Integrand size = 513, antiderivative size = 31 \[ \int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+e^{2 x} \left (1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )\right )+e^x \left (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 \left (16 x-16 x^3+8 x^4-8 x^5\right )\right )}{1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )}} \left (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 \left (64 x^4-96 x^5\right )+e^4 \left (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8\right )+e^{2 x} \left (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 \left (6 x^2-6 x^4\right )+e^4 \left (6 x-12 x^3+6 x^5\right )\right )+e^x \left (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 \left (24 x^2-8 x^4-16 x^5-8 x^6\right )+e^4 \left (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7\right )\right )\right )}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 \left (3 x^2-3 x^4\right )+e^4 \left (3 x-6 x^3+3 x^5\right )} \, dx=e^{1+\left (4+e^x-\frac {4 (-1+x) x^2}{e^4+\frac {1}{x}-x}\right )^2} \] Output:
exp((4+exp(x)-4*(-1+x)*x^2/(exp(4)+1/x-x))^2+1)
Leaf count is larger than twice the leaf count of optimal. \(176\) vs. \(2(31)=62\).
Time = 1.08 (sec) , antiderivative size = 176, normalized size of antiderivative = 5.68 \[ \int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+e^{2 x} \left (1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )\right )+e^x \left (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 \left (16 x-16 x^3+8 x^4-8 x^5\right )\right )}{1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )}} \left (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 \left (64 x^4-96 x^5\right )+e^4 \left (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8\right )+e^{2 x} \left (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 \left (6 x^2-6 x^4\right )+e^4 \left (6 x-12 x^3+6 x^5\right )\right )+e^x \left (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 \left (24 x^2-8 x^4-16 x^5-8 x^6\right )+e^4 \left (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7\right )\right )\right )}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 \left (3 x^2-3 x^4\right )+e^4 \left (3 x-6 x^3+3 x^5\right )} \, dx=e^{\frac {17 e^8 x^2+8 e^{8+x} x^2+e^{8+2 x} x^2-2 e^{4+2 x} x \left (-1+x^2\right )+e^{2 x} \left (-1+x^2\right )^2-8 e^{4+x} x \left (-2+2 x^2-x^3+x^4\right )+8 e^x (-1+x)^2 \left (1+2 x+x^2+x^3+x^4\right )+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+(-1+x)^2 \left (17+34 x+17 x^2+32 x^3+32 x^4+16 x^6\right )}{\left (1+e^4 x-x^2\right )^2}} \] Input:
Integrate[(E^((17 - 34*x^2 + 17*E^8*x^2 + 32*x^3 - 15*x^4 - 32*x^5 + 48*x^ 6 - 32*x^7 + 16*x^8 + E^4*(34*x - 34*x^3 + 32*x^4 - 32*x^5) + E^(2*x)*(1 - 2*x^2 + E^8*x^2 + x^4 + E^4*(2*x - 2*x^3)) + E^x*(8 - 16*x^2 + 8*E^8*x^2 + 8*x^3 - 8*x^5 + 8*x^6 + E^4*(16*x - 16*x^3 + 8*x^4 - 8*x^5)))/(1 - 2*x^2 + E^8*x^2 + x^4 + E^4*(2*x - 2*x^3)))*(96*x^2 - 128*x^3 - 128*x^4 + 288*x ^5 - 192*x^6 + 32*x^7 + 96*x^8 - 64*x^9 + E^8*(64*x^4 - 96*x^5) + E^4*(160 *x^3 - 224*x^4 - 96*x^5 + 224*x^6 - 160*x^7 + 96*x^8) + E^(2*x)*(2 - 6*x^2 + 2*E^12*x^3 + 6*x^4 - 2*x^6 + E^8*(6*x^2 - 6*x^4) + E^4*(6*x - 12*x^3 + 6*x^5)) + E^x*(8 - 24*x^3 + 8*E^12*x^3 - 16*x^4 + 32*x^5 + 16*x^6 - 8*x^7 - 8*x^8 + E^8*(24*x^2 - 8*x^4 - 16*x^5 - 8*x^6) + E^4*(24*x - 8*x^3 - 40*x ^4 - 16*x^5 + 24*x^6 + 16*x^7))))/(1 - 3*x^2 + E^12*x^3 + 3*x^4 - x^6 + E^ 8*(3*x^2 - 3*x^4) + E^4*(3*x - 6*x^3 + 3*x^5)),x]
Output:
E^((17*E^8*x^2 + 8*E^(8 + x)*x^2 + E^(8 + 2*x)*x^2 - 2*E^(4 + 2*x)*x*(-1 + x^2) + E^(2*x)*(-1 + x^2)^2 - 8*E^(4 + x)*x*(-2 + 2*x^2 - x^3 + x^4) + 8* E^x*(-1 + x)^2*(1 + 2*x + x^2 + x^3 + x^4) + E^4*(34*x - 34*x^3 + 32*x^4 - 32*x^5) + (-1 + x)^2*(17 + 34*x + 17*x^2 + 32*x^3 + 32*x^4 + 16*x^6))/(1 + E^4*x - x^2)^2)
