Integrand size = 408, antiderivative size = 36 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=x+\frac {x}{\log (2)-\frac {2 e^x}{x \left (-e^x+\left (3+\frac {5}{x}\right )^2+\log (x)\right )}} \]
\[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx \]
Integrate[((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2] + (625 + 15 00*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3 + (4 *x^3 + x^4)*Log[2] + x^4*Log[2]^2) + E^x*(-10*x^2 + 22*x^3 + 18*x^4 + (-10 0*x - 170*x^2 - 96*x^3 - 18*x^4)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[ 2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2] + (50*x^2 + 60*x^3 + 18*x^4)*Lo g[2]^2 + E^x*(-4*x^3 + 2*x^4 + (-4*x^3 - 2*x^4)*Log[2] - 2*x^4*Log[2]^2))* Log[x] + (x^4*Log[2] + x^4*Log[2]^2)*Log[x]^2)/((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3*Log[2] + x^4*Log[2]^2 ) + E^x*((-100*x - 120*x^2 - 36*x^3)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)* Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3*Log[2] - 2* x^4*Log[2]^2))*Log[x] + x^4*Log[2]^2*Log[x]^2),x]
Integrate[((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2] + (625 + 15 00*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3 + (4 *x^3 + x^4)*Log[2] + x^4*Log[2]^2) + E^x*(-10*x^2 + 22*x^3 + 18*x^4 + (-10 0*x - 170*x^2 - 96*x^3 - 18*x^4)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[ 2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2] + (50*x^2 + 60*x^3 + 18*x^4)*Lo g[2]^2 + E^x*(-4*x^3 + 2*x^4 + (-4*x^3 - 2*x^4)*Log[2] - 2*x^4*Log[2]^2))* Log[x] + (x^4*Log[2] + x^4*Log[2]^2)*Log[x]^2)/((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3*Log[2] + x^4*Log[2]^2 ) + E^x*((-100*x - 120*x^2 - 36*x^3)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)* Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3*Log[2] - 2* x^4*Log[2]^2))*Log[x] + x^4*Log[2]^2*Log[x]^2), x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (x^4 \log ^2(2)+x^4 \log (2)\right ) \log ^2(x)+\left (e^x \left (2 x^4-2 x^4 \log ^2(2)-4 x^3+\left (-2 x^4-4 x^3\right ) \log (2)\right )+\left (18 x^4+60 x^3+50 x^2\right ) \log ^2(2)+\left (18 x^4+60 x^3+50 x^2\right ) \log (2)\right ) \log (x)+e^{2 x} \left (x^4 \log ^2(2)+4 x^3+4 x^2+\left (x^4+4 x^3\right ) \log (2)\right )+e^x \left (18 x^4+22 x^3-10 x^2+\left (-18 x^4-60 x^3-50 x^2\right ) \log ^2(2)+\left (-18 x^4-96 x^3-170 x^2-100 x\right ) \log (2)\right )+\left (81 x^4+540 x^3+1350 x^2+1500 x+625\right ) \log ^2(2)+\left (81 x^4+540 x^3+1350 x^2+1500 x+625\right ) \log (2)}{x^4 \log ^2(2) \log ^2(x)+e^{2 x} \left (x^4 \log ^2(2)+4 x^3 \log (2)+4 x^2\right )+e^x \left (\left (-36 x^3-120 x^2-100 x\right ) \log (2)+\left (-18 x^4-60 x^3-50 x^2\right ) \log ^2(2)\right )+\left (e^x \left (-2 x^4 \log ^2(2)-4 x^3 \log (2)\right )+\left (18 x^4+60 x^3+50 x^2\right ) \log ^2(2)\right ) \log (x)+\left (81 x^4+540 x^3+1350 x^2+1500 x+625\right ) \log ^2(2)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (x^4 \log ^2(2)+x^4 \log (2)\right ) \log ^2(x)+\left (e^x \left (2 x^4-2 x^4 \log ^2(2)-4 x^3+\left (-2 x^4-4 x^3\right ) \log (2)\right )+\left (18 x^4+60 x^3+50 x^2\right ) \log ^2(2)+\left (18 x^4+60 x^3+50 x^2\right ) \log (2)\right ) \log (x)+e^{2 x} \left (x^4 \log ^2(2)+4 x^3+4 x^2+\left (x^4+4 x^3\right ) \log (2)\right )+e^x \left (18 x^4+22 x^3-10 x^2+\left (-18 x^4-60 x^3-50 x^2\right ) \log ^2(2)+\left (-18 x^4-96 x^3-170 x^2-100 x\right ) \log (2)\right )+\left (81 x^4+540 x^3+1350 x^2+1500 x+625\right ) \left (\log ^2(2)+\log (2)\right )}{x^4 \log ^2(2) \log ^2(x)+e^{2 x} \left (x^4 \log ^2(2)+4 x^3 \log (2)+4 x^2\right )+e^x \left (\left (-36 