Integrand size = 496, antiderivative size = 35 \[ \int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx=\left (x+\log ^2(4)\right )^2 \left (-e^x-x+\log \left (2 e^{-\frac {5}{(-6+x) x}}\right )\right )^2 \] Output:
(ln(2/exp(5/x/(-6+x)))-exp(x)-x)^2*(4*ln(2)^2+x)^2
Leaf count is larger than twice the leaf count of optimal. \(376\) vs. \(2(35)=70\).
Time = 0.34 (sec) , antiderivative size = 376, normalized size of antiderivative = 10.74 \[ \int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx=\frac {-300 x+x^8-25 \log ^4(4)+2 x^7 \left (-6+e^x+\log ^2(4)\right )+x^2 \left (-2110-720 \log ^2(4)+36 e^{2 x} \log ^4(4)\right )+x^6 \left (36+e^{2 x}-24 \log ^2(4)+\log ^4(4)+4 e^x \left (-6+\log ^2(4)\right )\right )-12 x^3 \left (-6 e^x \log ^4(4)+e^{2 x} \log ^2(4) \left (-6+\log ^2(4)\right )-20 \left (3+\log ^2(4)\right )\right )+2 x^5 \left (e^{2 x} \left (-6+\log ^2(4)\right )-6 \log ^2(4) \left (-6+\log ^2(4)\right )+e^x \left (36-24 \log ^2(4)+\log ^4(4)\right )\right )+x^4 \left (-24 e^x \log ^2(4) \left (-6+\log ^2(4)\right )+e^{2 x} \left (36-24 \log ^2(4)+\log ^4(4)\right )+4 \left (-15-5 \log ^2(4)+9 \log ^4(4)\right )\right )-2 (-6+x) x \left (x^5+5 \log ^4(4)+x^4 \left (-6+e^x+2 \log ^2(4)\right )-6 x \left (-5+e^x \log ^4(4)\right )+x^2 \left (-5-6 \log ^4(4)+e^x \log ^2(4) \left (-12+\log ^2(4)\right )\right )+x^3 \left (\log ^2(4) \left (-12+\log ^2(4)\right )+2 e^x \left (-3+\log ^2(4)\right )\right )\right ) \log \left (2 e^{-\frac {5}{(-6+x) x}}\right )+(-6+x)^2 x^3 \left (x+2 \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(-6+x) x}}\right )}{(-6+x)^2 x^2} \] Input:
Integrate[(60*x^3 - 20*x^4 + 144*x^5 - 48*x^6 + 4*x^7 + (120*x^2 - 40*x^3 + 216*x^4 - 72*x^5 + 6*x^6)*Log[4]^2 + (60*x - 20*x^2 + 72*x^3 - 24*x^4 + 2*x^5)*Log[4]^4 + E^(2*x)*(72*x^3 + 48*x^4 - 22*x^5 + 2*x^6 + (72*x^2 + 12 0*x^3 - 46*x^4 + 4*x^5)*Log[4]^2 + (72*x^2 - 24*x^3 + 2*x^4)*Log[4]^4) + E ^x*(60*x^2 - 20*x^3 + 216*x^4 - 18*x^6 + 2*x^7 + (120*x - 40*x^2 + 288*x^3 + 48*x^4 - 40*x^5 + 4*x^6)*Log[4]^2 + (60 - 20*x + 72*x^2 + 48*x^3 - 22*x ^4 + 2*x^5)*Log[4]^4) + (-60*x^2 + 20*x^3 - 216*x^4 + 72*x^5 - 6*x^6 + (-1 20*x + 40*x^2 - 288*x^3 + 96*x^4 - 8*x^5)*Log[4]^2 + (-60 + 20*x - 72*x^2 + 24*x^3 - 2*x^4)*Log[4]^4 + E^x*(-144*x^3 - 24*x^4 + 20*x^5 - 2*x^6 + (-1 44*x^2 - 96*x^3 + 44*x^4 - 4*x^5)*Log[4]^2 + (-72*x^2 + 24*x^3 - 2*x^4)*Lo g[4]^4))*Log[2/E^(5/(-6*x + x^2))] + (72*x^3 - 24*x^4 + 2*x^5 + (72*x^2 - 24*x^3 + 2*x^4)*Log[4]^2)*Log[2/E^(5/(-6*x + x^2))]^2)/(36*x^2 - 12*x^3 + x^4),x]
Output:
(-300*x + x^8 - 25*Log[4]^4 + 2*x^7*(-6 + E^x + Log[4]^2) + x^2*(-2110 - 7 20*Log[4]^2 + 36*E^(2*x)*Log[4]^4) + x^6*(36 + E^(2*x) - 24*Log[4]^2 + Log [4]^4 + 4*E^x*(-6 + Log[4]^2)) - 12*x^3*(-6*E^x*Log[4]^4 + E^(2*x)*Log[4]^ 2*(-6 + Log[4]^2) - 20*(3 + Log[4]^2)) + 2*x^5*(E^(2*x)*(-6 + Log[4]^2) - 6*Log[4]^2*(-6 + Log[4]^2) + E^x*(36 - 24*Log[4]^2 + Log[4]^4)) + x^4*(-24 *E^x*Log[4]^2*(-6 + Log[4]^2) + E^(2*x)*(36 - 24*Log[4]^2 + Log[4]^4) + 4* (-15 - 5*Log[4]^2 + 9*Log[4]^4)) - 2*(-6 + x)*x*(x^5 + 5*Log[4]^4 + x^4*(- 6 + E^x + 2*Log[4]^2) - 6*x*(-5 + E^x*Log[4]^4) + x^2*(-5 - 6*Log[4]^4 + E ^x*Log[4]^2*(-12 + Log[4]^2)) + x^3*(Log[4]^2*(-12 + Log[4]^2) + 2*E^x*(-3 + Log[4]^2)))*Log[2/E^(5/((-6 + x)*x))] + (-6 + x)^2*x^3*(x + 2*Log[4]^2) *Log[2/E^(5/((-6 + x)*x))]^2)/((-6 + x)^2*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.