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (-64 x^9+96 x^8+32 x^7-192 x^6+288 x^5-128 x^4-128 x^3+96 x^2+e^8 \left (64 x^4-96 x^5\right )+e^{2 x} \left (-2 x^6+6 x^4+2 e^{12} x^3-6 x^2+e^4 \left (6 x^5-12 x^3+6 x\right )+e^8 \left (6 x^2-6 x^4\right )+2\right )+e^4 \left (96 x^8-160 x^7+224 x^6-96 x^5-224 x^4+160 x^3\right )+e^x \left (-8 x^8-8 x^7+16 x^6+32 x^5-16 x^4+8 e^{12} x^3-24 x^3+e^8 \left (-8 x^6-16 x^5-8 x^4+24 x^2\right )+e^4 \left (16 x^7+24 x^6-16 x^5-40 x^4-8 x^3+24 x\right )+8\right )\right ) \exp \left (\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3+17 e^8 x^2-34 x^2+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )+e^{2 x} \left (x^4+e^4 \left (2 x-2 x^3\right )+e^8 x^2-2 x^2+1\right )+e^x \left (8 x^6-8 x^5+8 x^3+8 e^8 x^2-16 x^2+e^4 \left (-8 x^5+8 x^4-16 x^3+16 x\right )+8\right )+17}{x^4+e^4 \left (2 x-2 x^3\right )+e^8 x^2-2 x^2+1}\right )}{-x^6+3 x^4+e^{12} x^3-3 x^2+e^4 \left (3 x^5-6 x^3+3 x\right )+e^8 \left (3 x^2-3 x^4\right )+1} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int -\frac {\left (-64 x^9+96 x^8+32 x^7-192 x^6+288 x^5-128 x^4-128 x^3+96 x^2+e^8 \left (64 x^4-96 x^5\right )+e^{2 x} \left (-2 x^6+6 x^4+2 e^{12} x^3-6 x^2+e^4 \left (6 x^5-12 x^3+6 x\right )+e^8 \left (6 x^2-6 x^4\right )+2\right )+e^4 \left (96 x^8-160 x^7+224 x^6-96 x^5-224 x^4+160 x^3\right )+e^x \left (-8 x^8-8 x^7+16 x^6+32 x^5-16 x^4+8 e^{12} x^3-24 x^3+e^8 \left (-8 x^6-16 x^5-8 x^4+24 x^2\right )+e^4 \left (16 x^7+24 x^6-16 x^5-40 x^4-8 x^3+24 x\right )+8\right )\right ) \exp \left (\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3+17 e^8 x^2-34 x^2+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )+e^{2 x} \left (x^4+e^4 \left (2 x-2 x^3\right )+e^8 x^2-2 x^2+1\right )+e^x \left (8 x^6-8 x^5+8 x^3+8 e^8 x^2-16 x^2+e^4 \left (-8 x^5+8 x^4-16 x^3+16 x\right )+8\right )+17}{x^4+e^4 \left (2 x-2 x^3\right )+e^8 x^2-2 x^2+1}\right )}{\left (x^2-e^4 x-1\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\int -\frac {2 \exp \left (\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3+17 e^8 x^2-34 x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1}\right ) \left (-32 x^9+48 x^8+16 x^7-96 x^6+144 x^5-64 x^4-64 x^3+48 x^2+16 e^8 \left (2 x^4-3 x^5\right )+16 e^4 \left (3 x^8-5 x^7+7 x^6-3 x^5-7 x^4+5 x^3\right )+e^{2 x} \left (-x^6+3 x^4+e^{12} x^3-3 x^2+3 e^8 \left (x^2-x^4\right )+3 e^4 \left (x^5-2 x^3+x\right )+1\right )+4 e^x \left (-x^8-x^7+2 x^6+4 x^5-2 x^4+e^{12} x^3-3 x^3+e^8 \left (-x^6-2 x^5-x^4+3 x^2\right )+e^4 \left (2 x^7+3 x^6-2 x^5-5 x^4-x^3+3 x\right )+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3+17 e^8 x^2-34 x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1}\right ) \left (-32 x^9+48 x^8+16 x^7-96 x^6+144 x^5-64 x^4-64 x^3+48 x^2+16 e^8 \left (2 x^4-3 x^5\right )+16 e^4 \left (3 x^8-5 x^7+7 x^6-3 x^5-7 x^4+5 x^3\right )+e^{2 x} \left (-x^6+3 x^4+e^{12} x^3-3 x^2+3 e^8 \left (x^2-x^4\right )+3 e^4 \left (x^5-2 x^3+x\right )+1\right )+4 e^x \left (-x^8-x^7+2 x^6+4 x^5-2 x^4+e^{12} x^3-3 x^3+e^8 \left (-x^6-2 x^5-x^4+3 x^2\right )+e^4 \left (2 x^7+3 x^6-2 x^5-5 x^4-x^3+3 x\right )+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}\right ) \left (-32 x^9+48 x^8+16 x^7-96 x^6+144 x^5-64 x^4-64 x^3+48 x^2+16 e^8 \left (2 x^4-3 x^5\right )+16 e^4 \left (3 x^8-5 x^7+7 x^6-3 x^5-7 x^4+5 x^3\right )+e^{2 x} \left (-x^6+3 x^4+e^{12} x^3-3 x^2+3 e^8 \left (x^2-x^4\right )+3 e^4 \left (x^5-2 x^3+x\right )+1\right )+4 e^x \left (-x^8-x^7+2 x^6+4 x^5-2 x^4+e^{12} x^3-3 x^3+e^8 \left (-x^6-2 