Integrand size = 637, antiderivative size = 38 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=x+\frac {x^2}{\frac {x \left (-\frac {2}{x}+x\right )}{-4+x^2}+\left (e^4-x-\log (x)\right )^2} \]
Time = 0.25 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.82 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=x+\frac {x^2 \left (-4+x^2\right )}{-2-3 x^2+x^4+e^8 \left (-4+x^2\right )-2 e^4 x \left (-4+x^2\right )-2 \left (e^4-x\right ) \left (-4+x^2\right ) \log (x)+\left (-4+x^2\right ) \log ^2(x)} \]
Integrate[(4 + 16*x - 20*x^2 - 8*x^3 + 21*x^4 + 2*x^5 - 8*x^6 + x^8 + E^16 *(16 - 8*x^2 + x^4) + E^12*(-64*x + 32*x^3 - 4*x^5) + E^8*(16 + 32*x + 84* x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6) + E^4*(-32*x^2 - 56*x^3 + 16*x^4 + 30*x^5 - 2*x^6 - 4*x^7) + (32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 + 4*x ^7 + E^12*(-64 + 32*x^2 - 4*x^4) + E^8*(192*x - 96*x^3 + 12*x^5) + E^4*(-3 2 - 64*x - 168*x^2 + 32*x^3 + 92*x^4 - 4*x^5 - 12*x^6))*Log[x] + (16 + 32* x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + E^8*(96 - 48*x^2 + 6*x^4) + E^4*(-192*x + 96*x^3 - 12*x^5))*Log[x]^2 + (64*x - 32*x^3 + 4*x^5 + E^4*( -64 + 32*x^2 - 4*x^4))*Log[x]^3 + (16 - 8*x^2 + x^4)*Log[x]^4)/(4 + 12*x^2 + 5*x^4 - 6*x^6 + x^8 + E^16*(16 - 8*x^2 + x^4) + E^12*(-64*x + 32*x^3 - 4*x^5) + E^8*(16 + 84*x^2 - 46*x^4 + 6*x^6) + E^4*(-32*x - 40*x^3 + 28*x^5 - 4*x^7) + (32*x + 40*x^3 - 28*x^5 + 4*x^7 + E^12*(-64 + 32*x^2 - 4*x^4) + E^8*(192*x - 96*x^3 + 12*x^5) + E^4*(-32 - 168*x^2 + 92*x^4 - 12*x^6))*L og[x] + (16 + 84*x^2 - 46*x^4 + 6*x^6 + E^8*(96 - 48*x^2 + 6*x^4) + E^4*(- 192*x + 96*x^3 - 12*x^5))*Log[x]^2 + (64*x - 32*x^3 + 4*x^5 + E^4*(-64 + 3 2*x^2 - 4*x^4))*Log[x]^3 + (16 - 8*x^2 + x^4)*Log[x]^4),x]
x + (x^2*(-4 + x^2))/(-2 - 3*x^2 + x^4 + E^8*(-4 + x^2) - 2*E^4*x*(-4 + x^ 2) - 2*(E^4 - x)*(-4 + x^2)*Log[x] + (-4 + x^2)*Log[x]^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.
| \(\displaystyle \int \frac {x^8-8 x^6+2 x^5+21 x^4-8 x^3-20 x^2+e^{12} \left (-4 x^5+32 x^3-64 x\right )+e^{16} \left (x^4-8 x^2+16\right )+\left (x^4-8 x^2+16\right ) \log ^4(x)+\left (4 x^5-32 x^3+e^4 \left (-4 x^4+32 x^2-64\right )+64 x\right ) \log ^3(x)+e^8 \left (6 x^6+2 x^5-46 x^4-16 x^3+84 x^2+32 x+16\right )+\left (6 x^6+2 x^5-46 x^4-16 x^3+84 x^2+e^4 \left (-12 x^5+96 x^3-192 x\right )+e^8 \left (6 x^4-48 x^2+96\right )+32 x+16\right ) \log ^2(x)+e^4 \left (-4 x^7-2 x^6+30 x^5+16 x^4-56 x^3-32 x^2\right )+\left (4 x^7+2 x^6-30 x^5-16 x^4+56 x^3+32 x^2+e^8 \left (12 x^5-96 x^3+192 x\right )+e^{12} \left (-4 x^4+32 x^2-64\right )+e^4 \left (-12 x^6-4 x^5+92 x^4+32 x^3-168 x^2-64 x-32\right )\right ) \log (x)+16 x+4}{x^8-6 x^6+5 x^4+12 x^2+e^{12} \left (-4 x^5+32 x^3-64 x\right )+e^{16} \left (x^4-8 x^2+16\right )+\left (x^4-8 x^2+16\right ) \log ^4(x)+e^4 \left (-4 x^7+28 x^5-40 x^3-32 x\right )+e^8 \left (6 x^6-46 x^4+84 x^2+16\right )+\left (4 x^5-32 x^3+e^4 \left (-4 x^4+32 x^2-64\right )+64 x\right ) \log ^3(x)+\left (6 x^6-46 