x^3-120 x^2-100 x\right ) \log (2)+\left (-18 x^4-60 x^3-50 x^2\right ) \log ^2(2)\right )+\left (e^x \left (-2 x^4 \log ^2(2)-4 x^3 \log (2)\right )+\left (18 x^4+60 x^3+50 x^2\right ) \log ^2(2)\right ) \log (x)+\left (81 x^4+540 x^3+1350 x^2+1500 x+625\right ) \log ^2(2)}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^4 \log (2) (1+\log (2)) \log ^2(x)-2 x^2 \left (e^x x \left (x \left (-1+\log ^2(2)+\log (2)\right )+2+\log (4)\right )-(3 x+5)^2 \log (2) (1+\log (2))\right ) \log (x)+e^{2 x} x^2 \left (x^2 \log (2) (1+\log (2))+x (4+\log (16))+4\right )-2 e^x x \left (9 x^3 \left (-1+\log ^2(2)+\log (2)\right )+x^2 \left (-11+30 \log ^2(2)+48 \log (2)\right )+5 x \left (1+5 \log ^2(2)+17 \log (2)\right )+50 \log (2)\right )+(3 x+5)^4 \log (2) (1+\log (2))}{\left (x^2 \log (2) \log (x)-e^x x (x \log (2)+2)+(3 x+5)^2 \log (2)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^2 \log (2) (1+\log (2))+x (4+\log (16))+4}{(x \log (2)+2)^2}+\frac {2 x \left (x^3 \log (2) \log (x)+9 x^3 \log (2)+2 x^2 \log (x)+18 x^2 \left (1+\frac {29 \log (2)}{18}\right )-4 x \log (x)+30 x \log (2) \log (16)+22 x \left (1-\frac {5}{22} \log (2) (24 \log (2)-11)\right )-10 \left (1+10 \log ^2(2)-(1+\log (4)) \log (32)\right )\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )}+\frac {\log (2) \left (9 x^2+x^2 \log (x)+30 x+25\right ) \left (x^4 \log (4) \log (x)+18 x^4 \log (2)+4 x^3 \left (1+\frac {1}{4} \left (\log (2) \log (16)-\log ^2(4)\right )\right ) \log (x)+36 x^3 \left (1+\frac {29 \log (2)}{18}\right )+80 x^2 \left (1+\frac {1}{8} \left (-12 \log ^2(2)+\log (8) \log (16)+\log (2048)\right )\right )-4 x^2 \log (x)+25 x \log (2) \log (16)+100 x (1-(\log (2)-1) \log (2))+100\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \left (\frac {x^2 \log (2) (1+\log (2))+x (4+\log (16))+4}{(x \log (2)+2)^2}+\frac {2 x \left (x^3 \log (2) \log (x)+9 x^3 \log (2)+2 x^2 \log (x)+18 x^2 \left (1+\frac {29 \log (2)}{18}\right )+22 x \left (1-\frac {5}{22} \log (2) (24 \log (2)-11)\right ) \left (1-\frac {30 \log (2) \log (16)}{-22+120 \log ^2(2)-55 \log (2)}\right )-4 x \log (x)-10 \left (1+10 \log ^2(2)-(1+\log (4)) \log (32)\right )\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )}+\frac {\log (2) \left (9 x^2+x^2 \log (x)+30 x+25\right ) \left (x^4 \log (4) \log (x)+18 x^4 \log (2)+4 x^3 \left (1+\frac {1}{4} \left (\log (2) \log (16)-\log ^2(4)\right )\right ) \log (x)+36 x^3 \left (1+\frac {29 \log (2)}{18}\right )+80 x^2 \left (1+\frac {1}{8} \left (-12 \log ^2(2)+\log (8) \log (16)+\log (2048)\right )\right )-4 x^2 \log (x)+100 x (1-(\log (2)-1) \log (2)) \left (1+\frac {\log (2) \log (16)}{4-4 \log ^2(2)+\log (16)}\right )+100\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^2 \log (2) (1+\log (2))+x (4+\log (16))+4}{(x \log (2)+2)^2}+\frac {2 x \left (x^3 \log (2) \log (x)+9 x^3 \log (2)+2 x^2 \log (x)+18 x^2 \left (1+\frac {29 \log (2)}{18}\right )-4 x \log (x)+22 x \left (1+\frac {5 \log (2)}{2}\right )-10 \left (1+10 \log ^2(2)-(1+\log (4)) \log (32)\right )\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )}+\frac {\log (2) \left (9 x^2+x^2 \log (x)+30 x+25\right ) \left (4 x^4 (1-(\log (2)-1) \log (2)) \log (4) \log (x)+72 x^4 \log (2) (1-(\log (2)-1) \log (2))+144 x^3 \left (1-\frac {1}{72} \log (2) \left (-188+116 \log ^2(2)+72 \log (2)-29 \log (16)\right )\right )+16 x^3 \left (1+\frac {1}{4} \left (-4 \log ^4(2)-\log ^2(4)+\log (2) \left (\log (16)-\log ^2(4)\right )+\log ^2(2) \left (-4+\log ^2(4)+\log (16)\right )+\log (16)\right )\right ) \log (x)+320 x^2 \left (1+\frac {1}{4} \left (6 \log ^4(2)-10 \log ^2(2)+\log (16) \left (1-\frac {3 \log ^2(2)}{2}-\frac {\left (-1+\log ^2(2)-\log (2)\right ) (\log (8) \log (16)+\log (2048))}{\log (256)}\right )\right )\right )-16 x^2 (1-(\log (2)-1) \log (2)) \log (x)+400 x \left (1-\log ^3(2)+\log (4)\right )+400 (1-(\log (2)-1) \log (2))\right )}{\left (4-4 \log ^2(2)+\log (16)\right ) (x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^2 \log (2) (1+\log (2))+x (4+\log (16))+4}{(x \log (2)+2)^2}+\frac {2 x \left (x^3 \log (2) \log (x)+9 x^3 \log (2)+2 x^2 \log (x)+18 x^2 \left (1+\frac {29 \log (2)}{18}\right )-4 x \log (x)+22 x \left (1+\frac {\log (32)}{2}\right )-10 \left (1+10 \log ^2(2)-(1+\log (4)) \log (32)\right )\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )}+\frac {2 \log (2) \left (9 x^2+x^2 \log (x)+30 x+25\right ) \left (2 x^4 (1-(\log (2)-1) \log (2)) \log (4) \log (256) \log (x)+36 x^4 \log (2) (1-(\log (2)-1) \log (2)) \log (256)+72 x^3 \left (1-\frac {1}{18} \log (2) \left (-47+29 \log ^2(2)-11 \log (2)\right )\right ) \log (256)+8 x^3 \left (1+\frac {1}{4} \left (-4 \log ^4(2)-\log ^2(4)+\log (2) \left (\log (16)-\log ^2(4)\right )+\log ^2(2) \left (-4+\log ^2(4)+\log (16)\right )+\log (16)\right )\right ) \log (256) \log (x)+40 x^2 \log (8) \log ^2(16) \left (1-\log ^2(2)+\frac {\log (256) \left (4+6 \log ^4(2)-10 \log ^2(2)+\log (16) \left (1+\frac {(2+\log (4)) \log (2048)-\log ^2(2) (3 \log (256)+2 \log (2048))}{\log (65536)}\right )\right )}{\log (8) \log ^2(16)}+\log (2)\right )-8 x^2 (1-(\log (2)-1) \log (2)) \log (256) \log (x)+200 x \left (1-\log ^3(2)+\log (4)\right ) \log (256)+200 (1-(\log (2)-1) \log (2)) \log (256)\right )}{\left (4-4 \log ^2(2)+\log (16)\right ) \log (256) (x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^2 \log (2) (1+\log (2))+x (4+\log (16))+4}{(x \log (2)+2)^2}+\frac {2 x \left (x^3 \log (2) \log (x)+9 x^3 \log (2)+2 x^2 \log (x)+18 x^2 \left (1+\frac {29 \log (2)}{18}\right )-4 x \log (x)+22 x \left (1+\frac {\log (32)}{2}\right )-10 \left (1+10 \log ^2(2)-(1+\log (4)) \log (32)\right )\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )}+\frac {4 \log (2) \left (9 x^2+x^2 \log (x)+30 x+25\right ) \left (x^4 (1-(\log (2)-1) \log (2)) \log (4) \log (256) \log (65536) \log (x)+18 x^4 \log (2) (1-(\log (2)-1) \log (2)) \log (256) \log (65536)+36 x^3 \left (1-\frac {1}{18} \log (2) \left (-47+29 \log ^2(2)-11 \log (2)\right )\right ) \log (256) \log (65536)+4 x^3 \left (1+\frac {1}{4} \left (-4 \log ^4(2)-\log ^2(4)+\log (2) \left (\log (16)-\log ^2(4)\right )+\log ^2(2) \left (-4+\log ^2(4)+\log (16)\right )+\log (16)\right )\right ) \log (256) \log (65536) \log (x)-60 x^2 \log ^2(2) \log (16) \log ^2(256) \left (1-\frac {\log (2048) \left (2-2 \log ^2(2)+\frac {\left (\left (1-\log ^2(2)+\log (2)\right ) \log (8) \log ^2(16)+2 \left (2+3 \log ^4(2)-5 \log ^2(2)+\log (4)\right ) \log (256)\right ) \log (65536)}{\log (16) \log (256) \log (2048)}+\log (4)\right )}{3 \log ^2(2) \log (256)}\right )-4 x^2 (1-(\log (2)-1) \log (2)) \log (256) \log (65536) \log (x)+100 x \left (1-\log ^3(2)+\log (4)\right ) \log (256) \log (65536)+100 (1-(\log (2)-1) \log (2)) \log (256) \log (65536)\right )}{\left (4-4 \log ^2(2)+\log (16)\right ) \log (256) \log (65536) (x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^2 \log (2) (1+\log (2))+x (4+\log (16))+4}{(x \log (2)+2)^2}+\frac {2 x \left (x^3 \log (2) \log (x)+9 x^3 \log (2)+2 x^2 \log (x)+18 x^2 \left (1+\frac {29 \log (2)}{18}\right )-4 x \log (x)+22 x \left (1+\frac {\log (32)}{2}\right )-10 \left (1+10 \log ^2(2)-(1+\log (4)) \log (32)\right )\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )}+\frac {4 \log (2) \left (9 