x^5-x^4+3 x^2\right )+e^4 \left (2 x^7+3 x^6-2 x^5-5 x^4-x^3+3 x\right )+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {32 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} x^9}{\left (-x^2+e^4 x+1\right )^3}+\frac {48 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} x^8}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} x^7}{\left (-x^2+e^4 x+1\right )^3}-\frac {96 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} x^6}{\left (-x^2+e^4 x+1\right )^3}+\frac {144 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} x^5}{\left (-x^2+e^4 x+1\right )^3}-\frac {64 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} x^4}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {64 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} x^3}{\left (-x^2+e^4 x+1\right )^3}+\frac {48 e^{\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}}+\frac {4 e^{x+\frac {16 x^8-32 x^7+48 x^6-32 x^5-15 x^4+32 x^3-34 \left (1-\frac {e^8}{2}\right ) x^2+2 e^4 \left (-16 x^5+16 x^4-17 x^3+17 x\right )+e^{2 x} \left (x^4+e^8 x^2-2 x^2+2 e^4 \left (x-x^3\right )+1\right )+8 e^x \left (x^6-x^5+x^3+e^8 x^2-2 x^2+e^4 \left (-x^5+x^4-2 x^3+2 x\right )+1\right )+17}{x^4-2 e^4 x^3-\left (2-e^8\right ) x^2+2 e^4 x+1}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+8} (3 x-2) x^4}{\left (-x^2+e^4 x+1\right )^3}+\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}+4} (x-1) \left (3 x^4-2 x^3+5 x^2+2 x-5\right ) x^3}{\left (-x^2+e^4 x+1\right )^3}-\frac {16 e^{\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} (x-1)^3 (2 x+3) \left (x^3+x+1\right ) x^2}{\left (-x^2+e^4 x+1\right )^3}+e^{2 x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}}+\frac {4 e^{x+\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}} \left (x^6+\left (1-e^4\right ) x^5-\left (1+2 e^4\right ) x^4-3 x^3+\left (1+e^8\right ) x^2+2 e^4 x+1\right )}{\left (-x^2+e^4 x+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {8 e^x \left (x^4+x^3+x^2+2 x+1\right ) (x-1)^2+\left (16 x^6+32 x^4+32 x^3+17 x^2+34 x+17\right ) (x-1)^2+8 e^{x+8} x^2+e^{2 x+8} x^2+17 e^8 x^2+e^{2 x} \left (x^2-1\right )^2-2 e^{2 x+4} x \left (x^2-1\right )-8 e^{x+4} x \left (x^4-x^3+2 x^2-2\right )+e^4 \left (-32 x^5+32 x^4-34 x^3+34 x\right )}{\left (-x^2+e^4 x+1\right )^2}\right ) \left (16 e^8 (2-3 x) x^4+e^{2 (x+6)} x^3+4 e^{x+12} x^3+16 e^4 \left (3 x^5-5 x^4+7 x^3-3 x^2-7 x+5\right ) x^3-3 e^{2 x+8} \left (x^2-1\right ) x^2-4 e^{x+8} \left (x^4+2 x^3+x^2-3\right ) x^2-16 (x-1)^3 \left (2 x^4+3 x^3+2 x^2+5 x+3\right ) x^2+3 e^{2 x+4} \left (x^2-1\right )^2 x+4 e^{x+4} \left (2 x^6+3 x^5-2 x^4-5 x^3-x^2+3\right ) x-e^{2 x} \left (x^2-1\right )^3-4 e^x (x-1)^3 \left (x^5+4 x^4+7 x^3+6 x^2+3 x+1\right )\right )}{\left (-x^2+e^4 x+1\right )^3}dx\) |
Input:
Int[(E^((17 - 34*x^2 + 17*E^8*x^2 + 32*x^3 - 15*x^4 - 32*x^5 + 48*x^6 - 32 *x^7 + 16*x^8 + E^4*(34*x - 34*x^3 + 32*x^4 - 32*x^5) + E^(2*x)*(1 - 2*x^2 + E^8*x^2 + x^4 + E^4*(2*x - 2*x^3)) + E^x*(8 - 16*x^2 + 8*E^8*x^2 + 8*x^ 3 - 8*x^5 + 8*x^6 + E^4*(16*x - 16*x^3 + 8*x^4 - 8*x^5)))/(1 - 2*x^2 + E^8 *x^2 + x^4 + E^4*(2*x - 2*x^3)))*(96*x^2 - 128*x^3 - 128*x^4 + 288*x^5 - 1 92*x^6 + 32*x^7 + 96*x^8 - 64*x^9 + E^8*(64*x^4 - 96*x^5) + E^4*(160*x^3 - 224*x^4 - 96*x^5 + 224*x^6 - 160*x^7 + 96*x^8) + E^(2*x)*(2 - 6*x^2 + 2*E ^12*x^3 + 6*x^4 - 2*x^6 + E^8*(6*x^2 - 6*x^4) + E^4*(6*x - 12*x^3 + 6*x^5) ) + E^x*(8 - 24*x^3 + 8*E^12*x^3 - 16*x^4 + 32*x^5 + 16*x^6 - 8*x^7 - 8*x^ 8 + E^8*(24*x^2 - 8*x^4 - 16*x^5 - 8*x^6) + E^4*(24*x - 8*x^3 - 40*x^4 - 1 6*x^5 + 24*x^6 + 16*x^7))))/(1 - 3*x^2 + E^12*x^3 + 3*x^4 - x^6 + E^8*(3*x ^2 - 3*x^4) + E^4*(3*x - 6*x^3 + 3*x^5)),x]
Output:
$Aborted
Timed out.
