128 x^5-64 x^6))+e^{2 x} (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} (8 x^3+24 x^6)+e^5 (-32 x^3+16 x^4-96 x^6+48 x^7))+e^{3 x} (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} (-8 x^4-8 x^7)+e^5 (32 x^4-16 x^5+32 x^7-16 x^8))+e^{4 x} (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} (x^2+2 x^5+x^8)+e^5 (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9))} \, dx\) [2729]

Optimal result

Integrand size = 726, antiderivative size = 34 \[ \int \frac {e^x \left (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )\right )+e^{2 x} \left (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (-8 x+8 x^2+128 x^5-64 x^6\right )\right )+e^{3 x} \left (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{4 x} \left (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{5 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )+e^x \left (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (128 x^5-64 x^6\right )\right )+e^{2 x} \left (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (-32 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{3 x} \left (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{4 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )} \, dx=-2+e^x+\frac {1}{\left (-2+e^5+x\right ) \left (x+\left (2 e^{-x} x-x^2\right )^2\right )} \] Output:

1/(exp(5)+x-2)/((2*x/exp(x)-x^2)^2+x)+exp(x)-2
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(114\) vs. \(2(34)=68\).

Time = 10.34 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.35 \[ \int \frac {e^x \left (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )\right )+e^{2 x} \left (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (-8 x+8 x^2+128 x^5-64 x^6\right )\right )+e^{3 x} \left (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{4 x} \left (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{5 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )+e^x \left (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (128 x^5-64 x^6\right )\right )+e^{2 x} \left (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (-32 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{3 x} \left (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{4 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )} \, dx=\frac {e^x \left (4 e^5 x^2+4 (-2+x) x^2-4 e^{5+x} x^3+e^x \left (1+8 x^3-4 x^4\right )+e^{5+2 x} \left (x+x^4\right )+e^{2 x} x \left (-2+x-2 x^3+x^4\right )\right )}{x \left (-2+e^5+x\right ) \left (4 x-4 e^x x^2+e^{2 x} \left (1+x^3\right )\right )} \] Input:

Integrate[(E^x*(64*x^4 + 16*E^10*x^4 - 64*x^5 + 16*x^6 + E^5*(-64*x^4 + 32 
*x^5)) + E^(2*x)*(16*x - 28*x^2 + 8*x^3 - 128*x^5 - 32*E^10*x^5 + 128*x^6 
- 32*x^7 + E^5*(-8*x + 8*x^2 + 128*x^5 - 64*x^6)) + E^(3*x)*(-24*x^2 + 56* 
x^3 - 36*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 + E^10*(8*x^3 + 24*x^6) + 
E^5*(12*x^2 - 36*x^3 + 16*x^4 - 96*x^6 + 48*x^7)) + E^(4*x)*(2 - 2*x + 8*x 
^3 - 37*x^4 + 32*x^5 - 8*x^6 - 32*x^7 + 32*x^8 - 8*x^9 + E^10*(-8*x^4 - 8* 
x^7) + E^5*(-1 - 4*x^3 + 32*x^4 - 16*x^5 + 32*x^7 - 16*x^8)) + E^(5*x)*(4* 
x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*x^7 + 4*x^8 - 4*x^9 + x^10 + E^10*(x 
^2 + 2*x^5 + x^8) + E^5*(-4*x^2 + 2*x^3 - 8*x^5 + 4*x^6 - 4*x^8 + 2*x^9))) 
/(64*x^4 + 16*E^10*x^4 - 64*x^5 + 16*x^6 + E^5*(-64*x^4 + 32*x^5) + E^x*(- 
128*x^5 - 32*E^10*x^5 + 128*x^6 - 32*x^7 + E^5*(128*x^5 - 64*x^6)) + E^(2* 
x)*(32*x^3 - 32*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 + E^10*(8*x^3 + 24* 
x^6) + E^5*(-32*x^3 + 16*x^4 - 96*x^6 + 48*x^7)) + E^(3*x)*(-32*x^4 + 32*x 
^5 - 8*x^6 - 32*x^7 + 32*x^8 - 8*x^9 + E^10*(-8*x^4 - 8*x^7) + E^5*(32*x^4 
 - 16*x^5 + 32*x^7 - 16*x^8)) + E^(4*x)*(4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x 
^6 + 2*x^7 + 4*x^8 - 4*x^9 + x^10 + E^10*(x^2 + 2*x^5 + x^8) + E^5*(-4*x^2 
 + 2*x^3 - 8*x^5 + 4*x^6 - 4*x^8 + 2*x^9))),x]
 

Output:

(E^x*(4*E^5*x^2 + 4*(-2 + x)*x^2 - 4*E^(5 + x)*x^3 + E^x*(1 + 8*x^3 - 4*x^ 
4) + E^(5 + 2*x)*(x + x^4) + E^(2*x)*x*(-2 + x - 2*x^3 + x^4)))/(x*(-2 + E 
^5 + x)*(4*x - 4*E^x*x^2 + E^(2*x)*(1 + x^3)))
 

Rubi [F]

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.