x^4+84 x^2+e^4 \left (-12 x^5+96 x^3-192 x\right )+e^8 \left (6 x^4-48 x^2+96\right )+16\right ) \log ^2(x)+\left (4 x^7-28 x^5+40 x^3+e^8 \left (12 x^5-96 x^3+192 x\right )+e^{12} \left (-4 x^4+32 x^2-64\right )+e^4 \left (-12 x^6+92 x^4-168 x^2-32\right )+32 x\right ) \log (x)+4} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^8-8 x^6+2 x^5+21 x^4-8 x^3-20 x^2-4 e^{12} \left (x^2-4\right )^2 x+e^{16} \left (x^2-4\right )^2+\left (x^2-4\right )^2 \log ^4(x)-4 \left (e^4-x\right ) \left (x^2-4\right )^2 \log ^3(x)+2 \left (x^2-4\right ) \left (3 x^4+x^3-11 x^2-6 e^4 \left (x^2-4\right ) x+3 e^8 \left (x^2-4\right )-4 x-2\right ) \log ^2(x)+2 \left (x^2-4\right ) \left (6 e^8 \left (x^2-4\right ) x-2 e^{12} \left (x^2-4\right )+\left (2 x^3+x^2-7 x-4\right ) x^2+e^4 \left (-6 x^4-2 x^3+22 x^2+8 x+4\right )\right ) \log (x)-2 e^4 \left (2 x^5+x^4-15 x^3-8 x^2+28 x+16\right ) x^2+2 e^8 \left (3 x^6+x^5-23 x^4-8 x^3+42 x^2+16 x+8\right )+16 x+4}{\left (-x^4+3 x^2+2 e^4 \left (x^2-4\right ) x-e^8 \left (x^2-4\right )-\left (x^2-4\right ) \log ^2(x)+2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)+2\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {2 x \left (x^2-4\right )}{x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2}-\frac {2 x \left (-e^4 (x+1) \left (x^2-4\right )^2+(x+1) \left (x^2-4\right )^2 \log (x)+x \left (x^5+x^4-8 x^3-8 x^2+14 x+16\right )\right )}{\left (x^4-3 x^2-2 e^4 \left (x^2-4\right ) x+e^8 \left (x^2-4\right )+\left (x^2-4\right ) \log ^2(x)-2 \left (e^4-x\right ) \left (x^2-4\right ) \log (x)-2\right )^2}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x \left (4-x^2\right )}{-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )}+\frac {2 x \left (-x^6-\left (1-e^4\right ) x^5-x^5 \log (x)+8 \left (1+\frac {e^4}{8}\right ) x^4-x^4 \log (x)+8 \left (1-e^4\right ) x^3+8 x^3 \log (x)-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 x^2 \log (x)-16 \left (1-e^4\right ) x-16 x \log (x)-16 \log (x)+16 e^4\right )}{\left (-x^4+2 e^4 x^3-2 x^3 \log (x)+3 \left (1-\frac {e^8}{3}\right ) x^2-x^2 \log ^2(x)+2 e^4 x^2 \log (x)-8 e^4 x+4 \log ^2(x)+8 x \log (x)-8 e^4 \log (x)+2 \left (1+2 e^8\right )\right )^2}+1\right )dx\) |
Int[(4 + 16*x - 20*x^2 - 8*x^3 + 21*x^4 + 2*x^5 - 8*x^6 + x^8 + E^16*(16 - 8*x^2 + x^4) + E^12*(-64*x + 32*x^3 - 4*x^5) + E^8*(16 + 32*x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6) + E^4*(-32*x^2 - 56*x^3 + 16*x^4 + 30*x^5 - 2*x^6 - 4*x^7) + (32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 + 4*x^7 + E ^12*(-64 + 32*x^2 - 4*x^4) + E^8*(192*x - 96*x^3 + 12*x^5) + E^4*(-32 - 64 *x - 168*x^2 + 32*x^3 + 92*x^4 - 4*x^5 - 12*x^6))*Log[x] + (16 + 32*x + 84 *x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + E^8*(96 - 48*x^2 + 6*x^4) + E^4*( -192*x + 96*x^3 - 12*x^5))*Log[x]^2 + (64*x - 32*x^3 + 4*x^5 + E^4*(-64 + 32*x^2 - 4*x^4))*Log[x]^3 + (16 - 8*x^2 + x^4)*Log[x]^4)/(4 + 12*x^2 + 5*x ^4 - 6*x^6 + x^8 + E^16*(16 - 8*x^2 + x^4) + E^12*(-64*x + 32*x^3 - 4*x^5) + E^8*(16 + 84*x^2 - 46*x^4 + 6*x^6) + E^4*(-32*x - 40*x^3 + 28*x^5 - 4*x ^7) + (32*x + 40*x^3 - 28*x^5 + 4*x^7 + E^12*(-64 + 32*x^2 - 4*x^4) + E^8* (192*x - 96*x^3 + 12*x^5) + E^4*(-32 - 168*x^2 + 92*x^4 - 12*x^6))*Log[x] + (16 + 84*x^2 - 46*x^4 + 6*x^6 + E^8*(96 - 48*x^2 + 6*x^4) + E^4*(-192*x + 96*x^3 - 12*x^5))*Log[x]^2 + (64*x - 32*x^3 + 4*x^5 + E^4*(-64 + 32*x^2 - 4*x^4))*Log[x]^3 + (16 - 8*x^2 + x^4)*Log[x]^4),x]