\[\int \frac {\left (\left (2 x^{3} {\mathrm e}^{12}+\left (-6 x^{4}+6 x^{2}\right ) {\mathrm e}^{8}+\left (6 x^{5}-12 x^{3}+6 x \right ) {\mathrm e}^{4}-2 x^{6}+6 x^{4}-6 x^{2}+2\right ) {\mathrm e}^{2 x}+\left (8 x^{3} {\mathrm e}^{12}+\left (-8 x^{6}-16 x^{5}-8 x^{4}+24 x^{2}\right ) {\mathrm e}^{8}+\left (16 x^{7}+24 x^{6}-16 x^{5}-40 x^{4}-8 x^{3}+24 x \right ) {\mathrm e}^{4}-8 x^{8}-8 x^{7}+16 x^{6}+32 x^{5}-16 x^{4}-24 x^{3}+8\right ) {\mathrm e}^{x}+\left (-96 x^{5}+64 x^{4}\right ) {\mathrm e}^{8}+\left (96 x^{8}-160 x^{7}+224 x^{6}-96 x^{5}-224 x^{4}+160 x^{3}\right ) {\mathrm e}^{4}-64 x^{9}+96 x^{8}+32 x^{7}-192 x^{6}+288 x^{5}-128 x^{4}-128 x^{3}+96 x^{2}\right ) {\mathrm e}^{\frac {\left (x^{2} {\mathrm e}^{8}+\left (-2 x^{3}+2 x \right ) {\mathrm e}^{4}+x^{4}-2 x^{2}+1\right ) {\mathrm e}^{2 x}+\left (8 x^{2} {\mathrm e}^{8}+\left (-8 x^{5}+8 x^{4}-16 x^{3}+16 x \right ) {\mathrm e}^{4}+8 x^{6}-8 x^{5}+8 x^{3}-16 x^{2}+8\right ) {\mathrm e}^{x}+17 x^{2} {\mathrm e}^{8}+\left (-32 x^{5}+32 x^{4}-34 x^{3}+34 x \right ) {\mathrm e}^{4}+16 x^{8}-32 x^{7}+48 x^{6}-32 x^{5}-15 x^{4}+32 x^{3}-34 x^{2}+17}{x^{2} {\mathrm e}^{8}+\left (-2 x^{3}+2 x \right ) {\mathrm e}^{4}+x^{4}-2 x^{2}+1}}}{x^{3} {\mathrm e}^{12}+\left (-3 x^{4}+3 x^{2}\right ) {\mathrm e}^{8}+\left (3 x^{5}-6 x^{3}+3 x \right ) {\mathrm e}^{4}-x^{6}+3 x^{4}-3 x^{2}+1}d x\]
Input:
int(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp(4)-2*x ^6+6*x^4-6*x^2+2)*exp(x)^2+(8*x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x^2)*ex p(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7+16*x^6+ 32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160*x^7+2 24*x^6-96*x^5-224*x^4+160*x^3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+288*x^5 -128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+x^4-2*x^2+ 1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6-8*x^5+ 8*x^3-16*x^2+8)*exp(x)+17*x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)*exp(4) +16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp(4)^2+(-2*x^ 3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3*x^5-6 *x^3+3*x)*exp(4)-x^6+3*x^4-3*x^2+1),x)
Output:
int(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp(4)-2*x ^6+6*x^4-6*x^2+2)*exp(x)^2+(8*x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x^2)*ex p(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7+16*x^6+ 32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160*x^7+2 24*x^6-96*x^5-224*x^4+160*x^3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+288*x^5 -128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+x^4-2*x^2+ 1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6-8*x^5+ 8*x^3-16*x^2+8)*exp(x)+17*x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)*exp(4) +16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp(4)^2+(-2*x^ 3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3*x^5-6 *x^3+3*x)*exp(4)-x^6+3*x^4-3*x^2+1),x)
Leaf count of result is larger than twice the leaf count of optimal. 179 vs. \(2 (30) = 60\).
Time = 0.10 (sec) , antiderivative size = 179, normalized size of antiderivative = 5.77 \[ \int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+e^{2 x} \left (1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )\right )+e^x \left (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 \left (16 x-16 x^3+8 x^4-8 x^5\right )\right )}{1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )}} \left (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 \left (64 x^4-96 x^5\right )+e^4 \left (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8\right )+e^{2 x} \left (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 \left (6 x^2-6 x^4\right )+e^4 \left (6 x-12 x^3+6 x^5\right )\right )+e^x \left (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 \left (24 x^2-8 x^4-16 x^5-8 x^6\right )+e^4 \left (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7\right )\right )\right )}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 \left (3 x^2-3 x^4\right )+e^4 \left (3 x-6 x^3+3 x^5\right )} \, dx=e^{\left (\frac {16 \, x^{8} - 32 \, x^{7} + 48 \, x^{6} - 32 \, x^{5} - 15 \, x^{4} + 32 \, x^{3} + 17 \, x^{2} e^{8} - 34 \, x^{2} - 2 \, {\left (16 \, x^{5} - 16 \, x^{4} + 17 \, x^{3} - 17 \, x\right )} e^{4} + {\left (x^{4} + x^{2} e^{8} - 2 \, x^{2} - 2 \, {\left (x^{3} - x\right )} e^{4} + 1\right )} e^{\left (2 \, x\right )} + 8 \, {\left (x^{6} - x^{5} + x^{3} + x^{2} e^{8} - 2 \, x^{2} - {\left (x^{5} - x^{4} + 2 \, x^{3} - 2 \, x\right )} e^{4} + 1\right )} e^{x} + 17}{x^{4} + x^{2} e^{8} - 2 \, x^{2} - 2 \, {\left (x^{3} - x\right )} e^{4} + 1}\right )} \] Input:
integrate(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp( 4)-2*x^6+6*x^4-6*x^2+2)*exp(x)^2+(8*x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x ^2)*exp(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7+1 6*x^6+32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160 *x^7+224*x^6-96*x^5-224*x^4+160*x^3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+2 88*x^5-128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+x^4- 2*x^2+1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6- 8*x^5+8*x^3-16*x^2+8)*exp(x)+17*x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)* exp(4)+16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp(4)^2+ (-2*x^3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3 *x^5-6*x^3+3*x)*exp(4)-x^6+3*x^4-3*x^2+1),x, algorithm="fricas")
Output:
e^((16*x^8 - 32*x^7 + 48*x^6 - 32*x^5 - 15*x^4 + 32*x^3 + 17*x^2*e^8 - 34* x^2 - 2*(16*x^5 - 16*x^4 + 17*x^3 - 17*x)*e^4 + (x^4 + x^2*e^8 - 2*x^2 - 2 *(x^3 - x)*e^4 + 1)*e^(2*x) + 8*(x^6 - x^5 + x^3 + x^2*e^8 - 2*x^2 - (x^5 - x^4 + 2*x^3 - 2*x)*e^4 + 1)*e^x + 17)/(x^4 + x^2*e^8 - 2*x^2 - 2*(x^3 - x)*e^4 + 1))
Leaf count of result is larger than twice the leaf count of optimal. 187 vs. \(2 (26) = 52\).