\(\displaystyle \int \frac {e^x \left (16 x^6-64 x^5+16 e^{10} x^4+64 x^4+e^5 \left (32 x^5-64 x^4\right )\right )+e^{2 x} \left (-32 x^7+128 x^6-32 e^{10} x^5-128 x^5+8 x^3-28 x^2+e^5 \left (-64 x^6+128 x^5+8 x^2-8 x\right )+16 x\right )+e^{4 x} \left (-8 x^9+32 x^8-32 x^7-8 x^6+32 x^5-37 x^4+8 x^3+e^{10} \left (-8 x^7-8 x^4\right )+e^5 \left (-16 x^8+32 x^7-16 x^5+32 x^4-4 x^3-1\right )-2 x+2\right )+e^{3 x} \left (24 x^8-96 x^7+96 x^6+8 x^5-36 x^4+56 x^3-24 x^2+e^{10} \left (24 x^6+8 x^3\right )+e^5 \left (48 x^7-96 x^6+16 x^4-36 x^3+12 x^2\right )\right )+e^{5 x} \left (x^{10}-4 x^9+4 x^8+2 x^7-8 x^6+8 x^5+x^4-4 x^3+4 x^2+e^{10} \left (x^8+2 x^5+x^2\right )+e^5 \left (2 x^9-4 x^8+4 x^6-8 x^5+2 x^3-4 x^2\right )\right )}{16 x^6-64 x^5+16 e^{10} x^4+64 x^4+e^5 \left (32 x^5-64 x^4\right )+e^x \left (-32 x^7+128 x^6-32 e^{10} x^5-128 x^5+e^5 \left (128 x^5-64 x^6\right )\right )+e^{3 x} \left (-8 x^9+32 x^8-32 x^7-8 x^6+32 x^5-32 x^4+e^{10} \left (-8 x^7-8 x^4\right )+e^5 \left (-16 x^8+32 x^7-16 x^5+32 x^4\right )\right )+e^{2 x} \left (24 x^8-96 x^7+96 x^6+8 x^5-32 x^4+32 x^3+e^{10} \left (24 x^6+8 x^3\right )+e^5 \left (48 x^7-96 x^6+16 x^4-32 x^3\right )\right )+e^{4 x} \left (x^{10}-4 x^9+4 x^8+2 x^7-8 x^6+8 x^5+x^4-4 x^3+4 x^2+e^{10} \left (x^8+2 x^5+x^2\right )+e^5 \left (2 x^9-4 x^8+4 x^6-8 x^5+2 x^3-4 x^2\right )\right )} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {e^x \left (16 x^6-64 x^5+16 e^{10} x^4+64 x^4+e^5 \left (32 x^5-64 x^4\right )\right )+e^{2 x} \left (-32 x^7+128 x^6-32 e^{10} x^5-128 x^5+8 x^3-28 x^2+e^5 \left (-64 x^6+128 x^5+8 x^2-8 x\right )+16 x\right )+e^{4 x} \left (-8 x^9+32 x^8-32 x^7-8 x^6+32 x^5-37 x^4+8 x^3+e^{10} \left (-8 x^7-8 x^4\right )+e^5 \left (-16 x^8+32 x^7-16 x^5+32 x^4-4 x^3-1\right )-2 x+2\right )+e^{3 x} \left (24 x^8-96 x^7+96 x^6+8 x^5-36 x^4+56 x^3-24 x^2+e^{10} \left (24 x^6+8 x^3\right )+e^5 \left (48 x^7-96 x^6+16 x^4-36 x^3+12 x^2\right )\right )+e^{5 x} \left (x^{10}-4 x^9+4 x^8+2 x^7-8 x^6+8 x^5+x^4-4 x^3+4 x^2+e^{10} \left (x^8+2 x^5+x^2\right )+e^5 \left (2 x^9-4 x^8+4 x^6-8 x^5+2 x^3-4 x^2\right )\right )}{16 x^6-64 x^5+\left (64+16 e^{10}\right ) x^4+e^5 \left (32 x^5-64 x^4\right )+e^x \left (-32 x^7+128 x^6-32 e^{10} x^5-128 x^5+e^5 \left (128 x^5-64 x^6\right )\right )+e^{3 x} \left (-8 x^9+32 x^8-32 x^7-8 x^6+32 x^5-32 x^4+e^{10} \left (-8 x^7-8 x^4\right )+e^5 \left (-16 x^8+32 x^7-16 x^5+32 x^4\right )\right )+e^{2 x} \left (24 x^8-96 x^7+96 x^6+8 x^5-32 x^4+32 x^3+e^{10} \left (24 x^6+8 x^3\right )+e^5 \left (48 x^7-96 x^6+16 x^4-32 x^3\right )\right )+e^{4 x} \left (x^{10}-4 x^9+4 x^8+2 x^7-8 x^6+8 x^5+x^4-4 x^3+4 x^2+e^{10} \left (x^8+2 x^5+x^2\right )+e^5 \left (2 x^9-4 x^8+4 x^6-8 x^5+2 x^3-4 x^2\right )\right )}dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^x \left (-32 e^{x+10} x^5+16 (x-2)^2 x^4+32 e^5 (x-2) x^4+16 e^{10} x^4+e^{4 x+10} \left (x^4+x\right )^2+2 e^{4 x+5} (x-2) \left (x^4+x\right )^2+8 e^{2 (x+5)} \left (3 x^3+1\right ) x^3-8 e^{x+5} \left (8 x^5-16 x^4-x+1\right ) x-8 e^{3 x+10} \left (x^3+1\right ) x^4+4 e^{2 x+5} \left (12 x^5-24 x^4+4 x^2-9 x+3\right ) x^2+e^{4 x} \left (x^4-2 x^3+x-2\right )^2 x^2-4 e^x \left (8 x^6-32 x^5+32 x^4-2 x^2+7 x-4\right ) x-e^{3 x+5} \left (16 x^8-32 x^7+16 x^5-32 x^4+4 x^3+1\right )+4 e^{2 x} \left (6 x^6-24 x^5+24 x^4+2 x^3-9 x^2+14 x-6\right ) x^2+e^{3 x} \left (-8 x^9+32 x^8-32 x^7-8 x^6+32 x^5-37 x^4+8 x^3-2 x+2\right )\right )}{\left (-x-e^5+2\right )^2 x^2 \left (e^{2 x} \left (x^3+1\right )-4 e^x x^2+4 x\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {4 e^x \left (2 e^x x^7+2 e^x x^6-4 x^6-4 x^5-9 e^x x^3-4 x^3+8 x^2-2 e^x x+e^x\right )}{x \left (x+e^5-2\right ) \left (x^3+1\right )^2 \left (e^{2 x} x^3-4 e^x x^2+4 x+e^{2 x}\right )^2}+\frac {e^x \left (-5 e^x x^7-4 x^7+8 \left (1-\frac {e^5}{2}\right ) e^x x^6+4 \left (1-e^5\right ) x^6+8 \left (1-\frac {e^5}{2}\right ) x^5-7 e^x x^4-4 x^4+16 \left (1-\frac {e^5}{4}\right ) x^3+10 \left (1-\frac {e^5}{2}\right ) e^x x^3-16 \left (1-\frac {e^5}{2}\right ) x^2-2 e^x x+2 \left (1-\frac {e^5}{2}\right ) e^x\right )}{\left (-x-e^5+2\right )^2 x^2 \left (x^3+1\right )^2 \left (e^{2 x} x^3-4 e^x x^2+4 x+e^{2 x}\right )}+e^x\right )dx\)