3.9.90.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(86\) vs. \(2(37)=74\).
Time = 0.81 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.29
| method | result | size |
| risch | \(x +\frac {x^{2} \left (x^{2}-4\right )}{x^{2} \ln \left (x \right )^{2}-2 x^{2} {\mathrm e}^{4} \ln \left (x \right )+2 x^{3} \ln \left (x \right )+x^{2} {\mathrm e}^{8}-2 x^{3} {\mathrm e}^{4}+x^{4}-4 \ln \left (x \right )^{2}+8 \,{\mathrm e}^{4} \ln \left (x \right )-8 x \ln \left (x \right )-4 \,{\mathrm e}^{8}+8 x \,{\mathrm e}^{4}-3 x^{2}-2}\) | \(87\) |
| default | \(x -\frac {{\mathrm e}^{2 \ln \left (x \right )+8}-2 \ln \left (x \right ) {\mathrm e}^{2 \ln \left (x \right )+4}-2 \,{\mathrm e}^{3 \ln \left (x \right )+4}+x^{2} \ln \left (x \right )^{2}+2 x^{3} \ln \left (x \right )-4 \,{\mathrm e}^{8}+8 \,{\mathrm e}^{4} \ln \left (x \right )+8 \,{\mathrm e}^{\ln \left (x \right )+4}-4 \ln \left (x \right )^{2}-8 x \ln \left (x \right )+x^{2}-2}{{\mathrm e}^{2 \ln \left (x \right )+8}-2 \,{\mathrm e}^{3 \ln \left (x \right )+4}-2 \ln \left (x \right ) {\mathrm e}^{2 \ln \left (x \right )+4}+x^{4}+2 x^{3} \ln \left (x \right )+x^{2} \ln \left (x \right )^{2}-4 \,{\mathrm e}^{8}+8 \,{\mathrm e}^{\ln \left (x \right )+4}+8 \,{\mathrm e}^{4} \ln \left (x \right )-3 x^{2}-8 x \ln \left (x \right )-4 \ln \left (x \right )^{2}-2}\) | \(162\) |
| parallelrisch | \(-\frac {2 x +4 x \,{\mathrm e}^{8}-{\mathrm e}^{8} x^{3}-8 x^{2} {\mathrm e}^{4}-2 x^{4} \ln \left (x \right )+4 x \ln \left (x \right )^{2}-8 x \,{\mathrm e}^{4} \ln \left (x \right )+2 x^{4} {\mathrm e}^{4}-x^{3} \ln \left (x \right )^{2}-x^{4}+3 x^{3}+4 x^{2}-x^{5}+8 x^{2} \ln \left (x \right )+2 \ln \left (x \right ) {\mathrm e}^{4} x^{3}}{x^{2} \ln \left (x \right )^{2}-2 x^{2} {\mathrm e}^{4} \ln \left (x \right )+2 x^{3} \ln \left (x \right )+x^{2} {\mathrm e}^{8}-2 x^{3} {\mathrm e}^{4}+x^{4}-4 \ln \left (x \right )^{2}+8 \,{\mathrm e}^{4} \ln \left (x \right )-8 x \ln \left (x \right )-4 \,{\mathrm e}^{8}+8 x \,{\mathrm e}^{4}-3 x^{2}-2}\) | \(182\) |
int(((x^4-8*x^2+16)*ln(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)* ln(x)^3+((6*x^4-48*x^2+96)*exp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6+2* x^5-46*x^4-16*x^3+84*x^2+32*x+16)*ln(x)^2+((-4*x^4+32*x^2-64)*exp(4)^3+(12 *x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6-4*x^5+92*x^4+32*x^3-168*x^2-64*x-32)* exp(4)+4*x^7+2*x^6-30*x^5-16*x^4+56*x^3+32*x^2)*ln(x)+(x^4-8*x^2+16)*exp(4 )^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32*x+1 