Time = 6.38 (sec) , antiderivative size = 187, normalized size of antiderivative = 6.03 \[ \int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+e^{2 x} \left (1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )\right )+e^x \left (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 \left (16 x-16 x^3+8 x^4-8 x^5\right )\right )}{1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )}} \left (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 \left (64 x^4-96 x^5\right )+e^4 \left (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8\right )+e^{2 x} \left (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 \left (6 x^2-6 x^4\right )+e^4 \left (6 x-12 x^3+6 x^5\right )\right )+e^x \left (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 \left (24 x^2-8 x^4-16 x^5-8 x^6\right )+e^4 \left (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7\right )\right )\right )}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 \left (3 x^2-3 x^4\right )+e^4 \left (3 x-6 x^3+3 x^5\right )} \, dx=e^{\frac {16 x^{8} - 32 x^{7} + 48 x^{6} - 32 x^{5} - 15 x^{4} + 32 x^{3} - 34 x^{2} + 17 x^{2} e^{8} + \left (- 32 x^{5} + 32 x^{4} - 34 x^{3} + 34 x\right ) e^{4} + \left (x^{4} - 2 x^{2} + x^{2} e^{8} + \left (- 2 x^{3} + 2 x\right ) e^{4} + 1\right ) e^{2 x} + \left (8 x^{6} - 8 x^{5} + 8 x^{3} - 16 x^{2} + 8 x^{2} e^{8} + \left (- 8 x^{5} + 8 x^{4} - 16 x^{3} + 16 x\right ) e^{4} + 8\right ) e^{x} + 17}{x^{4} - 2 x^{2} + x^{2} e^{8} + \left (- 2 x^{3} + 2 x\right ) e^{4} + 1}} \] Input:
integrate(((2*x**3*exp(4)**3+(-6*x**4+6*x**2)*exp(4)**2+(6*x**5-12*x**3+6* x)*exp(4)-2*x**6+6*x**4-6*x**2+2)*exp(x)**2+(8*x**3*exp(4)**3+(-8*x**6-16* x**5-8*x**4+24*x**2)*exp(4)**2+(16*x**7+24*x**6-16*x**5-40*x**4-8*x**3+24* x)*exp(4)-8*x**8-8*x**7+16*x**6+32*x**5-16*x**4-24*x**3+8)*exp(x)+(-96*x** 5+64*x**4)*exp(4)**2+(96*x**8-160*x**7+224*x**6-96*x**5-224*x**4+160*x**3) *exp(4)-64*x**9+96*x**8+32*x**7-192*x**6+288*x**5-128*x**4-128*x**3+96*x** 2)*exp(((x**2*exp(4)**2+(-2*x**3+2*x)*exp(4)+x**4-2*x**2+1)*exp(x)**2+(8*x **2*exp(4)**2+(-8*x**5+8*x**4-16*x**3+16*x)*exp(4)+8*x**6-8*x**5+8*x**3-16 *x**2+8)*exp(x)+17*x**2*exp(4)**2+(-32*x**5+32*x**4-34*x**3+34*x)*exp(4)+1 6*x**8-32*x**7+48*x**6-32*x**5-15*x**4+32*x**3-34*x**2+17)/(x**2*exp(4)**2 +(-2*x**3+2*x)*exp(4)+x**4-2*x**2+1))/(x**3*exp(4)**3+(-3*x**4+3*x**2)*exp (4)**2+(3*x**5-6*x**3+3*x)*exp(4)-x**6+3*x**4-3*x**2+1),x)
Output:
exp((16*x**8 - 32*x**7 + 48*x**6 - 32*x**5 - 15*x**4 + 32*x**3 - 34*x**2 + 17*x**2*exp(8) + (-32*x**5 + 32*x**4 - 34*x**3 + 34*x)*exp(4) + (x**4 - 2 *x**2 + x**2*exp(8) + (-2*x**3 + 2*x)*exp(4) + 1)*exp(2*x) + (8*x**6 - 8*x **5 + 8*x**3 - 16*x**2 + 8*x**2*exp(8) + (-8*x**5 + 8*x**4 - 16*x**3 + 16* x)*exp(4) + 8)*exp(x) + 17)/(x**4 - 2*x**2 + x**2*exp(8) + (-2*x**3 + 2*x) *exp(4) + 1))
Leaf count of result is larger than twice the leaf count of optimal. 917 vs. \(2 (30) = 60\).