x^2+x^2 \log (x)+30 x+25\right ) \left (x^4 (1-(\log (2)-1) \log (2)) \log (4) \log (256) \log (65536) \log (x)+18 x^4 \log (2) (1-(\log (2)-1) \log (2)) \log (256) \log (65536)+36 x^3 \left (1-\frac {1}{18} \log (2) \left (-47+29 \log ^2(2)-11 \log (2)\right )\right ) \log (256) \log (65536)+4 x^3 \left (1+\frac {1}{4} \left (-4 \log ^4(2)-\log ^2(4)+\log (2) \left (\log (16)-\log ^2(4)\right )+\log ^2(2) \left (-4+\log ^2(4)+\log (16)\right )+\log (16)\right )\right ) \log (256) \log (65536) \log (x)-60 x^2 \log ^2(2) \log (16) \log ^2(256) \left (1-\frac {\log (4) \log (2048) \left (1+\frac {\log (256) \left (1-\log ^2(2)+\frac {\left (\left (1-\log ^2(2)+\log (2)\right ) \log (8) \log ^2(16)+2 \left (2+3 \log ^4(2)-5 \log ^2(2)+\log (4)\right ) \log (256)\right ) \log (65536)}{\log ^2(256) \log (2048)}\right )}{\log (4) \log (16)}\right )}{3 \log ^2(2) \log (256)}\right )-4 x^2 (1-(\log (2)-1) \log (2)) \log (256) \log (65536) \log (x)+100 x \left (1-\log ^3(2)+\log (4)\right ) \log (256) \log (65536)+100 (1-(\log (2)-1) \log (2)) \log (256) \log (65536)\right )}{\left (4-4 \log ^2(2)+\log (16)\right ) \log (256) \log (65536) (x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {x^2 \log (2) (1+\log (2))+x (4+\log (16))+4}{(x \log (2)+2)^2}+\frac {2 x \left (x^3 \log (2) \log (x)+9 x^3 \log (2)+2 x^2 \log (x)+18 x^2 \left (1+\frac {29 \log (2)}{18}\right )-4 x \log (x)+22 x \left (1+\frac {\log (32)}{2}\right )-10 \left (1+10 \log ^2(2)-(1+\log (4)) \log (32)\right )\right )}{(x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )}+\frac {4 \log (2) \left (9 x^2+x^2 \log (x)+30 x+25\right ) \left (x^4 (1-(\log (2)-1) \log (2)) \log (4) \log (256) \log (65536) \log (x)+18 x^4 \log (2) (1-(\log (2)-1) \log (2)) \log (256) \log (65536)+36 x^3 \left (1-\frac {1}{18} \log (2) \left (-47+29 \log ^2(2)-11 \log (2)\right )\right ) \log (256) \log (65536)+4 x^3 \left (1+\frac {1}{4} \left (-4 \log ^4(2)-\log ^2(4)+\log (2) \left (\log (16)-\log ^2(4)\right )+\log ^2(2) \left (-4+\log ^2(4)+\log (16)\right )+\log (16)\right )\right ) \log (256) \log (65536) \log (x)-60 x^2 \log ^2(2) \log (16) \log ^2(256) \left (1-\frac {\log (4) \log (2048) \left (1+\frac {\log (256) \left (1-\log ^2(2)+\frac {\left (\left (1-\log ^2(2)+\log (2)\right ) \log (8) \log ^2(16)+2 \left (2+3 \log ^4(2)-5 \log ^2(2)+\log (4)\right ) \log (256)\right ) \log (65536)}{\log ^2(256) \log (2048)}\right )}{\log (4) \log (16)}\right )}{3 \log ^2(2) \log (256)}\right )-4 x^2 (1-(\log (2)-1) \log (2)) \log (256) \log (65536) \log (x)+100 x \left (1-\log ^3(2)+\log (4)\right ) \log (256) \log (65536)+100 (1-(\log (2)-1) \log (2)) \log (256) \log (65536)\right )}{\left (4-4 \log ^2(2)+\log (16)\right ) \log (256) \log (65536) (x \log (2)+2)^2 \left (x^2 (-\log (2)) \log (x)+e^x x^2 \log (2)-9 x^2 \log (2)+2 e^x x-30 x \log (2)-25 \log (2)\right )^2}\right )dx\) |
Int[((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2] + (625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3 + (4*x^3 + x^4)*Log[2] + x^4*Log[2]^2) + E^x*(-10*x^2 + 22*x^3 + 18*x^4 + (-100*x - 170*x^2 - 96*x^3 - 18*x^4)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2] + (50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3 + 2*x^4 + (-4*x^3 - 2*x^4)*Log[2] - 2*x^4*Log[2]^2))*Log[x] + (x^4*Log[2] + x^4*Log[2]^2)*Log[x]^2)/((625 + 1500*x + 1350*x^2 + 540*x ^3 + 81*x^4)*Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3*Log[2] + x^4*Log[2]^2) + E^ x*((-100*x - 120*x^2 - 36*x^3)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[2] ^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3*Log[2] - 2*x^4*Lo g[2]^2))*Log[x] + x^4*Log[2]^2*Log[x]^2),x]