6)*exp(4)^2+(-4*x^7-2*x^6+30*x^5+16*x^4-56*x^3-32*x^2)*exp(4)+x^8-8*x^6+2* x^5+21*x^4-8*x^3-20*x^2+16*x+4)/((x^4-8*x^2+16)*ln(x)^4+((-4*x^4+32*x^2-64 )*exp(4)+4*x^5-32*x^3+64*x)*ln(x)^3+((6*x^4-48*x^2+96)*exp(4)^2+(-12*x^5+9 6*x^3-192*x)*exp(4)+6*x^6-46*x^4+84*x^2+16)*ln(x)^2+((-4*x^4+32*x^2-64)*ex p(4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6+92*x^4-168*x^2-32)*exp(4)+4 *x^7-28*x^5+40*x^3+32*x)*ln(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x^5+32*x^3-64*x )*exp(4)^3+(6*x^6-46*x^4+84*x^2+16)*exp(4)^2+(-4*x^7+28*x^5-40*x^3-32*x)*e xp(4)+x^8-6*x^6+5*x^4+12*x^2+4),x,method=_RETURNVERBOSE)
x+x^2*(x^2-4)/(x^2*ln(x)^2-2*x^2*exp(4)*ln(x)+2*x^3*ln(x)+x^2*exp(8)-2*x^3 *exp(4)+x^4-4*ln(x)^2+8*exp(4)*ln(x)-8*x*ln(x)-4*exp(8)+8*x*exp(4)-3*x^2-2 )
Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (35) = 70\).
Time = 0.28 (sec) , antiderivative size = 141, normalized size of antiderivative = 3.71 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\frac {x^{5} + x^{4} - 3 \, x^{3} + {\left (x^{3} - 4 \, x\right )} \log \left (x\right )^{2} - 4 \, x^{2} + {\left (x^{3} - 4 \, x\right )} e^{8} - 2 \, {\left (x^{4} - 4 \, x^{2}\right )} e^{4} + 2 \, {\left (x^{4} - 4 \, x^{2} - {\left (x^{3} - 4 \, x\right )} e^{4}\right )} \log \left (x\right ) - 2 \, x}{x^{4} + {\left (x^{2} - 4\right )} \log \left (x\right )^{2} - 3 \, x^{2} + {\left (x^{2} - 4\right )} e^{8} - 2 \, {\left (x^{3} - 4 \, x\right )} e^{4} + 2 \, {\left (x^{3} - {\left (x^{2} - 4\right )} e^{4} - 4 \, x\right )} \log \left (x\right ) - 2} \]
integrate(((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3 +64*x)*log(x)^3+((6*x^4-48*x^2+96)*exp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+ 6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32*x+16)*log(x)^2+((-4*x^4+32*x^2-64)*exp (4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6-4*x^5+92*x^4+32*x^3-168*x^2- 64*x-32)*exp(4)+4*x^7+2*x^6-30*x^5-16*x^4+56*x^3+32*x^2)*log(x)+(x^4-8*x^2 +16)*exp(4)^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6+2*x^5-46*x^4-16*x^3+84* x^2+32*x+16)*exp(4)^2+(-4*x^7-2*x^6+30*x^5+16*x^4-56*x^3-32*x^2)*exp(4)+x^ 8-8*x^6+2*x^5+21*x^4-8*x^3-20*x^2+16*x+4)/((x^4-8*x^2+16)*log(x)^4+((-4*x^ 4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*exp(4)^ 2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6-46*x^4+84*x^2+16)*log(x)^2+((-4*x^4+ 32*x^2-64)*exp(4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6+92*x^4-168*x^2 -32)*exp(4)+4*x^7-28*x^5+40*x^3+32*x)*log(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x ^5+32*x^3-64*x)*exp(4)^3+(6*x^6-46*x^4+84*x^2+16)*exp(4)^2+(-4*x^7+28*x^5- 40*x^3-32*x)*exp(4)+x^8-6*x^6+5*x^4+12*x^2+4),x, algorithm=\
(x^5 + x^4 - 3*x^3 + (x^3 - 4*x)*log(x)^2 - 4*x^2 + (x^3 - 4*x)*e^8 - 2*(x ^4 - 4*x^2)*e^4 + 2*(x^4 - 4*x^2 - (x^3 - 4*x)*e^4)*log(x) - 2*x)/(x^4 + ( x^2 - 4)*log(x)^2 - 3*x^2 + (x^2 - 4)*e^8 - 2*(x^3 - 4*x)*e^4 + 2*(x^3 - ( x^2 - 4)*e^4 - 4*x)*log(x) - 2)
Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (26) = 52\).