Time = 15.93 (sec) , antiderivative size = 917, normalized size of antiderivative = 29.58 \[ \int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+e^{2 x} \left (1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )\right )+e^x \left (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 \left (16 x-16 x^3+8 x^4-8 x^5\right )\right )}{1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )}} \left (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 \left (64 x^4-96 x^5\right )+e^4 \left (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8\right )+e^{2 x} \left (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 \left (6 x^2-6 x^4\right )+e^4 \left (6 x-12 x^3+6 x^5\right )\right )+e^x \left (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 \left (24 x^2-8 x^4-16 x^5-8 x^6\right )+e^4 \left (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7\right )\right )\right )}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 \left (3 x^2-3 x^4\right )+e^4 \left (3 x-6 x^3+3 x^5\right )} \, dx =\text {Too large to display} \] Input:
integrate(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp( 4)-2*x^6+6*x^4-6*x^2+2)*exp(x)^2+(8*x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x ^2)*exp(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7+1 6*x^6+32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160 *x^7+224*x^6-96*x^5-224*x^4+160*x^3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+2 88*x^5-128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+x^4- 2*x^2+1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6- 8*x^5+8*x^3-16*x^2+8)*exp(x)+17*x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)* exp(4)+16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp(4)^2+ (-2*x^3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3 *x^5-6*x^3+3*x)*exp(4)-x^6+3*x^4-3*x^2+1),x, algorithm="maxima")
Output:
e^(16*x^4 + 32*x^3*e^4 - 32*x^3 + 48*x^2*e^8 - 64*x^2*e^4 + 8*x^2*e^x + 80 *x^2 + 64*x*e^12 - 96*x*e^8 + 160*x*e^4 + 8*x*e^(x + 4) - 8*x*e^x - 96*x + 16*x*e^28/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 32*x*e^24/(x^ 4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 112*x*e^20/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 96*x*e^20/(x^2 - x*e^4 - 1) - 160*x*e^16 /(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 160*x*e^16/(x^2 - x*e^4 - 1) + 224*x*e^12/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 416*x *e^12/(x^2 - x*e^4 - 1) - 192*x*e^8/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x *e^4 + 1) - 416*x*e^8/(x^2 - x*e^4 - 1) + 112*x*e^4/(x^4 - 2*x^3*e^4 + x^2 *(e^8 - 2) + 2*x*e^4 + 1) + 352*x*e^4/(x^2 - x*e^4 - 1) + 8*x*e^(x + 12)/( x^2 - x*e^4 - 1) - 8*x*e^(x + 8)/(x^2 - x*e^4 - 1) + 16*x*e^(x + 4)/(x^2 - x*e^4 - 1) - 8*x*e^x/(x^2 - x*e^4 - 1) - 32*x/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 128*x/(x^2 - x*e^4 - 1) + 16*e^24/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 16*e^24/(x^2 - x*e^4 - 1) - 32*e^20/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 32*e^20/(x^2 - x*e^4 - 1) + 9 6*e^16/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) + 176*e^16/(x^2 - x *e^4 - 1) - 128*e^12/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 256 *e^12/(x^2 - x*e^4 - 1) + 144*e^8/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e ^4 + 1) + 416*e^8/(x^2 - x*e^4 - 1) - 96*e^4/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 2) + 2*x*e^4 + 1) - 320*e^4/(x^2 - x*e^4 - 1) + 8*e^(x + 8)/(x^2 - x*e...
\[ \int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+e^{2 x} \left (1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )\right )+e^x \left (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 \left (16 x-16 x^3+8 x^4-8 x^5\right )\right )}{1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )}} \left (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 \left (64 x^4-96 x^5\right )+e^4 \left (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8\right )+e^{2 x} \left (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 \left (6 x^2-6 x^4\right )+e^4 \left (6 x-12 x^3+6 x^5\right )\right )+e^x \left (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 \left (24 x^2-8 x^4-16 x^5-8 x^6\right )+e^4 \left (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7\right )\right )\right )}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 \left (3 x^2-3 x^4\right )+e^4 \left (3 x-6 x^3+3 x^5\right )} \, dx=\int { \frac {2 \, {\left (32 \, x^{9} - 48 \, x^{8} - 16 \, x^{7} + 96 \, x^{6} - 144 \, x^{5} + 64 \, x^{4} + 64 \, x^{3} - 48 \, x^{2} + 16 \, {\left (3 \, x^{5} - 2 \, x^{4}\right )} e^{8} - 16 \, {\left (3 \, x^{8} - 5 \, x^{7} + 7 \, x^{6} - 3 \, x^{5} - 7 \, x^{4} + 5 \, x^{3}\right )} e^{4} + {\left (x^{6} - 3 \, x^{4} - x^{3} e^{12} + 3 \, x^{2} + 3 \, {\left (x^{4} - x^{2}\right )} e^{8} - 3 \, {\left (x^{5} - 2 \, x^{3} + x\right )} e^{4} - 1\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{8} + x^{7} - 2 \, x^{6} - 4 \, x^{5} + 2 \, x^{4} - x^{3} e^{12} + 3 \, x^{3} + {\left (x^{6} + 2 \, x^{5} + x^{4} - 3 \, x^{2}\right )} e^{8} - {\left (2 \, x^{7} + 3 \, x^{6} - 2 \, x^{5} - 5 \, x^{4} - x^{3} + 3 \, x\right )} e^{4} - 1\right )} e^{x}\right )} e^{\left (\frac {16 \, x^{8} - 32 \, x^{7} + 48 \, x^{6} - 32 \, x^{5} - 15 \, x^{4} + 32 \, x^{3} + 17 \, x^{2} e^{8} - 34 \, x^{2} - 2 \, {\left (16 \, x^{5} - 16 \, x^{4} + 17 \, x^{3} - 17 \, x\right )} e^{4} + {\left (x^{4} + x^{2} e^{8} - 2 \, x^{2} - 2 \, {\left (x^{3} - x\right )} e^{4} + 1\right )} e^{\left (2 \, x\right )} + 8 \, {\left (x^{6} - x^{5} + x^{3} + x^{2} e^{8} - 2 \, x^{2} - {\left (x^{5} - x^{4} + 2 \, x^{3} - 2 \, x\right )} e^{4} + 1\right )} e^{x} + 17}{x^{4} + x^{2} e^{8} - 2 \, x^{2} - 2 \, {\left (x^{3} - x\right )} e^{4} + 1}\right )}}{x^{6} - 3 \, x^{4} - x^{3} e^{12} + 3 \, x^{2} + 3 \, {\left (x^{4} - x^{2}\right )} e^{8} - 3 \, {\left (x^{5} - 2 \, x^{3} + x\right )} e^{4} - 1} \,d x } \] Input:
integrate(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp( 4)-2*x^6+6*x^4-6*x^2+2)*exp(x)^2+(8*x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x ^2)*exp(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7+1 6*x^6+32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160 *x^7+224*x^6-96*x^5-224*x^4+160*x^3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+2 88*x^5-128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+x^4- 2*x^2+1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6- 8*x^5+8*x^3-16*x^2+8)*exp(x)+17*x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)* exp(4)+16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp(4)^2+ (-2*x^3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3 *x^5-6*x^3+3*x)*exp(4)-x^6+3*x^4-3*x^2+1),x, algorithm="giac")
Output:
integrate(2*(32*x^9 - 48*x^8 - 16*x^7 + 96*x^6 - 144*x^5 + 64*x^4 + 64*x^3 - 48*x^2 + 16*(3*x^5 - 2*x^4)*e^8 - 16*(3*x^8 - 5*x^7 + 7*x^6 - 3*x^5 - 7 *x^4 + 5*x^3)*e^4 + (x^6 - 3*x^4 - x^3*e^12 + 3*x^2 + 3*(x^4 - x^2)*e^8 - 3*(x^5 - 2*x^3 + x)*e^4 - 1)*e^(2*x) + 4*(x^8 + x^7 - 2*x^6 - 4*x^5 + 2*x^ 4 - x^3*e^12 + 3*x^3 + (x^6 + 2*x^5 + x^4 - 3*x^2)*e^8 - (2*x^7 + 3*x^6 - 2*x^5 - 5*x^4 - x^3 + 3*x)*e^4 - 1)*e^x)*e^((16*x^8 - 32*x^7 + 48*x^6 - 32 *x^5 - 15*x^4 + 32*x^3 + 17*x^2*e^8 - 34*x^2 - 2*(16*x^5 - 16*x^4 + 17*x^3 - 17*x)*e^4 + (x^4 + x^2*e^8 - 2*x^2 - 2*(x^3 - x)*e^4 + 1)*e^(2*x) + 8*( x^6 - x^5 + x^3 + x^2*e^8 - 2*x^2 - (x^5 - x^4 + 2*x^3 - 2*x)*e^4 + 1)*e^x + 17)/(x^4 + x^2*e^8 - 2*x^2 - 2*(x^3 - x)*e^4 + 1))/(x^6 - 3*x^4 - x^3*e ^12 + 3*x^2 + 3*(x^4 - x^2)*e^8 - 3*(x^5 - 2*x^3 + x)*e^4 - 1), x)
Time = 5.59 (sec) , antiderivative size = 1097, normalized size of antiderivative = 35.39 \[ \int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+e^{2 x} \left (1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )\right )+e^x \left (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 \left (16 x-16 x^3+8 x^4-8 x^5\right )\right )}{1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )}} \left (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 \left (64 x^4-96 x^5\right )+e^4 \left (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8\right )+e^{2 x} \left (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 \left (6 x^2-6 x^4\right )+e^4 \left (6 x-12 x^3+6 x^5\right )\right )+e^x \left (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 \left (24 x^2-8 x^4-16 x^5-8 x^6\right )+e^4 \left (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7\right )\right )\right )}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 \left (3 x^2-3 x^4\right )+e^4 \left (3 x-6 x^3+3 x^5\right )} \, dx=\text {Too large to display} \] Input:
int((exp((17*x^2*exp(8) + exp(4)*(34*x - 34*x^3 + 32*x^4 - 32*x^5) + exp(x )*(8*x^2*exp(8) + exp(4)*(16*x - 16*x^3 + 8*x^4 - 8*x^5) - 16*x^2 + 8*x^3 - 8*x^5 + 8*x^6 + 8) - 34*x^2 + 32*x^3 - 15*x^4 - 32*x^5 + 48*x^6 - 32*x^7 + 16*x^8 + exp(2*x)*(exp(4)*(2*x - 2*x^3) + x^2*exp(8) - 2*x^2 + x^4 + 1) + 17)/(exp(4)*(2*x - 2*x^3) + x^2*exp(8) - 2*x^2 + x^4 + 1))*(exp(2*x)*(e xp(4)*(6*x - 12*x^3 + 6*x^5) + exp(8)*(6*x^2 - 6*x^4) + 2*x^3*exp(12) - 6* x^2 + 6*x^4 - 2*x^6 + 2) + exp(4)*(160*x^3 - 224*x^4 - 96*x^5 + 224*x^6 - 160*x^7 + 96*x^8) + exp(x)*(exp(4)*(24*x - 8*x^3 - 40*x^4 - 16*x^5 + 24*x^ 6 + 16*x^7) + 8*x^3*exp(12) - 24*x^3 - 16*x^4 + 32*x^5 + 16*x^6 - 8*x^7 - 8*x^8 - exp(8)*(8*x^4 - 24*x^2 + 16*x^5 + 8*x^6) + 8) + exp(8)*(64*x^4 - 9 6*x^5) + 96*x^2 - 128*x^3 - 128*x^4 + 288*x^5 - 192*x^6 + 32*x^7 + 96*x^8 - 64*x^9))/(exp(4)*(3*x - 6*x^3 + 3*x^5) + exp(8)*(3*x^2 - 3*x^4) + x^3*ex p(12) - 3*x^2 + 3*x^4 - x^6 + 1),x)
Output:
exp(17/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((x^ 4*exp(2*x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*ex p(-(2*x^2*exp(2*x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((2*x*exp(2*x)*exp(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((8*x^4*exp(4)*exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x ^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(8*x^5*exp(4)*exp(x))/(2*x*exp(4) - 2*x ^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((8*x^2*exp(8)*exp(x))/(2*x* exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(16*x^3*exp(4) *exp(x))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(e xp(2*x)/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((1 7*x^2*exp(8))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))* exp((32*x^4*exp(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(34*x^3*exp(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(32*x^5*exp(4))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(2*x^3*exp(2*x)*exp(4))/(2*x*exp(4) - 2*x^3*exp(4 ) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((x^2*exp(2*x)*exp(8))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((8*x^3*exp(x))/(2*x*exp (4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(8*x^5*exp(x))/(2 *x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp((8*x^6*exp(x ))/(2*x*exp(4) - 2*x^3*exp(4) + x^2*exp(8) - 2*x^2 + x^4 + 1))*exp(-(16...