3.20.8.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 1.04 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.69
| method | result | size |
| risch | \(x +\frac {x}{\ln \left (2\right )}-\frac {2 x^{2} {\mathrm e}^{x}}{\ln \left (2\right ) \left (x^{2} \ln \left (2\right ) {\mathrm e}^{x}-x^{2} \ln \left (2\right ) \ln \left (x \right )-9 x^{2} \ln \left (2\right )-30 x \ln \left (2\right )+2 \,{\mathrm e}^{x} x -25 \ln \left (2\right )\right )}\) | \(61\) |
| parallelrisch | \(\frac {2 x^{3} \ln \left (2\right ) \ln \left (x \right )+50 x +50 x \ln \left (2\right )+60 x^{2} \ln \left (2\right )+18 x^{3} \ln \left (2\right )-4 \,{\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x^{3}-2 x^{3} \ln \left (2\right ) {\mathrm e}^{x}+18 x^{3}+60 x^{2}+2 x^{3} \ln \left (x \right )}{2 x^{2} \ln \left (2\right ) \ln \left (x \right )-2 x^{2} \ln \left (2\right ) {\mathrm e}^{x}+18 x^{2} \ln \left (2\right )+60 x \ln \left (2\right )-4 \,{\mathrm e}^{x} x +50 \ln \left (2\right )}\) | \(116\) |
int(((x^4*ln(2)^2+x^4*ln(2))*ln(x)^2+((-2*x^4*ln(2)^2+(-2*x^4-4*x^3)*ln(2) +2*x^4-4*x^3)*exp(x)+(18*x^4+60*x^3+50*x^2)*ln(2)^2+(18*x^4+60*x^3+50*x^2) *ln(2))*ln(x)+(x^4*ln(2)^2+(x^4+4*x^3)*ln(2)+4*x^3+4*x^2)*exp(x)^2+((-18*x ^4-60*x^3-50*x^2)*ln(2)^2+(-18*x^4-96*x^3-170*x^2-100*x)*ln(2)+18*x^4+22*x ^3-10*x^2)*exp(x)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*ln(2)^2+(81*x^4+540 *x^3+1350*x^2+1500*x+625)*ln(2))/(x^4*ln(2)^2*ln(x)^2+((-2*x^4*ln(2)^2-4*x ^3*ln(2))*exp(x)+(18*x^4+60*x^3+50*x^2)*ln(2)^2)*ln(x)+(x^4*ln(2)^2+4*x^3* ln(2)+4*x^2)*exp(x)^2+((-18*x^4-60*x^3-50*x^2)*ln(2)^2+(-36*x^3-120*x^2-10 0*x)*ln(2))*exp(x)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*ln(2)^2),x,method= _RETURNVERBOSE)
x+x/ln(2)-2/ln(2)*x^2*exp(x)/(x^2*ln(2)*exp(x)-x^2*ln(2)*ln(x)-9*x^2*ln(2) -30*x*ln(2)+2*exp(x)*x-25*ln(2))
Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (37) = 74\).
Time = 0.26 (sec) , antiderivative size = 102, normalized size of antiderivative = 2.83 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\frac {9 \, x^{3} + 30 \, x^{2} - {\left (x^{3} \log \left (2\right ) + x^{3} + 2 \, x^{2}\right )} e^{x} + {\left (9 \, x^{3} + 30 \, x^{2} + 25 \, x\right )} \log \left (2\right ) + {\left (x^{3} \log \left (2\right ) + x^{3}\right )} \log \left (x\right ) + 25 \, x}{x^{2} \log \left (2\right ) \log \left (x\right ) - {\left (x^{2} \log \left (2\right ) + 2 \, x\right )} e^{x} + {\left (9 \, x^{2} + 30 \, x + 25\right )} \log \left (2\right )} \]
integrate(((x^4*log(2)^2+x^4*log(2))*log(x)^2+((-2*x^4*log(2)^2+(-2*x^4-4* x^3)*log(2)+2*x^4-4*x^3)*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2+(18*x^4+60 *x^3+50*x^2)*log(2))*log(x)+(x^4*log(2)^2+(x^4+4*x^3)*log(2)+4*x^3+4*x^2)* exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-18*x^4-96*x^3-170*x^2-100*x)* log(2)+18*x^4+22*x^3-10*x^2)*exp(x)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*l og(2)^2+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2))/(x^4*log(2)^2*log(x)^ 2+((-2*x^4*log(2)^2-4*x^3*log(2))*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2)* log(x)+(x^4*log(2)^2+4*x^3*log(2)+4*x^2)*exp(x)^2+((-18*x^4-60*x^3-50*x^2) *log(2)^2+(-36*x^3-120*x^2-100*x)*log(2))*exp(x)+(81*x^4+540*x^3+1350*x^2+ 1500*x+625)*log(2)^2),x, algorithm=\
(9*x^3 + 30*x^2 - (x^3*log(2) + x^3 + 2*x^2)*e^x + (9*x^3 + 30*x^2 + 25*x) *log(2) + (x^3*log(2) + x^3)*log(x) + 25*x)/(x^2*log(2)*log(x) - (x^2*log( 2) + 2*x)*e^x + (9*x^2 + 30*x + 25)*log(2))
Leaf count of result is larger than twice the leaf count of optimal. 143 vs. \(2 (26) = 52\).