Time = 0.48 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.16 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=x + \frac {x^{4} - 4 x^{2}}{x^{4} - 2 x^{3} e^{4} - 3 x^{2} + x^{2} e^{8} + 8 x e^{4} + \left (x^{2} - 4\right ) \log {\left (x \right )}^{2} + \left (2 x^{3} - 2 x^{2} e^{4} - 8 x + 8 e^{4}\right ) \log {\left (x \right )} - 4 e^{8} - 2} \]
integrate(((x**4-8*x**2+16)*ln(x)**4+((-4*x**4+32*x**2-64)*exp(4)+4*x**5-3 2*x**3+64*x)*ln(x)**3+((6*x**4-48*x**2+96)*exp(4)**2+(-12*x**5+96*x**3-192 *x)*exp(4)+6*x**6+2*x**5-46*x**4-16*x**3+84*x**2+32*x+16)*ln(x)**2+((-4*x* *4+32*x**2-64)*exp(4)**3+(12*x**5-96*x**3+192*x)*exp(4)**2+(-12*x**6-4*x** 5+92*x**4+32*x**3-168*x**2-64*x-32)*exp(4)+4*x**7+2*x**6-30*x**5-16*x**4+5 6*x**3+32*x**2)*ln(x)+(x**4-8*x**2+16)*exp(4)**4+(-4*x**5+32*x**3-64*x)*ex p(4)**3+(6*x**6+2*x**5-46*x**4-16*x**3+84*x**2+32*x+16)*exp(4)**2+(-4*x**7 -2*x**6+30*x**5+16*x**4-56*x**3-32*x**2)*exp(4)+x**8-8*x**6+2*x**5+21*x**4 -8*x**3-20*x**2+16*x+4)/((x**4-8*x**2+16)*ln(x)**4+((-4*x**4+32*x**2-64)*e xp(4)+4*x**5-32*x**3+64*x)*ln(x)**3+((6*x**4-48*x**2+96)*exp(4)**2+(-12*x* *5+96*x**3-192*x)*exp(4)+6*x**6-46*x**4+84*x**2+16)*ln(x)**2+((-4*x**4+32* x**2-64)*exp(4)**3+(12*x**5-96*x**3+192*x)*exp(4)**2+(-12*x**6+92*x**4-168 *x**2-32)*exp(4)+4*x**7-28*x**5+40*x**3+32*x)*ln(x)+(x**4-8*x**2+16)*exp(4 )**4+(-4*x**5+32*x**3-64*x)*exp(4)**3+(6*x**6-46*x**4+84*x**2+16)*exp(4)** 2+(-4*x**7+28*x**5-40*x**3-32*x)*exp(4)+x**8-6*x**6+5*x**4+12*x**2+4),x)
x + (x**4 - 4*x**2)/(x**4 - 2*x**3*exp(4) - 3*x**2 + x**2*exp(8) + 8*x*exp (4) + (x**2 - 4)*log(x)**2 + (2*x**3 - 2*x**2*exp(4) - 8*x + 8*exp(4))*log (x) - 4*exp(8) - 2)
Leaf count of result is larger than twice the leaf count of optimal. 144 vs. \(2 (35) = 70\).