Time = 0.40 (sec) , antiderivative size = 292, normalized size of antiderivative = 9.42 \[ \int \frac {e^{\frac {17-34 x^2+17 e^8 x^2+32 x^3-15 x^4-32 x^5+48 x^6-32 x^7+16 x^8+e^4 \left (34 x-34 x^3+32 x^4-32 x^5\right )+e^{2 x} \left (1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )\right )+e^x \left (8-16 x^2+8 e^8 x^2+8 x^3-8 x^5+8 x^6+e^4 \left (16 x-16 x^3+8 x^4-8 x^5\right )\right )}{1-2 x^2+e^8 x^2+x^4+e^4 \left (2 x-2 x^3\right )}} \left (96 x^2-128 x^3-128 x^4+288 x^5-192 x^6+32 x^7+96 x^8-64 x^9+e^8 \left (64 x^4-96 x^5\right )+e^4 \left (160 x^3-224 x^4-96 x^5+224 x^6-160 x^7+96 x^8\right )+e^{2 x} \left (2-6 x^2+2 e^{12} x^3+6 x^4-2 x^6+e^8 \left (6 x^2-6 x^4\right )+e^4 \left (6 x-12 x^3+6 x^5\right )\right )+e^x \left (8-24 x^3+8 e^{12} x^3-16 x^4+32 x^5+16 x^6-8 x^7-8 x^8+e^8 \left (24 x^2-8 x^4-16 x^5-8 x^6\right )+e^4 \left (24 x-8 x^3-40 x^4-16 x^5+24 x^6+16 x^7\right )\right )\right )}{1-3 x^2+e^{12} x^3+3 x^4-x^6+e^8 \left (3 x^2-3 x^4\right )+e^4 \left (3 x-6 x^3+3 x^5\right )} \, dx=\frac {e^{\frac {e^{2 x} e^{8} x^{2}-2 e^{2 x} e^{4} x^{3}+2 e^{2 x} e^{4} x +e^{2 x} x^{4}-2 e^{2 x} x^{2}+e^{2 x}+8 e^{x} e^{8} x^{2}+8 e^{x} e^{4} x^{4}-16 e^{x} e^{4} x^{3}+16 e^{x} e^{4} x +8 e^{x} x^{6}+8 e^{x} x^{4}+8 e^{x} x^{3}-16 e^{x} x^{2}+8 e^{x}+32 e^{4} x^{4}+16 x^{8}+48 x^{6}+32 x^{3}}{e^{8} x^{2}-2 e^{4} x^{3}+2 e^{4} x +x^{4}-2 x^{2}+1}} e^{17}}{e^{\frac {8 e^{x} e^{4} x^{5}+8 e^{x} x^{5}+8 e^{x} x^{4}+32 e^{4} x^{5}+32 x^{7}+32 x^{5}+32 x^{4}}{e^{8} x^{2}-2 e^{4} x^{3}+2 e^{4} x +x^{4}-2 x^{2}+1}}} \] Input:
int(((2*x^3*exp(4)^3+(-6*x^4+6*x^2)*exp(4)^2+(6*x^5-12*x^3+6*x)*exp(4)-2*x ^6+6*x^4-6*x^2+2)*exp(x)^2+(8*x^3*exp(4)^3+(-8*x^6-16*x^5-8*x^4+24*x^2)*ex p(4)^2+(16*x^7+24*x^6-16*x^5-40*x^4-8*x^3+24*x)*exp(4)-8*x^8-8*x^7+16*x^6+ 32*x^5-16*x^4-24*x^3+8)*exp(x)+(-96*x^5+64*x^4)*exp(4)^2+(96*x^8-160*x^7+2 24*x^6-96*x^5-224*x^4+160*x^3)*exp(4)-64*x^9+96*x^8+32*x^7-192*x^6+288*x^5 -128*x^4-128*x^3+96*x^2)*exp(((x^2*exp(4)^2+(-2*x^3+2*x)*exp(4)+x^4-2*x^2+ 1)*exp(x)^2+(8*x^2*exp(4)^2+(-8*x^5+8*x^4-16*x^3+16*x)*exp(4)+8*x^6-8*x^5+ 8*x^3-16*x^2+8)*exp(x)+17*x^2*exp(4)^2+(-32*x^5+32*x^4-34*x^3+34*x)*exp(4) +16*x^8-32*x^7+48*x^6-32*x^5-15*x^4+32*x^3-34*x^2+17)/(x^2*exp(4)^2+(-2*x^ 3+2*x)*exp(4)+x^4-2*x^2+1))/(x^3*exp(4)^3+(-3*x^4+3*x^2)*exp(4)^2+(3*x^5-6 *x^3+3*x)*exp(4)-x^6+3*x^4-3*x^2+1),x)
Output:
(e**((e**(2*x)*e**8*x**2 - 2*e**(2*x)*e**4*x**3 + 2*e**(2*x)*e**4*x + e**( 2*x)*x**4 - 2*e**(2*x)*x**2 + e**(2*x) + 8*e**x*e**8*x**2 + 8*e**x*e**4*x* *4 - 16*e**x*e**4*x**3 + 16*e**x*e**4*x + 8*e**x*x**6 + 8*e**x*x**4 + 8*e* *x*x**3 - 16*e**x*x**2 + 8*e**x + 32*e**4*x**4 + 16*x**8 + 48*x**6 + 32*x* *3)/(e**8*x**2 - 2*e**4*x**3 + 2*e**4*x + x**4 - 2*x**2 + 1))*e**17)/e**(( 8*e**x*e**4*x**5 + 8*e**x*x**5 + 8*e**x*x**4 + 32*e**4*x**5 + 32*x**7 + 32 *x**5 + 32*x**4)/(e**8*x**2 - 2*e**4*x**3 + 2*e**4*x + x**4 - 2*x**2 + 1))