\(\Big \downarrow \) 7299

\(\displaystyle \int \left (-\frac {4 e^x \left (2 e^x x^7+2 e^x x^6-4 x^6-4 x^5-9 e^x x^3-4 x^3+8 x^2-2 e^x x+e^x\right )}{x \left (x+e^5-2\right ) \left (x^3+1\right )^2 \left (e^{2 x} x^3-4 e^x x^2+4 x+e^{2 x}\right )^2}+\frac {e^x \left (-5 e^x x^7-4 x^7+8 \left (1-\frac {e^5}{2}\right ) e^x x^6+4 \left (1-e^5\right ) x^6+8 \left (1-\frac {e^5}{2}\right ) x^5-7 e^x x^4-4 x^4+16 \left (1-\frac {e^5}{4}\right ) x^3+10 \left (1-\frac {e^5}{2}\right ) e^x x^3-16 \left (1-\frac {e^5}{2}\right ) x^2-2 e^x x+2 \left (1-\frac {e^5}{2}\right ) e^x\right )}{\left (-x-e^5+2\right )^2 x^2 \left (x^3+1\right )^2 \left (e^{2 x} x^3-4 e^x x^2+4 x+e^{2 x}\right )}+e^x\right )dx\)

Input:

Int[(E^x*(64*x^4 + 16*E^10*x^4 - 64*x^5 + 16*x^6 + E^5*(-64*x^4 + 32*x^5)) 
 + E^(2*x)*(16*x - 28*x^2 + 8*x^3 - 128*x^5 - 32*E^10*x^5 + 128*x^6 - 32*x 
^7 + E^5*(-8*x + 8*x^2 + 128*x^5 - 64*x^6)) + E^(3*x)*(-24*x^2 + 56*x^3 - 
36*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 + E^10*(8*x^3 + 24*x^6) + E^5*(1 
2*x^2 - 36*x^3 + 16*x^4 - 96*x^6 + 48*x^7)) + E^(4*x)*(2 - 2*x + 8*x^3 - 3 
7*x^4 + 32*x^5 - 8*x^6 - 32*x^7 + 32*x^8 - 8*x^9 + E^10*(-8*x^4 - 8*x^7) + 
 E^5*(-1 - 4*x^3 + 32*x^4 - 16*x^5 + 32*x^7 - 16*x^8)) + E^(5*x)*(4*x^2 - 
4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*x^7 + 4*x^8 - 4*x^9 + x^10 + E^10*(x^2 + 2 
*x^5 + x^8) + E^5*(-4*x^2 + 2*x^3 - 8*x^5 + 4*x^6 - 4*x^8 + 2*x^9)))/(64*x 
^4 + 16*E^10*x^4 - 64*x^5 + 16*x^6 + E^5*(-64*x^4 + 32*x^5) + E^x*(-128*x^ 
5 - 32*E^10*x^5 + 128*x^6 - 32*x^7 + E^5*(128*x^5 - 64*x^6)) + E^(2*x)*(32 
*x^3 - 32*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 24*x^8 + E^10*(8*x^3 + 24*x^6) + 
 E^5*(-32*x^3 + 16*x^4 - 96*x^6 + 48*x^7)) + E^(3*x)*(-32*x^4 + 32*x^5 - 8 
*x^6 - 32*x^7 + 32*x^8 - 8*x^9 + E^10*(-8*x^4 - 8*x^7) + E^5*(32*x^4 - 16* 
x^5 + 32*x^7 - 16*x^8)) + E^(4*x)*(4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2 
*x^7 + 4*x^8 - 4*x^9 + x^10 + E^10*(x^2 + 2*x^5 + x^8) + E^5*(-4*x^2 + 2*x 
^3 - 8*x^5 + 4*x^6 - 4*x^8 + 2*x^9))),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(82\) vs. \(2(31)=62\).

Time = 14.97 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.44

method	result	size
risch	\(\frac {1}{\left (x^{3} {\mathrm e}^{5}+x^{4}-2 x^{3}+{\mathrm e}^{5}+x -2\right ) x}+{\mathrm e}^{x}+\frac {4 \,{\mathrm e}^{x} x -4}{\left (x^{3} {\mathrm e}^{5}+x^{4}-2 x^{3}+{\mathrm e}^{5}+x -2\right ) \left ({\mathrm e}^{2 x} x^{3}-4 \,{\mathrm e}^{x} x^{2}+{\mathrm e}^{2 x}+4 x \right )}\)	\(83\)
parallelrisch	\(\frac {-2 x^{4} {\mathrm e}^{3 x}-4 x^{4} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} x^{5}+x^{2} {\mathrm e}^{3 x}-2 x \,{\mathrm e}^{3 x}-8 \,{\mathrm e}^{x} x^{2}+8 \,{\mathrm e}^{2 x} x^{3}+4 \,{\mathrm e}^{x} x^{3}+{\mathrm e}^{2 x}+{\mathrm e}^{5} {\mathrm e}^{3 x} x^{4}-4 \,{\mathrm e}^{2 x} x^{3} {\mathrm e}^{5}+x \,{\mathrm e}^{5} {\mathrm e}^{3 x}+4 \,{\mathrm e}^{x} x^{2} {\mathrm e}^{5}}{x \left ({\mathrm e}^{2 x} x^{3} {\mathrm e}^{5}+x^{4} {\mathrm e}^{2 x}-2 \,{\mathrm e}^{2 x} x^{3}-4 \,{\mathrm e}^{x} x^{2} {\mathrm e}^{5}-4 \,{\mathrm e}^{x} x^{3}+{\mathrm e}^{5} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x}+8 \,{\mathrm e}^{x} x^{2}+4 x \,{\mathrm e}^{5}-2 \,{\mathrm e}^{2 x}+4 x^{2}-8 x \right )}\)	\(197\)

Input:

int((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5 
)+x^10-4*x^9+4*x^8+2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^5+((-8*x^7-8* 
x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+32*x^8-3 
2*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp(5)^2+( 
48*x^7-96*x^6+16*x^4-36*x^3+12*x^2)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^5-36*x 
^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*x^2-8*x)*e 
xp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp(5)^2+ 
(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^2)*exp 
(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+2*x^7- 
8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32 
*x^7-16*x^5+32*x^4)*exp(5)-8*x^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)*exp(x) 
^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*exp(5)+24*x^8-96 
*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6+128*x 
^5)*exp(5)-32*x^7+128*x^6-128*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64*x^4)* 
exp(5)+16*x^6-64*x^5+64*x^4),x,method=_RETURNVERBOSE)
 

Output:

1/(x^3*exp(5)+x^4-2*x^3+exp(5)+x-2)/x+exp(x)+4*(exp(x)*x-1)/(x^3*exp(5)+x^ 
4-2*x^3+exp(5)+x-2)/(exp(x)^2*x^3-4*exp(x)*x^2+exp(x)^2+4*x)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (29) = 58\).