Time = 0.40 (sec) , antiderivative size = 144, normalized size of antiderivative = 3.79 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\frac {x^{5} - x^{4} {\left (2 \, e^{4} - 1\right )} + x^{3} {\left (e^{8} - 3\right )} + 4 \, x^{2} {\left (2 \, e^{4} - 1\right )} + {\left (x^{3} - 4 \, x\right )} \log \left (x\right )^{2} - 2 \, x {\left (2 \, e^{8} + 1\right )} + 2 \, {\left (x^{4} - x^{3} e^{4} - 4 \, x^{2} + 4 \, x e^{4}\right )} \log \left (x\right )}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 3\right )} + {\left (x^{2} - 4\right )} \log \left (x\right )^{2} + 8 \, x e^{4} + 2 \, {\left (x^{3} - x^{2} e^{4} - 4 \, x + 4 \, e^{4}\right )} \log \left (x\right ) - 4 \, e^{8} - 2} \]
integrate(((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3 +64*x)*log(x)^3+((6*x^4-48*x^2+96)*exp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+ 6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32*x+16)*log(x)^2+((-4*x^4+32*x^2-64)*exp (4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6-4*x^5+92*x^4+32*x^3-168*x^2- 64*x-32)*exp(4)+4*x^7+2*x^6-30*x^5-16*x^4+56*x^3+32*x^2)*log(x)+(x^4-8*x^2 +16)*exp(4)^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6+2*x^5-46*x^4-16*x^3+84* x^2+32*x+16)*exp(4)^2+(-4*x^7-2*x^6+30*x^5+16*x^4-56*x^3-32*x^2)*exp(4)+x^ 8-8*x^6+2*x^5+21*x^4-8*x^3-20*x^2+16*x+4)/((x^4-8*x^2+16)*log(x)^4+((-4*x^ 4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*exp(4)^ 2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6-46*x^4+84*x^2+16)*log(x)^2+((-4*x^4+ 32*x^2-64)*exp(4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6+92*x^4-168*x^2 -32)*exp(4)+4*x^7-28*x^5+40*x^3+32*x)*log(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x ^5+32*x^3-64*x)*exp(4)^3+(6*x^6-46*x^4+84*x^2+16)*exp(4)^2+(-4*x^7+28*x^5- 40*x^3-32*x)*exp(4)+x^8-6*x^6+5*x^4+12*x^2+4),x, algorithm=\
(x^5 - x^4*(2*e^4 - 1) + x^3*(e^8 - 3) + 4*x^2*(2*e^4 - 1) + (x^3 - 4*x)*l og(x)^2 - 2*x*(2*e^8 + 1) + 2*(x^4 - x^3*e^4 - 4*x^2 + 4*x*e^4)*log(x))/(x ^4 - 2*x^3*e^4 + x^2*(e^8 - 3) + (x^2 - 4)*log(x)^2 + 8*x*e^4 + 2*(x^3 - x ^2*e^4 - 4*x + 4*e^4)*log(x) - 4*e^8 - 2)
Leaf count of result is larger than twice the leaf count of optimal. 168 vs. \(2 (35) = 70\).
Time = 1.65 (sec) , antiderivative size = 168, normalized size of antiderivative = 4.42 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\frac {x^{5} - 2 \, x^{4} e^{4} + 2 \, x^{4} \log \left (x\right ) - 2 \, x^{3} e^{4} \log \left (x\right ) + x^{3} \log \left (x\right )^{2} + 2 \, x^{4} + x^{3} e^{8} - 3 \, x^{3} + 8 \, x^{2} e^{4} - 8 \, x^{2} \log \left (x\right ) + 8 \, x e^{4} \log \left (x\right ) - 4 \, x \log \left (x\right )^{2} - 8 \, x^{2} - 4 \, x e^{8} - 2 \, x}{x^{4} - 2 \, x^{3} e^{4} + 2 \, x^{3} \log \left (x\right ) - 2 \, x^{2} e^{4} \log \left (x\right ) + x^{2} \log \left (x\right )^{2} + x^{2} e^{8} - 3 \, x^{2} + 8 \, x e^{4} - 8 \, x \log \left (x\right ) + 8 \, e^{4} \log \left (x\right ) - 4 \, \log \left (x\right )^{2} - 4 \, e^{8} - 2} \]