| \(\displaystyle \int \frac {4 x^7-48 x^6+144 x^5-20 x^4+60 x^3+\left (2 x^5-24 x^4+72 x^3-20 x^2+60 x\right ) \log ^4(4)+\left (2 x^5-24 x^4+72 x^3+\left (2 x^4-24 x^3+72 x^2\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{x^2-6 x}}\right )+\left (6 x^6-72 x^5+216 x^4-40 x^3+120 x^2\right ) \log ^2(4)+e^{2 x} \left (2 x^6-22 x^5+48 x^4+72 x^3+\left (2 x^4-24 x^3+72 x^2\right ) \log ^4(4)+\left (4 x^5-46 x^4+120 x^3+72 x^2\right ) \log ^2(4)\right )+\left (-6 x^6+72 x^5-216 x^4+20 x^3-60 x^2+\left (-2 x^4+24 x^3-72 x^2+20 x-60\right ) \log ^4(4)+\left (-8 x^5+96 x^4-288 x^3+40 x^2-120 x\right ) \log ^2(4)+e^x \left (-2 x^6+20 x^5-24 x^4-144 x^3+\left (-2 x^4+24 x^3-72 x^2\right ) \log ^4(4)+\left (-4 x^5+44 x^4-96 x^3-144 x^2\right ) \log ^2(4)\right )\right ) \log \left (2 e^{-\frac {5}{x^2-6 x}}\right )+e^x \left (2 x^7-18 x^6+216 x^4-20 x^3+60 x^2+\left (2 x^5-22 x^4+48 x^3+72 x^2-20 x+60\right ) \log ^4(4)+\left (4 x^6-40 x^5+48 x^4+288 x^3-40 x^2+120 x\right ) \log ^2(4)\right )}{x^4-12 x^3+36 x^2} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {4 x^7-48 x^6+144 x^5-20 x^4+60 x^3+\left (2 x^5-24 x^4+72 x^3-20 x^2+60 x\right ) \log ^4(4)+\left (2 x^5-24 x^4+72 x^3+\left (2 x^4-24 x^3+72 x^2\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{x^2-6 x}}\right )+\left (6 x^6-72 x^5+216 x^4-40 x^3+120 x^2\right ) \log ^2(4)+e^{2 x} \left (2 x^6-22 x^5+48 x^4+72 x^3+\left (2 x^4-24 x^3+72 x^2\right ) \log ^4(4)+\left (4 x^5-46 x^4+120 x^3+72 x^2\right ) \log ^2(4)\right )+\left (-6 x^6+72 x^5-216 x^4+20 x^3-60 x^2+\left (-2 x^4+24 x^3-72 x^2+20 x-60\right ) \log ^4(4)+\left (-8 x^5+96 x^4-288 x^3+40 x^2-120 x\right ) \log ^2(4)+e^x \left (-2 x^6+20 x^5-24 x^4-144 x^3+\left (-2 x^4+24 x^3-72 x^2\right ) \log ^4(4)+\left (-4 x^5+44 x^4-96 x^3-144 x^2\right ) \log ^2(4)\right )\right ) \log \left (2 e^{-\frac {5}{x^2-6 x}}\right )+e^x \left (2 x^7-18 x^6+216 x^4-20 x^3+60 x^2+\left (2 x^5-22 x^4+48 x^3+72 x^2-20 x+60\right ) \log ^4(4)+\left (4 x^6-40 x^5+48 x^4+288 x^3-40 x^2+120 x\right ) \log ^2(4)\right )}{x^2 \left (x^2-12 x+36\right )}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (e^x+2\right ) x^5+x^4 \left (e^x \left (\log ^2(4)-11\right )-24+\log ^2(4)\right )-12 x^3 \left (e^x \left (\log ^2(4)-2\right )-6+\log ^2(4)\right )+2 x^2 \left (18 e^x \left (1+\log ^2(4)\right )-5+18 \log ^2(4)\right )-(x-6)^2 x^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right )-10 x \left (\log ^2(4)-3\right )+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{\frac {5}{(6-x) x}}\right )\right ) \left (\left (2+e^x\right ) x^5-\left (24-\log ^2(4)+e^x \left (11-\log ^2(4)\right )\right ) x^4+12 \left (6-\log ^2(4)+e^x \left (2-\log ^2(4)\right )\right ) x^3-2 \left (5-18 \log ^2(4)-18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(6-x)^2 \log \left (2 e^{\frac {5}{(6-x) x}}\right ) x^2+10 \left (3-\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (x+\log ^2(4)\right ) \left (x+e^x-\log \left (2 e^{-\frac {5}{(x-6) x}}\right )\right ) \left (\left (2+e^x\right ) x^5+\left (-24+\log ^2(4)+e^x \left (-11+\log ^2(4)\right )\right ) x^4-12 \left (-6+\log ^2(4)+e^x \left (-2+\log ^2(4)\right )\right ) x^3+2 \left (-5+18 \log ^2(4)+18 e^x \left (1+\log ^2(4)\right )\right ) x^2-(x-6)^2 \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (-3+\log ^2(4)\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x+\log ^2(4)\right ) x^4}{(x-6)^2}-\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) x^3}{(x-6)^2}-\frac {2 \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3}{(x-6)^2}+\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) x^2}{(x-6)^2}+\frac {24 \left (1-\frac {\log ^2(4)}{24}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2}{(x-6)^2}-\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) x}{(x-6)^2}-\frac {72 \left (1-\frac {\log ^2(4)}{6}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x}{(x-6)^2}-\left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x+\left (x+\log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{(x-6) x}}\right )-\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right )}{(x-6)^2}+e^{2 x} \left (x^2+\left (1+2 \log ^2(4)\right ) x+\log ^2(4) \left (1+\log ^2(4)\right )\right )+\frac {10 \left (1-\frac {18 \log ^2(4)}{5}\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2}+\frac {30 \log ^2(4) \left (x+\log ^2(4)\right )}{(x-6)^2 x}+\frac {10 \left (-3+\log ^2(4)\right ) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x}-\frac {30 \log ^2(4) \left (x+\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right )}{(x-6)^2 x^2}+\frac {e^x \left (x+\log ^2(4)\right ) \left (x^6-\log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^5-9 \left (1-\frac {\log ^2(4)}{9}\right ) x^5+10 \left (1-\frac {\log ^2(4)}{10}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^4-11 \log ^2(4) x^4-12 \left (1-\log ^2(4)\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^3+108 \left (1+\frac {2 \log ^2(4)}{9}\right ) x^3-72 \left (1+\frac {\log ^2(4)}{2}\right ) \log \left (2 e^{-\frac {5}{(x-6) x}}\right ) x^2-10 \left (1-\frac {18 \log ^2(4)}{5}\right ) x^2+30 \left (1-\frac {\log ^2(4)}{3}\right ) x+30 \log ^2(4)\right )}{(6-x)^2 x^2}\right )dx\) |
Input:
Int[(60*x^3 - 20*x^4 + 144*x^5 - 48*x^6 + 4*x^7 + (120*x^2 - 40*x^3 + 216* x^4 - 72*x^5 + 6*x^6)*Log[4]^2 + (60*x - 20*x^2 + 72*x^3 - 24*x^4 + 2*x^5) *Log[4]^4 + E^(2*x)*(72*x^3 + 48*x^4 - 22*x^5 + 2*x^6 + (72*x^2 + 120*x^3 - 46*x^4 + 4*x^5)*Log[4]^2 + (72*x^2 - 24*x^3 + 2*x^4)*Log[4]^4) + E^x*(60 *x^2 - 20*x^3 + 216*x^4 - 18*x^6 + 2*x^7 + (120*x - 40*x^2 + 288*x^3 + 48* x^4 - 40*x^5 + 4*x^6)*Log[4]^2 + (60 - 20*x + 72*x^2 + 48*x^3 - 22*x^4 + 2 *x^5)*Log[4]^4) + (-60*x^2 + 20*x^3 - 216*x^4 + 72*x^5 - 6*x^6 + (-120*x + 40*x^2 - 288*x^3 + 96*x^4 - 8*x^5)*Log[4]^2 + (-60 + 20*x - 72*x^2 + 24*x ^3 - 2*x^4)*Log[4]^4 + E^x*(-144*x^3 - 24*x^4 + 20*x^5 - 2*x^6 + (-144*x^2 - 96*x^3 + 44*x^4 - 4*x^5)*Log[4]^2 + (-72*x^2 + 24*x^3 - 2*x^4)*Log[4]^4 ))*Log[2/E^(5/(-6*x + x^2))] + (72*x^3 - 24*x^4 + 2*x^5 + (72*x^2 - 24*x^3 + 2*x^4)*Log[4]^2)*Log[2/E^(5/(-6*x + x^2))]^2)/(36*x^2 - 12*x^3 + x^4),x ]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(674\) vs. \(2(37)=74\).