Time = 0.41 (sec) , antiderivative size = 143, normalized size of antiderivative = 3.97 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=x \left (1 + \frac {1}{\log {\left (2 \right )}}\right ) + \frac {- 2 x^{3} \log {\left (x \right )} - 18 x^{3} - 60 x^{2} - 50 x}{- x^{3} \log {\left (2 \right )}^{2} \log {\left (x \right )} - 9 x^{3} \log {\left (2 \right )}^{2} - 2 x^{2} \log {\left (2 \right )} \log {\left (x \right )} - 30 x^{2} \log {\left (2 \right )}^{2} - 18 x^{2} \log {\left (2 \right )} - 60 x \log {\left (2 \right )} - 25 x \log {\left (2 \right )}^{2} + \left (x^{3} \log {\left (2 \right )}^{2} + 4 x^{2} \log {\left (2 \right )} + 4 x\right ) e^{x} - 50 \log {\left (2 \right )}} + \frac {4}{x \log {\left (2 \right )}^{3} + 2 \log {\left (2 \right )}^{2}} \]
integrate(((x**4*ln(2)**2+x**4*ln(2))*ln(x)**2+((-2*x**4*ln(2)**2+(-2*x**4 -4*x**3)*ln(2)+2*x**4-4*x**3)*exp(x)+(18*x**4+60*x**3+50*x**2)*ln(2)**2+(1 8*x**4+60*x**3+50*x**2)*ln(2))*ln(x)+(x**4*ln(2)**2+(x**4+4*x**3)*ln(2)+4* x**3+4*x**2)*exp(x)**2+((-18*x**4-60*x**3-50*x**2)*ln(2)**2+(-18*x**4-96*x **3-170*x**2-100*x)*ln(2)+18*x**4+22*x**3-10*x**2)*exp(x)+(81*x**4+540*x** 3+1350*x**2+1500*x+625)*ln(2)**2+(81*x**4+540*x**3+1350*x**2+1500*x+625)*l n(2))/(x**4*ln(2)**2*ln(x)**2+((-2*x**4*ln(2)**2-4*x**3*ln(2))*exp(x)+(18* x**4+60*x**3+50*x**2)*ln(2)**2)*ln(x)+(x**4*ln(2)**2+4*x**3*ln(2)+4*x**2)* exp(x)**2+((-18*x**4-60*x**3-50*x**2)*ln(2)**2+(-36*x**3-120*x**2-100*x)*l n(2))*exp(x)+(81*x**4+540*x**3+1350*x**2+1500*x+625)*ln(2)**2),x)
x*(1 + 1/log(2)) + (-2*x**3*log(x) - 18*x**3 - 60*x**2 - 50*x)/(-x**3*log( 2)**2*log(x) - 9*x**3*log(2)**2 - 2*x**2*log(2)*log(x) - 30*x**2*log(2)**2 - 18*x**2*log(2) - 60*x*log(2) - 25*x*log(2)**2 + (x**3*log(2)**2 + 4*x** 2*log(2) + 4*x)*exp(x) - 50*log(2)) + 4/(x*log(2)**3 + 2*log(2)**2)
Leaf count of result is larger than twice the leaf count of optimal. 174 vs. \(2 (37) = 74\).