integrate(((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3 +64*x)*log(x)^3+((6*x^4-48*x^2+96)*exp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+ 6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32*x+16)*log(x)^2+((-4*x^4+32*x^2-64)*exp (4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6-4*x^5+92*x^4+32*x^3-168*x^2- 64*x-32)*exp(4)+4*x^7+2*x^6-30*x^5-16*x^4+56*x^3+32*x^2)*log(x)+(x^4-8*x^2 +16)*exp(4)^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6+2*x^5-46*x^4-16*x^3+84* x^2+32*x+16)*exp(4)^2+(-4*x^7-2*x^6+30*x^5+16*x^4-56*x^3-32*x^2)*exp(4)+x^ 8-8*x^6+2*x^5+21*x^4-8*x^3-20*x^2+16*x+4)/((x^4-8*x^2+16)*log(x)^4+((-4*x^ 4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*exp(4)^ 2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6-46*x^4+84*x^2+16)*log(x)^2+((-4*x^4+ 32*x^2-64)*exp(4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6+92*x^4-168*x^2 -32)*exp(4)+4*x^7-28*x^5+40*x^3+32*x)*log(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x ^5+32*x^3-64*x)*exp(4)^3+(6*x^6-46*x^4+84*x^2+16)*exp(4)^2+(-4*x^7+28*x^5- 40*x^3-32*x)*exp(4)+x^8-6*x^6+5*x^4+12*x^2+4),x, algorithm=\
(x^5 - 2*x^4*e^4 + 2*x^4*log(x) - 2*x^3*e^4*log(x) + x^3*log(x)^2 + 2*x^4 + x^3*e^8 - 3*x^3 + 8*x^2*e^4 - 8*x^2*log(x) + 8*x*e^4*log(x) - 4*x*log(x) ^2 - 8*x^2 - 4*x*e^8 - 2*x)/(x^4 - 2*x^3*e^4 + 2*x^3*log(x) - 2*x^2*e^4*lo g(x) + x^2*log(x)^2 + x^2*e^8 - 3*x^2 + 8*x*e^4 - 8*x*log(x) + 8*e^4*log(x ) - 4*log(x)^2 - 4*e^8 - 2)
Timed out. \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\int \frac {16\,x+{\mathrm {e}}^8\,\left (6\,x^6+2\,x^5-46\,x^4-16\,x^3+84\,x^2+32\,x+16\right )+{\ln \left (x\right )}^4\,\left (x^4-8\,x^2+16\right )+{\mathrm {e}}^{16}\,\left (x^4-8\,x^2+16\right )-{\mathrm {e}}^{12}\,\left (4\,x^5-32\,x^3+64\,x\right )-{\mathrm {e}}^4\,\left (4\,x^7+2\,x^6-30\,x^5-16\,x^4+56\,x^3+32\,x^2\right )-20\,x^2-8\,x^3+21\,x^4+2\,x^5-8\,x^6+x^8+{\ln \left (x\right )}^3\,\left (64\,x-{\mathrm {e}}^4\,\left (4\,x^4-32\,x^2+64\right )-32\,x^3+4\,x^5\right )+{\ln \left (x\right )}^2\,\left (32\,x-{\mathrm {e}}^4\,\left (12\,x^5-96\,x^3+192\,x\right )+{\mathrm {e}}^8\,\left (6\,x^4-48\,x^2+96\right )+84\,x^2-16\,x^3-46\,x^4+2\,x^5+6\,x^6+16\right )+\ln \left (x\right )\,\left ({\mathrm {e}}^8\,\left (12\,x^5-96\,x^3+192\,x\right )-{\mathrm {e}}^4\,\left (12\,x^6+4\,x^5-92\,x^4-32\,x^3+168\,x^2+64\,x+32\right )-{\mathrm {e}}^{12}\,\left (4\,x^4-32\,x^2+64\right )+32\,x^2+56\,x^3-16\,x^4-30\,x^5+2\,x^6+4\,x^7\right )+4}{{\ln \left (x\right )}^4\,\left (x^4-8\,x^2+16\right )+{\mathrm {e}}^{16}\,\left (x^4-8\,x^2+16\right )-{\mathrm {e}}^{12}\,\left (4\,x^5-32\,x^3+64\,x\right )-{\mathrm {e}}^4\,\left (4\,x^7-28\,x^5+40\,x^3+32\,x\right )+{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^8\,\left (6\,x^4-48\,x^2+96\right )-{\mathrm {e}}^4\,\left (12\,x^5-96\,x^3+192\,x\right )+84\,x^2-46\,x^4+6\,x^6+16\right )+{\mathrm {e}}^8\,\left (6\,x^6-46\,x^4+84\,x^2+16\right )+12\,x^2+5\,x^4-6\,x^6+x^8+{\ln \left (x\right )}^3\,\left (64\,x-{\mathrm {e}}^4\,\left (4\,x^4-32\,x^2+64\right )-32\,x^3+4\,x^5\right )+\ln \left (x\right )\,\left (32\,x+{\mathrm {e}}^8\,\left (12\,x^5-96\,x^3+192\,x\right )-{\mathrm {e}}^{12}\,\left (4\,x^4-32\,x^2+64\right )-{\mathrm {e}}^4\,\left (12\,x^6-92\,x^4+168\,x^2+32\right )+40\,x^3-28\,x^5+4\,x^7\right )+4} \,d x \]