Time = 0.12 (sec) , antiderivative size = 141, normalized size of antiderivative = 4.15 \[ \int \frac {e^x \left (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )\right )+e^{2 x} \left (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (-8 x+8 x^2+128 x^5-64 x^6\right )\right )+e^{3 x} \left (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{4 x} \left (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{5 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )+e^x \left (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (128 x^5-64 x^6\right )\right )+e^{2 x} \left (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (-32 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{3 x} \left (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{4 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )} \, dx=\frac {{\left (x^{5} - 2 \, x^{4} + x^{2} + {\left (x^{4} + x\right )} e^{5} - 2 \, x\right )} e^{\left (3 \, x\right )} - {\left (4 \, x^{4} + 4 \, x^{3} e^{5} - 8 \, x^{3} - 1\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{3} + x^{2} e^{5} - 2 \, x^{2}\right )} e^{x}}{4 \, x^{3} + 4 \, x^{2} e^{5} - 8 \, x^{2} + {\left (x^{5} - 2 \, x^{4} + x^{2} + {\left (x^{4} + x\right )} e^{5} - 2 \, x\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{4} + x^{3} e^{5} - 2 \, x^{3}\right )} e^{x}} \] Input:

integrate((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2) 
*exp(5)+x^10-4*x^9+4*x^8+2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^5+((-8* 
x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+32 
*x^8-32*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp( 
5)^2+(48*x^7-96*x^6+16*x^4-36*x^3+12*x^2)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^ 
5-36*x^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*x^2- 
8*x)*exp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp 
(5)^2+(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^ 
2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+ 
2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16* 
x^8+32*x^7-16*x^5+32*x^4)*exp(5)-8*x^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)* 
exp(x)^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*exp(5)+24* 
x^8-96*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6 
+128*x^5)*exp(5)-32*x^7+128*x^6-128*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64 
*x^4)*exp(5)+16*x^6-64*x^5+64*x^4),x, algorithm="fricas")
 

Output:

((x^5 - 2*x^4 + x^2 + (x^4 + x)*e^5 - 2*x)*e^(3*x) - (4*x^4 + 4*x^3*e^5 - 
8*x^3 - 1)*e^(2*x) + 4*(x^3 + x^2*e^5 - 2*x^2)*e^x)/(4*x^3 + 4*x^2*e^5 - 8 
*x^2 + (x^5 - 2*x^4 + x^2 + (x^4 + x)*e^5 - 2*x)*e^(2*x) - 4*(x^4 + x^3*e^ 
5 - 2*x^3)*e^x)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 155 vs. \(2 (26) = 52\).

Time = 3.59 (sec) , antiderivative size = 155, normalized size of antiderivative = 4.56 \[ \int \frac {e^x \left (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )\right )+e^{2 x} \left (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (-8 x+8 x^2+128 x^5-64 x^6\right )\right )+e^{3 x} \left (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{4 x} \left (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{5 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )+e^x \left (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (128 x^5-64 x^6\right )\right )+e^{2 x} \left (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (-32 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{3 x} \left (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{4 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )} \, dx=\frac {4 x e^{x} - 4}{4 x^{5} - 8 x^{4} + 4 x^{4} e^{5} + 4 x^{2} - 8 x + 4 x e^{5} + \left (- 4 x^{6} - 4 x^{5} e^{5} + 8 x^{5} - 4 x^{3} - 4 x^{2} e^{5} + 8 x^{2}\right ) e^{x} + \left (x^{7} - 2 x^{6} + x^{6} e^{5} + 2 x^{4} - 4 x^{3} + 2 x^{3} e^{5} + x - 2 + e^{5}\right ) e^{2 x}} + e^{x} + \frac {1}{x^{5} + x^{4} \left (-2 + e^{5}\right ) + x^{2} + x \left (-2 + e^{5}\right )} \] Input:

integrate((((x**8+2*x**5+x**2)*exp(5)**2+(2*x**9-4*x**8+4*x**6-8*x**5+2*x* 
*3-4*x**2)*exp(5)+x**10-4*x**9+4*x**8+2*x**7-8*x**6+8*x**5+x**4-4*x**3+4*x 
**2)*exp(x)**5+((-8*x**7-8*x**4)*exp(5)**2+(-16*x**8+32*x**7-16*x**5+32*x* 
*4-4*x**3-1)*exp(5)-8*x**9+32*x**8-32*x**7-8*x**6+32*x**5-37*x**4+8*x**3-2 
*x+2)*exp(x)**4+((24*x**6+8*x**3)*exp(5)**2+(48*x**7-96*x**6+16*x**4-36*x* 
*3+12*x**2)*exp(5)+24*x**8-96*x**7+96*x**6+8*x**5-36*x**4+56*x**3-24*x**2) 
*exp(x)**3+(-32*x**5*exp(5)**2+(-64*x**6+128*x**5+8*x**2-8*x)*exp(5)-32*x* 
*7+128*x**6-128*x**5+8*x**3-28*x**2+16*x)*exp(x)**2+(16*x**4*exp(5)**2+(32 
*x**5-64*x**4)*exp(5)+16*x**6-64*x**5+64*x**4)*exp(x))/(((x**8+2*x**5+x**2 
)*exp(5)**2+(2*x**9-4*x**8+4*x**6-8*x**5+2*x**3-4*x**2)*exp(5)+x**10-4*x** 
9+4*x**8+2*x**7-8*x**6+8*x**5+x**4-4*x**3+4*x**2)*exp(x)**4+((-8*x**7-8*x* 
*4)*exp(5)**2+(-16*x**8+32*x**7-16*x**5+32*x**4)*exp(5)-8*x**9+32*x**8-32* 
x**7-8*x**6+32*x**5-32*x**4)*exp(x)**3+((24*x**6+8*x**3)*exp(5)**2+(48*x** 
7-96*x**6+16*x**4-32*x**3)*exp(5)+24*x**8-96*x**7+96*x**6+8*x**5-32*x**4+3 
2*x**3)*exp(x)**2+(-32*x**5*exp(5)**2+(-64*x**6+128*x**5)*exp(5)-32*x**7+1 
28*x**6-128*x**5)*exp(x)+16*x**4*exp(5)**2+(32*x**5-64*x**4)*exp(5)+16*x** 
6-64*x**5+64*x**4),x)
 