Time = 0.41 (sec) , antiderivative size = 174, normalized size of antiderivative = 4.83 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\frac {9 \, {\left (\log \left (2\right )^{3} + \log \left (2\right )^{2}\right )} x^{3} + 6 \, {\left (5 \, \log \left (2\right )^{3} + 5 \, \log \left (2\right )^{2} + 3 \, \log \left (2\right )\right )} x^{2} + 5 \, {\left (5 \, \log \left (2\right )^{3} + 5 \, \log \left (2\right )^{2} + 12 \, \log \left (2\right )\right )} x - {\left ({\left (\log \left (2\right )^{3} + \log \left (2\right )^{2}\right )} x^{3} + 2 \, {\left (\log \left (2\right )^{2} + \log \left (2\right )\right )} x^{2} + 4 \, x\right )} e^{x} + {\left ({\left (\log \left (2\right )^{3} + \log \left (2\right )^{2}\right )} x^{3} + 2 \, x^{2} \log \left (2\right )\right )} \log \left (x\right ) + 50 \, \log \left (2\right )}{x^{2} \log \left (2\right )^{3} \log \left (x\right ) + 9 \, x^{2} \log \left (2\right )^{3} + 30 \, x \log \left (2\right )^{3} + 25 \, \log \left (2\right )^{3} - {\left (x^{2} \log \left (2\right )^{3} + 2 \, x \log \left (2\right )^{2}\right )} e^{x}} \]
integrate(((x^4*log(2)^2+x^4*log(2))*log(x)^2+((-2*x^4*log(2)^2+(-2*x^4-4* x^3)*log(2)+2*x^4-4*x^3)*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2+(18*x^4+60 *x^3+50*x^2)*log(2))*log(x)+(x^4*log(2)^2+(x^4+4*x^3)*log(2)+4*x^3+4*x^2)* exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-18*x^4-96*x^3-170*x^2-100*x)* log(2)+18*x^4+22*x^3-10*x^2)*exp(x)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*l og(2)^2+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2))/(x^4*log(2)^2*log(x)^ 2+((-2*x^4*log(2)^2-4*x^3*log(2))*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2)* log(x)+(x^4*log(2)^2+4*x^3*log(2)+4*x^2)*exp(x)^2+((-18*x^4-60*x^3-50*x^2) *log(2)^2+(-36*x^3-120*x^2-100*x)*log(2))*exp(x)+(81*x^4+540*x^3+1350*x^2+ 1500*x+625)*log(2)^2),x, algorithm=\
(9*(log(2)^3 + log(2)^2)*x^3 + 6*(5*log(2)^3 + 5*log(2)^2 + 3*log(2))*x^2 + 5*(5*log(2)^3 + 5*log(2)^2 + 12*log(2))*x - ((log(2)^3 + log(2)^2)*x^3 + 2*(log(2)^2 + log(2))*x^2 + 4*x)*e^x + ((log(2)^3 + log(2)^2)*x^3 + 2*x^2 *log(2))*log(x) + 50*log(2))/(x^2*log(2)^3*log(x) + 9*x^2*log(2)^3 + 30*x* log(2)^3 + 25*log(2)^3 - (x^2*log(2)^3 + 2*x*log(2)^2)*e^x)
Leaf count of result is larger than twice the leaf count of optimal. 198 vs. \(2 (37) = 74\).
Time = 0.65 (sec) , antiderivative size = 198, normalized size of antiderivative = 5.50 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\frac {x^{3} e^{x} \log \left (2\right )^{2} - x^{3} \log \left (2\right )^{2} \log \left (x\right ) + x^{3} e^{x} \log \left (2\right ) - 9 \, x^{3} \log \left (2\right )^{2} + x^{2} e^{x} \log \left (2\right )^{2} - x^{3} \log \left (2\right ) \log \left (x\right ) - x^{2} \log \left (2\right )^{2} \log \left (x\right ) - 9 \, x^{3} \log \left (2\right ) + 3 \, x^{2} e^{x} \log \left (2\right ) - 39 \, x^{2} \log \left (2\right )^{2} - x^{2} \log \left (2\right ) \log \left (x\right ) - 39 \, x^{2} \log \left (2\right ) + 2 \, x e^{x} \log \left (2\right ) - 55 \, x \log \left (2\right )^{2} + 2 \, x e^{x} - 55 \, x \log \left (2\right ) - 25 \, \log \left (2\right )^{2} - 25 \, \log \left (2\right )}{x^{2} e^{x} \log \left (2\right )^{2} - x^{2} \log \left (2\right )^{2} \log \left (x\right ) - 9 \, x^{2} \log \left (2\right )^{2} + 2 \, x e^{x} \log \left (2\right ) - 30 \, x \log \left (2\right )^{2} - 25 \, \log \left (2\right )^{2}} \]
integrate(((x^4*log(2)^2+x^4*log(2))*log(x)^2+((-2*x^4*log(2)^2+(-2*x^4-4* x^3)*log(2)+2*x^4-4*x^3)*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2+(18*x^4+60 *x^3+50*x^2)*log(2))*log(x)+(x^4*log(2)^2+(x^4+4*x^3)*log(2)+4*x^3+4*x^2)* exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-18*x^4-96*x^3-170*x^2-100*x)* log(2)+18*x^4+22*x^3-10*x^2)*exp(x)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*l og(2)^2+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2))/(x^4*log(2)^2*log(x)^ 2+((-2*x^4*log(2)^2-4*x^3*log(2))*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2)* log(x)+(x^4*log(2)^2+4*x^3*log(2)+4*x^2)*exp(x)^2+((-18*x^4-60*x^3-50*x^2) *log(2)^2+(-36*x^3-120*x^2-100*x)*log(2))*exp(x)+(81*x^4+540*x^3+1350*x^2+ 1500*x+625)*log(2)^2),x, algorithm=\