int((16*x + exp(8)*(32*x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + 16) + log(x)^4*(x^4 - 8*x^2 + 16) + exp(16)*(x^4 - 8*x^2 + 16) - exp(12)*(64*x - 32*x^3 + 4*x^5) - exp(4)*(32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 + 4 *x^7) - 20*x^2 - 8*x^3 + 21*x^4 + 2*x^5 - 8*x^6 + x^8 + log(x)^3*(64*x - e xp(4)*(4*x^4 - 32*x^2 + 64) - 32*x^3 + 4*x^5) + log(x)^2*(32*x - exp(4)*(1 92*x - 96*x^3 + 12*x^5) + exp(8)*(6*x^4 - 48*x^2 + 96) + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + 16) + log(x)*(exp(8)*(192*x - 96*x^3 + 12*x^5) - exp(4)*(64*x + 168*x^2 - 32*x^3 - 92*x^4 + 4*x^5 + 12*x^6 + 32) - exp(12) *(4*x^4 - 32*x^2 + 64) + 32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 + 4*x^7 ) + 4)/(log(x)^4*(x^4 - 8*x^2 + 16) + exp(16)*(x^4 - 8*x^2 + 16) - exp(12) *(64*x - 32*x^3 + 4*x^5) - exp(4)*(32*x + 40*x^3 - 28*x^5 + 4*x^7) + log(x )^2*(exp(8)*(6*x^4 - 48*x^2 + 96) - exp(4)*(192*x - 96*x^3 + 12*x^5) + 84* x^2 - 46*x^4 + 6*x^6 + 16) + exp(8)*(84*x^2 - 46*x^4 + 6*x^6 + 16) + 12*x^ 2 + 5*x^4 - 6*x^6 + x^8 + log(x)^3*(64*x - exp(4)*(4*x^4 - 32*x^2 + 64) - 32*x^3 + 4*x^5) + log(x)*(32*x + exp(8)*(192*x - 96*x^3 + 12*x^5) - exp(12 )*(4*x^4 - 32*x^2 + 64) - exp(4)*(168*x^2 - 92*x^4 + 12*x^6 + 32) + 40*x^3 - 28*x^5 + 4*x^7) + 4),x)
int((16*x + exp(8)*(32*x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + 16) + log(x)^4*(x^4 - 8*x^2 + 16) + exp(16)*(x^4 - 8*x^2 + 16) - exp(12)*(64*x - 32*x^3 + 4*x^5) - exp(4)*(32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 + 4 *x^7) - 20*x^2 - 8*x^3 + 21*x^4 + 2*x^5 - 8*x^6 + x^8 + log(x)^3*(64*x - e xp(4)*(4*x^4 - 32*x^2 + 64) - 32*x^3 + 4*x^5) + log(x)^2*(32*x - exp(4)*(1 92*x - 96*x^3 + 12*x^5) + exp(8)*(6*x^4 - 48*x^2 + 96) + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + 16) + log(x)*(exp(8)*(192*x - 96*x^3 + 12*x^5) - exp(4)*(64*x + 168*x^2 - 32*x^3 - 92*x^4 + 4*x^5 + 12*x^6 + 32) - exp(12) *(4*x^4 - 32*x^2 + 64) + 32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 + 4*x^7 ) + 4)/(log(x)^4*(x^4 - 8*x^2 + 16) + exp(16)*(x^4 - 8*x^2 + 16) - exp(12) *(64*x - 32*x^3 + 4*x^5) - exp(4)*(32*x + 40*x^3 - 28*x^5 + 4*x^7) + log(x )^2*(exp(8)*(6*x^4 - 48*x^2 + 96) - exp(4)*(192*x - 96*x^3 + 12*x^5) + 84* x^2 - 46*x^4 + 6*x^6 + 16) + exp(8)*(84*x^2 - 46*x^4 + 6*x^6 + 16) + 12*x^ 2 + 5*x^4 - 6*x^6 + x^8 + log(x)^3*(64*x - exp(4)*(4*x^4 - 32*x^2 + 64) - 32*x^3 + 4*x^5) + log(x)*(32*x + exp(8)*(192*x - 96*x^3 + 12*x^5) - exp(12 )*(4*x^4 - 32*x^2 + 64) - exp(4)*(168*x^2 - 92*x^4 + 12*x^6 + 32) + 40*x^3 - 28*x^5 + 4*x^7) + 4), x)