Output:

(4*x*exp(x) - 4)/(4*x**5 - 8*x**4 + 4*x**4*exp(5) + 4*x**2 - 8*x + 4*x*exp 
(5) + (-4*x**6 - 4*x**5*exp(5) + 8*x**5 - 4*x**3 - 4*x**2*exp(5) + 8*x**2) 
*exp(x) + (x**7 - 2*x**6 + x**6*exp(5) + 2*x**4 - 4*x**3 + 2*x**3*exp(5) + 
 x - 2 + exp(5))*exp(2*x)) + exp(x) + 1/(x**5 + x**4*(-2 + exp(5)) + x**2 
+ x*(-2 + exp(5)))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 125 vs. \(2 (29) = 58\).

Time = 0.35 (sec) , antiderivative size = 125, normalized size of antiderivative = 3.68 \[ \int \frac {e^x \left (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )\right )+e^{2 x} \left (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (-8 x+8 x^2+128 x^5-64 x^6\right )\right )+e^{3 x} \left (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{4 x} \left (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{5 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )+e^x \left (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (128 x^5-64 x^6\right )\right )+e^{2 x} \left (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (-32 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{3 x} \left (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{4 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )} \, dx=\frac {{\left (x^{5} + x^{4} {\left (e^{5} - 2\right )} + x^{2} + x {\left (e^{5} - 2\right )}\right )} e^{\left (3 \, x\right )} - {\left (4 \, x^{4} + 4 \, x^{3} {\left (e^{5} - 2\right )} - 1\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{3} + x^{2} {\left (e^{5} - 2\right )}\right )} e^{x}}{4 \, x^{3} + 4 \, x^{2} {\left (e^{5} - 2\right )} + {\left (x^{5} + x^{4} {\left (e^{5} - 2\right )} + x^{2} + x {\left (e^{5} - 2\right )}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{4} + x^{3} {\left (e^{5} - 2\right )}\right )} e^{x}} \] Input:

integrate((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2) 
*exp(5)+x^10-4*x^9+4*x^8+2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^5+((-8* 
x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+32 
*x^8-32*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp( 
5)^2+(48*x^7-96*x^6+16*x^4-36*x^3+12*x^2)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^ 
5-36*x^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*x^2- 
8*x)*exp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp 
(5)^2+(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^ 
2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+ 
2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16* 
x^8+32*x^7-16*x^5+32*x^4)*exp(5)-8*x^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)* 
exp(x)^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*exp(5)+24* 
x^8-96*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6 
+128*x^5)*exp(5)-32*x^7+128*x^6-128*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64 
*x^4)*exp(5)+16*x^6-64*x^5+64*x^4),x, algorithm="maxima")
 

Output:

((x^5 + x^4*(e^5 - 2) + x^2 + x*(e^5 - 2))*e^(3*x) - (4*x^4 + 4*x^3*(e^5 - 
 2) - 1)*e^(2*x) + 4*(x^3 + x^2*(e^5 - 2))*e^x)/(4*x^3 + 4*x^2*(e^5 - 2) + 
 (x^5 + x^4*(e^5 - 2) + x^2 + x*(e^5 - 2))*e^(2*x) - 4*(x^4 + x^3*(e^5 - 2 
))*e^x)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 992 vs. \(2 (29) = 58\).

Time = 7.38 (sec) , antiderivative size = 992, normalized size of antiderivative = 29.18 \[ \int \frac {e^x \left (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )\right )+e^{2 x} \left (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (-8 x+8 x^2+128 x^5-64 x^6\right )\right )+e^{3 x} \left (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{4 x} \left (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{5 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )+e^x \left (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (128 x^5-64 x^6\right )\right )+e^{2 x} \left (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (-32 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{3 x} \left (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{4 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )} \, dx=\text {Too large to display} \] Input:

integrate((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2) 
*exp(5)+x^10-4*x^9+4*x^8+2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^5+((-8* 
x^7-8*x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+32 
*x^8-32*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp( 
5)^2+(48*x^7-96*x^6+16*x^4-36*x^3+12*x^2)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^ 
5-36*x^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*x^2- 
8*x)*exp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp 
(5)^2+(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^ 
2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+ 
2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16* 
x^8+32*x^7-16*x^5+32*x^4)*exp(5)-8*x^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)* 
exp(x)^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*exp(5)+24* 
x^8-96*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6 
+128*x^5)*exp(5)-32*x^7+128*x^6-128*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64 
*x^4)*exp(5)+16*x^6-64*x^5+64*x^4),x, algorithm="giac")
 

Output:

(18*x^5*e^(3*x) + x^5*e^(3*x + 20) - 8*x^5*e^(3*x + 15) + 24*x^5*e^(3*x + 
10) - 33*x^5*e^(3*x + 5) - 36*x^4*e^(3*x) - 63*x^4*e^(2*x) + x^4*e^(3*x + 
25) - 10*x^4*e^(3*x + 20) + 40*x^4*e^(3*x + 15) - 81*x^4*e^(3*x + 10) + 84 
*x^4*e^(3*x + 5) + 8*x^4*e^(2*x + 25) - 52*x^4*e^(2*x + 20) + 127*x^4*e^(2 
*x + 15) - 154*x^4*e^(2*x + 10) + 120*x^4*e^(2*x + 5) + 126*x^3*e^(2*x) - 
4*x^3*e^(2*x + 25) + 39*x^3*e^(2*x + 20) - 152*x^3*e^(2*x + 15) + 300*x^3* 
e^(2*x + 10) - 303*x^3*e^(2*x + 5) - 32*x^3*e^(x + 25) + 196*x^3*e^(x + 20 
) - 412*x^3*e^(x + 15) + 328*x^3*e^(x + 10) - 84*x^3*e^(x + 5) + 36*x^3*e^ 
x + 32*x^2*e^25 - 192*x^2*e^20 + 380*x^2*e^15 - 232*x^2*e^10 - 48*x^2*e^5 
+ 18*x^2*e^(3*x) + x^2*e^(3*x + 20) - 8*x^2*e^(3*x + 15) + 24*x^2*e^(3*x + 
 10) - 33*x^2*e^(3*x + 5) + 4*x^2*e^(x + 25) - 36*x^2*e^(x + 20) + 128*x^2 
*e^(x + 15) - 228*x^2*e^(x + 10) + 204*x^2*e^(x + 5) - 72*x^2*e^x + 36*x^2 
 - 4*x*e^20 + 32*x*e^15 - 96*x*e^10 + 132*x*e^5 - 36*x*e^(3*x) + 9*x*e^(2* 
x) + x*e^(3*x + 25) - 10*x*e^(3*x + 20) + 40*x*e^(3*x + 15) - 81*x*e^(3*x 
+ 10) + 84*x*e^(3*x + 5) + 8*x*e^(2*x + 25) - 48*x*e^(2*x + 20) + 95*x*e^( 
2*x + 15) - 58*x*e^(2*x + 10) - 12*x*e^(2*x + 5) - 72*x + 18*e^(2*x) + e^( 
2*x + 20) - 8*e^(2*x + 15) + 24*e^(2*x + 10) - 33*e^(2*x + 5))/(18*x^5*e^( 
2*x) + x^5*e^(2*x + 20) - 8*x^5*e^(2*x + 15) + 24*x^5*e^(2*x + 10) - 33*x^ 
5*e^(2*x + 5) - 36*x^4*e^(2*x) + x^4*e^(2*x + 25) - 10*x^4*e^(2*x + 20) + 
40*x^4*e^(2*x + 15) - 81*x^4*e^(2*x + 10) + 84*x^4*e^(2*x + 5) - 4*x^4*...
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e^x \left (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )\right )+e^{2 x} \left (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (-8 x+8 x^2+128 x^5-64 x^6\right )\right )+e^{3 x} \left (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{4 x} \left (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{5 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )+e^x \left (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (128 x^5-64 x^6\right )\right )+e^{2 x} \left (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (-32 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{3 x} \left (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{4 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )} \, dx=\int \frac {{\mathrm {e}}^{3\,x}\,\left ({\mathrm {e}}^5\,\left (48\,x^7-96\,x^6+16\,x^4-36\,x^3+12\,x^2\right )+{\mathrm {e}}^{10}\,\left (24\,x^6+8\,x^3\right )-24\,x^2+56\,x^3-36\,x^4+8\,x^5+96\,x^6-96\,x^7+24\,x^8\right )-{\mathrm {e}}^{2\,x}\,\left (32\,x^5\,{\mathrm {e}}^{10}-16\,x+{\mathrm {e}}^5\,\left (64\,x^6-128\,x^5-8\,x^2+8\,x\right )+28\,x^2-8\,x^3+128\,x^5-128\,x^6+32\,x^7\right )-{\mathrm {e}}^{4\,x}\,\left (2\,x+{\mathrm {e}}^5\,\left (16\,x^8-32\,x^7+16\,x^5-32\,x^4+4\,x^3+1\right )+{\mathrm {e}}^{10}\,\left (8\,x^7+8\,x^4\right )-8\,x^3+37\,x^4-32\,x^5+8\,x^6+32\,x^7-32\,x^8+8\,x^9-2\right )+{\mathrm {e}}^x\,\left (16\,x^4\,{\mathrm {e}}^{10}-{\mathrm {e}}^5\,\left (64\,x^4-32\,x^5\right )+64\,x^4-64\,x^5+16\,x^6\right )+{\mathrm {e}}^{5\,x}\,\left ({\mathrm {e}}^{10}\,\left (x^8+2\,x^5+x^2\right )-{\mathrm {e}}^5\,\left (-2\,x^9+4\,x^8-4\,x^6+8\,x^5-2\,x^3+4\,x^2\right )+4\,x^2-4\,x^3+x^4+8\,x^5-8\,x^6+2\,x^7+4\,x^8-4\,x^9+x^{10}\right )}{16\,x^4\,{\mathrm {e}}^{10}-{\mathrm {e}}^5\,\left (64\,x^4-32\,x^5\right )-{\mathrm {e}}^x\,\left (32\,x^5\,{\mathrm {e}}^{10}-{\mathrm {e}}^5\,\left (128\,x^5-64\,x^6\right )+128\,x^5-128\,x^6+32\,x^7\right )+{\mathrm {e}}^{4\,x}\,\left ({\mathrm {e}}^{10}\,\left (x^8+2\,x^5+x^2\right )-{\mathrm {e}}^5\,\left (-2\,x^9+4\,x^8-4\,x^6+8\,x^5-2\,x^3+4\,x^2\right )+4\,x^2-4\,x^3+x^4+8\,x^5-8\,x^6+2\,x^7+4\,x^8-4\,x^9+x^{10}\right )-{\mathrm {e}}^{3\,x}\,\left ({\mathrm {e}}^{10}\,\left (8\,x^7+8\,x^4\right )+32\,x^4-32\,x^5+8\,x^6+32\,x^7-32\,x^8+8\,x^9-{\mathrm {e}}^5\,\left (-16\,x^8+32\,x^7-16\,x^5+32\,x^4\right )\right )+{\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^{10}\,\left (24\,x^6+8\,x^3\right )+32\,x^3-32\,x^4+8\,x^5+96\,x^6-96\,x^7+24\,x^8-{\mathrm {e}}^5\,\left (-48\,x^7+96\,x^6-16\,x^4+32\,x^3\right )\right )+64\,x^4-64\,x^5+16\,x^6} \,d x \] Input:

int((exp(3*x)*(exp(5)*(12*x^2 - 36*x^3 + 16*x^4 - 96*x^6 + 48*x^7) + exp(1 
0)*(8*x^3 + 24*x^6) - 24*x^2 + 56*x^3 - 36*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 
 24*x^8) - exp(2*x)*(32*x^5*exp(10) - 16*x + exp(5)*(8*x - 8*x^2 - 128*x^5 
 + 64*x^6) + 28*x^2 - 8*x^3 + 128*x^5 - 128*x^6 + 32*x^7) - exp(4*x)*(2*x 
+ exp(5)*(4*x^3 - 32*x^4 + 16*x^5 - 32*x^7 + 16*x^8 + 1) + exp(10)*(8*x^4 
+ 8*x^7) - 8*x^3 + 37*x^4 - 32*x^5 + 8*x^6 + 32*x^7 - 32*x^8 + 8*x^9 - 2) 
+ exp(x)*(16*x^4*exp(10) - exp(5)*(64*x^4 - 32*x^5) + 64*x^4 - 64*x^5 + 16 
*x^6) + exp(5*x)*(exp(10)*(x^2 + 2*x^5 + x^8) - exp(5)*(4*x^2 - 2*x^3 + 8* 
x^5 - 4*x^6 + 4*x^8 - 2*x^9) + 4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*x^7 
 + 4*x^8 - 4*x^9 + x^10))/(16*x^4*exp(10) - exp(5)*(64*x^4 - 32*x^5) - exp 
(x)*(32*x^5*exp(10) - exp(5)*(128*x^5 - 64*x^6) + 128*x^5 - 128*x^6 + 32*x 
^7) + exp(4*x)*(exp(10)*(x^2 + 2*x^5 + x^8) - exp(5)*(4*x^2 - 2*x^3 + 8*x^ 
5 - 4*x^6 + 4*x^8 - 2*x^9) + 4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*x^7 + 
 4*x^8 - 4*x^9 + x^10) - exp(3*x)*(exp(10)*(8*x^4 + 8*x^7) + 32*x^4 - 32*x 
^5 + 8*x^6 + 32*x^7 - 32*x^8 + 8*x^9 - exp(5)*(32*x^4 - 16*x^5 + 32*x^7 - 
16*x^8)) + exp(2*x)*(exp(10)*(8*x^3 + 24*x^6) + 32*x^3 - 32*x^4 + 8*x^5 + 
96*x^6 - 96*x^7 + 24*x^8 - exp(5)*(32*x^3 - 16*x^4 + 96*x^6 - 48*x^7)) + 6 
4*x^4 - 64*x^5 + 16*x^6),x)
 

Output:

int((exp(3*x)*(exp(5)*(12*x^2 - 36*x^3 + 16*x^4 - 96*x^6 + 48*x^7) + exp(1 
0)*(8*x^3 + 24*x^6) - 24*x^2 + 56*x^3 - 36*x^4 + 8*x^5 + 96*x^6 - 96*x^7 + 
 24*x^8) - exp(2*x)*(32*x^5*exp(10) - 16*x + exp(5)*(8*x - 8*x^2 - 128*x^5 
 + 64*x^6) + 28*x^2 - 8*x^3 + 128*x^5 - 128*x^6 + 32*x^7) - exp(4*x)*(2*x 
+ exp(5)*(4*x^3 - 32*x^4 + 16*x^5 - 32*x^7 + 16*x^8 + 1) + exp(10)*(8*x^4 
+ 8*x^7) - 8*x^3 + 37*x^4 - 32*x^5 + 8*x^6 + 32*x^7 - 32*x^8 + 8*x^9 - 2) 
+ exp(x)*(16*x^4*exp(10) - exp(5)*(64*x^4 - 32*x^5) + 64*x^4 - 64*x^5 + 16 
*x^6) + exp(5*x)*(exp(10)*(x^2 + 2*x^5 + x^8) - exp(5)*(4*x^2 - 2*x^3 + 8* 
x^5 - 4*x^6 + 4*x^8 - 2*x^9) + 4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*x^7 
 + 4*x^8 - 4*x^9 + x^10))/(16*x^4*exp(10) - exp(5)*(64*x^4 - 32*x^5) - exp 
(x)*(32*x^5*exp(10) - exp(5)*(128*x^5 - 64*x^6) + 128*x^5 - 128*x^6 + 32*x 
^7) + exp(4*x)*(exp(10)*(x^2 + 2*x^5 + x^8) - exp(5)*(4*x^2 - 2*x^3 + 8*x^ 
5 - 4*x^6 + 4*x^8 - 2*x^9) + 4*x^2 - 4*x^3 + x^4 + 8*x^5 - 8*x^6 + 2*x^7 + 
 4*x^8 - 4*x^9 + x^10) - exp(3*x)*(exp(10)*(8*x^4 + 8*x^7) + 32*x^4 - 32*x 
^5 + 8*x^6 + 32*x^7 - 32*x^8 + 8*x^9 - exp(5)*(32*x^4 - 16*x^5 + 32*x^7 - 
16*x^8)) + exp(2*x)*(exp(10)*(8*x^3 + 24*x^6) + 32*x^3 - 32*x^4 + 8*x^5 + 
96*x^6 - 96*x^7 + 24*x^8 - exp(5)*(32*x^3 - 16*x^4 + 96*x^6 - 48*x^7)) + 6 
4*x^4 - 64*x^5 + 16*x^6), x)
 