(x^3*e^x*log(2)^2 - x^3*log(2)^2*log(x) + x^3*e^x*log(2) - 9*x^3*log(2)^2 + x^2*e^x*log(2)^2 - x^3*log(2)*log(x) - x^2*log(2)^2*log(x) - 9*x^3*log(2 ) + 3*x^2*e^x*log(2) - 39*x^2*log(2)^2 - x^2*log(2)*log(x) - 39*x^2*log(2) + 2*x*e^x*log(2) - 55*x*log(2)^2 + 2*x*e^x - 55*x*log(2) - 25*log(2)^2 - 25*log(2))/(x^2*e^x*log(2)^2 - x^2*log(2)^2*log(x) - 9*x^2*log(2)^2 + 2*x* e^x*log(2) - 30*x*log(2)^2 - 25*log(2)^2)
Timed out. \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\int \frac {\left (x^4\,{\ln \left (2\right )}^2+x^4\,\ln \left (2\right )\right )\,{\ln \left (x\right )}^2+\left ({\ln \left (2\right )}^2\,\left (18\,x^4+60\,x^3+50\,x^2\right )-{\mathrm {e}}^x\,\left (2\,x^4\,{\ln \left (2\right )}^2+\ln \left (2\right )\,\left (2\,x^4+4\,x^3\right )+4\,x^3-2\,x^4\right )+\ln \left (2\right )\,\left (18\,x^4+60\,x^3+50\,x^2\right )\right )\,\ln \left (x\right )+{\ln \left (2\right )}^2\,\left (81\,x^4+540\,x^3+1350\,x^2+1500\,x+625\right )-{\mathrm {e}}^x\,\left ({\ln \left (2\right )}^2\,\left (18\,x^4+60\,x^3+50\,x^2\right )+\ln \left (2\right )\,\left (18\,x^4+96\,x^3+170\,x^2+100\,x\right )+10\,x^2-22\,x^3-18\,x^4\right )+{\mathrm {e}}^{2\,x}\,\left (x^4\,{\ln \left (2\right )}^2+\ln \left (2\right )\,\left (x^4+4\,x^3\right )+4\,x^2+4\,x^3\right )+\ln \left (2\right )\,\left (81\,x^4+540\,x^3+1350\,x^2+1500\,x+625\right )}{{\ln \left (2\right )}^2\,\left (81\,x^4+540\,x^3+1350\,x^2+1500\,x+625\right )+\ln \left (x\right )\,\left ({\ln \left (2\right )}^2\,\left (18\,x^4+60\,x^3+50\,x^2\right )-{\mathrm {e}}^x\,\left (2\,{\ln \left (2\right )}^2\,x^4+4\,\ln \left (2\right )\,x^3\right )\right )-{\mathrm {e}}^x\,\left ({\ln \left (2\right )}^2\,\left (18\,x^4+60\,x^3+50\,x^2\right )+\ln \left (2\right )\,\left (36\,x^3+120\,x^2+100\,x\right )\right )+{\mathrm {e}}^{2\,x}\,\left ({\ln \left (2\right )}^2\,x^4+4\,\ln \left (2\right )\,x^3+4\,x^2\right )+x^4\,{\ln \left (2\right )}^2\,{\ln \left (x\right )}^2} \,d x \]
int((log(2)^2*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 625) - exp(x)*(log(2 )^2*(50*x^2 + 60*x^3 + 18*x^4) + log(2)*(100*x + 170*x^2 + 96*x^3 + 18*x^4 ) + 10*x^2 - 22*x^3 - 18*x^4) + log(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4 ) - exp(x)*(2*x^4*log(2)^2 + log(2)*(4*x^3 + 2*x^4) + 4*x^3 - 2*x^4) + log (2)*(50*x^2 + 60*x^3 + 18*x^4)) + exp(2*x)*(x^4*log(2)^2 + log(2)*(4*x^3 + x^4) + 4*x^2 + 4*x^3) + log(2)*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 62 5) + log(x)^2*(x^4*log(2)^2 + x^4*log(2)))/(log(2)^2*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 625) + log(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4) - ex p(x)*(2*x^4*log(2)^2 + 4*x^3*log(2))) - exp(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4) + log(2)*(100*x + 120*x^2 + 36*x^3)) + exp(2*x)*(x^4*log(2)^2 + 4*x^3*log(2) + 4*x^2) + x^4*log(2)^2*log(x)^2),x)
int((log(2)^2*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 625) - exp(x)*(log(2 )^2*(50*x^2 + 60*x^3 + 18*x^4) + log(2)*(100*x + 170*x^2 + 96*x^3 + 18*x^4 ) + 10*x^2 - 22*x^3 - 18*x^4) + log(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4 ) - exp(x)*(2*x^4*log(2)^2 + log(2)*(4*x^3 + 2*x^4) + 4*x^3 - 2*x^4) + log (2)*(50*x^2 + 60*x^3 + 18*x^4)) + exp(2*x)*(x^4*log(2)^2 + log(2)*(4*x^3 + x^4) + 4*x^2 + 4*x^3) + log(2)*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 62 5) + log(x)^2*(x^4*log(2)^2 + x^4*log(2)))/(log(2)^2*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 625) + log(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4) - ex p(x)*(2*x^4*log(2)^2 + 4*x^3*log(2))) - exp(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4) + log(2)*(100*x + 120*x^2 + 36*x^3)) + exp(2*x)*(x^4*log(2)^2 + 4*x^3*log(2) + 4*x^2) + x^4*log(2)^2*log(x)^2), x)