Reduce [F]

\[ \int \frac {e^x \left (64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )\right )+e^{2 x} \left (16 x-28 x^2+8 x^3-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (-8 x+8 x^2+128 x^5-64 x^6\right )\right )+e^{3 x} \left (-24 x^2+56 x^3-36 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (12 x^2-36 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{4 x} \left (2-2 x+8 x^3-37 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (-1-4 x^3+32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{5 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )}{64 x^4+16 e^{10} x^4-64 x^5+16 x^6+e^5 \left (-64 x^4+32 x^5\right )+e^x \left (-128 x^5-32 e^{10} x^5+128 x^6-32 x^7+e^5 \left (128 x^5-64 x^6\right )\right )+e^{2 x} \left (32 x^3-32 x^4+8 x^5+96 x^6-96 x^7+24 x^8+e^{10} \left (8 x^3+24 x^6\right )+e^5 \left (-32 x^3+16 x^4-96 x^6+48 x^7\right )\right )+e^{3 x} \left (-32 x^4+32 x^5-8 x^6-32 x^7+32 x^8-8 x^9+e^{10} \left (-8 x^4-8 x^7\right )+e^5 \left (32 x^4-16 x^5+32 x^7-16 x^8\right )\right )+e^{4 x} \left (4 x^2-4 x^3+x^4+8 x^5-8 x^6+2 x^7+4 x^8-4 x^9+x^{10}+e^{10} \left (x^2+2 x^5+x^8\right )+e^5 \left (-4 x^2+2 x^3-8 x^5+4 x^6-4 x^8+2 x^9\right )\right )} \, dx=\text {too large to display} \] Input:

int((((x^8+2*x^5+x^2)*exp(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5 
)+x^10-4*x^9+4*x^8+2*x^7-8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^5+((-8*x^7-8* 
x^4)*exp(5)^2+(-16*x^8+32*x^7-16*x^5+32*x^4-4*x^3-1)*exp(5)-8*x^9+32*x^8-3 
2*x^7-8*x^6+32*x^5-37*x^4+8*x^3-2*x+2)*exp(x)^4+((24*x^6+8*x^3)*exp(5)^2+( 
48*x^7-96*x^6+16*x^4-36*x^3+12*x^2)*exp(5)+24*x^8-96*x^7+96*x^6+8*x^5-36*x 
^4+56*x^3-24*x^2)*exp(x)^3+(-32*x^5*exp(5)^2+(-64*x^6+128*x^5+8*x^2-8*x)*e 
xp(5)-32*x^7+128*x^6-128*x^5+8*x^3-28*x^2+16*x)*exp(x)^2+(16*x^4*exp(5)^2+ 
(32*x^5-64*x^4)*exp(5)+16*x^6-64*x^5+64*x^4)*exp(x))/(((x^8+2*x^5+x^2)*exp 
(5)^2+(2*x^9-4*x^8+4*x^6-8*x^5+2*x^3-4*x^2)*exp(5)+x^10-4*x^9+4*x^8+2*x^7- 
8*x^6+8*x^5+x^4-4*x^3+4*x^2)*exp(x)^4+((-8*x^7-8*x^4)*exp(5)^2+(-16*x^8+32 
*x^7-16*x^5+32*x^4)*exp(5)-8*x^9+32*x^8-32*x^7-8*x^6+32*x^5-32*x^4)*exp(x) 
^3+((24*x^6+8*x^3)*exp(5)^2+(48*x^7-96*x^6+16*x^4-32*x^3)*exp(5)+24*x^8-96 
*x^7+96*x^6+8*x^5-32*x^4+32*x^3)*exp(x)^2+(-32*x^5*exp(5)^2+(-64*x^6+128*x 
^5)*exp(5)-32*x^7+128*x^6-128*x^5)*exp(x)+16*x^4*exp(5)^2+(32*x^5-64*x^4)* 
exp(5)+16*x^6-64*x^5+64*x^4),x)
 

Output:

int(e**(5*x)/(e**(4*x)*e**10*x**6 + 2*e**(4*x)*e**10*x**3 + e**(4*x)*e**10 
 + 2*e**(4*x)*e**5*x**7 - 4*e**(4*x)*e**5*x**6 + 4*e**(4*x)*e**5*x**4 - 8* 
e**(4*x)*e**5*x**3 + 2*e**(4*x)*e**5*x - 4*e**(4*x)*e**5 + e**(4*x)*x**8 - 
 4*e**(4*x)*x**7 + 4*e**(4*x)*x**6 + 2*e**(4*x)*x**5 - 8*e**(4*x)*x**4 + 8 
*e**(4*x)*x**3 + e**(4*x)*x**2 - 4*e**(4*x)*x + 4*e**(4*x) - 8*e**(3*x)*e* 
*10*x**5 - 8*e**(3*x)*e**10*x**2 - 16*e**(3*x)*e**5*x**6 + 32*e**(3*x)*e** 
5*x**5 - 16*e**(3*x)*e**5*x**3 + 32*e**(3*x)*e**5*x**2 - 8*e**(3*x)*x**7 + 
 32*e**(3*x)*x**6 - 32*e**(3*x)*x**5 - 8*e**(3*x)*x**4 + 32*e**(3*x)*x**3 
- 32*e**(3*x)*x**2 + 24*e**(2*x)*e**10*x**4 + 8*e**(2*x)*e**10*x + 48*e**( 
2*x)*e**5*x**5 - 96*e**(2*x)*e**5*x**4 + 16*e**(2*x)*e**5*x**2 - 32*e**(2* 
x)*e**5*x + 24*e**(2*x)*x**6 - 96*e**(2*x)*x**5 + 96*e**(2*x)*x**4 + 8*e** 
(2*x)*x**3 - 32*e**(2*x)*x**2 + 32*e**(2*x)*x - 32*e**x*e**10*x**3 - 64*e* 
*x*e**5*x**4 + 128*e**x*e**5*x**3 - 32*e**x*x**5 + 128*e**x*x**4 - 128*e** 
x*x**3 + 16*e**10*x**2 + 32*e**5*x**3 - 64*e**5*x**2 + 16*x**4 - 64*x**3 + 
 64*x**2),x)*e**10 - 4*int(e**(5*x)/(e**(4*x)*e**10*x**6 + 2*e**(4*x)*e**1 
0*x**3 + e**(4*x)*e**10 + 2*e**(4*x)*e**5*x**7 - 4*e**(4*x)*e**5*x**6 + 4* 
e**(4*x)*e**5*x**4 - 8*e**(4*x)*e**5*x**3 + 2*e**(4*x)*e**5*x - 4*e**(4*x) 
*e**5 + e**(4*x)*x**8 - 4*e**(4*x)*x**7 + 4*e**(4*x)*x**6 + 2*e**(4*x)*x** 
5 - 8*e**(4*x)*x**4 + 8*e**(4*x)*x**3 + e**(4*x)*x**2 - 4*e**(4*x)*x + 4*e 
**(4*x) - 8*e**(3*x)*e**10*x**5 - 8*e**(3*x)*e**10*x**2 - 16*e**(3*x)*e...