Time = 103.62 (sec) , antiderivative size = 675, normalized size of antiderivative = 19.29
| method | result | size |
| risch | \(\left (8 x \ln \left (2\right )^{2}+x^{2}\right ) \ln \left ({\mathrm e}^{\frac {5}{x \left (-6+x \right )}}\right )^{2}+\frac {\left (96 x^{2} \ln \left (2\right )^{3}+32 x^{3} \ln \left (2\right )^{4}-192 x^{2} \ln \left (2\right )^{4}-96 x^{3} \ln \left (2\right )^{2}+12 x^{3} \ln \left (2\right )-2 x^{4} \ln \left (2\right )+2 \,{\mathrm e}^{x} x^{4}-12 \,{\mathrm e}^{x} x^{3}+16 x^{4} \ln \left (2\right )^{2}+160 \ln \left (2\right )^{4}-12 x^{4}+2 x^{5}+16 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{3}-96 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}-192 \ln \left (2\right )^{4} {\mathrm e}^{x} x +32 \ln \left (2\right )^{4} {\mathrm e}^{x} x^{2}-16 x^{3} \ln \left (2\right )^{3}\right ) \ln \left ({\mathrm e}^{\frac {5}{x \left (-6+x \right )}}\right )}{x \left (-6+x \right )}+\frac {-8 \,{\mathrm e}^{x} \ln \left (2\right ) x^{6}+96 \,{\mathrm e}^{x} \ln \left (2\right ) x^{5}+8 x^{7} {\mathrm e}^{x}+96 x^{6} \ln \left (2\right )+64 x^{6} \ln \left (2\right )^{4}-736 x^{5} \ln \left (2\right )^{4}+1152 x^{3} \ln \left (2\right )^{4}-288 x^{5} \ln \left (2\right )+1536 \ln \left (2\right )^{5} x^{4}+144 \,{\mathrm e}^{2 x} x^{4}+1104 x^{5} \ln \left (2\right )^{2}-2304 x^{4} \ln \left (2\right )^{3}-8 x^{7} \ln \left (2\right )-96 x^{6} {\mathrm e}^{x}+768 \ln \left (2\right )^{3} x^{5}-4608 \ln \left (2\right )^{5} x^{3}+3840 \ln \left (2\right )^{5} x +144 x^{4} \ln \left (2\right )^{2}-1600 \ln \left (2\right )^{4}+4 x^{8}+288 x^{5} {\mathrm e}^{x}+144 x^{6}-48 x^{7}-768 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{5}+2304 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{4}-288 \ln \left (2\right ) {\mathrm e}^{x} x^{4}-128 \ln \left (2\right )^{5} x^{5}+4608 \ln \left (2\right )^{4} {\mathrm e}^{x} x^{3}-1536 \ln \left (2\right )^{4} {\mathrm e}^{x} x^{4}-64 \ln \left (2\right )^{3} x^{6}+32 \ln \left (2\right )^{2} x^{7}-768 \ln \left (2\right )^{4} {\mathrm e}^{2 x} x^{3}-380 \ln \left (2\right )^{2} x^{6}+1920 x^{4} \ln \left (2\right )^{4}-2304 \ln \left (2\right )^{3} {\mathrm e}^{x} x^{3}-384 \,{\mathrm e}^{2 x} \ln \left (2\right )^{2} x^{4}-64 \ln \left (2\right )^{3} {\mathrm e}^{x} x^{5}+768 \ln \left (2\right )^{3} {\mathrm e}^{x} x^{4}+4 x^{6} {\mathrm e}^{2 x}-48 x^{5} {\mathrm e}^{2 x}+1152 \ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{3}-640 x^{2} \ln \left (2\right )^{5}+1536 \ln \left (2\right )^{5} x^{3} {\mathrm e}^{x}-4608 \ln \left (2\right )^{5} x^{2} {\mathrm e}^{x}+2304 \ln \left (2\right )^{4} {\mathrm e}^{2 x} x^{2}+32 \,{\mathrm e}^{2 x} \ln \left (2\right )^{2} x^{5}+64 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{6}+64 \ln \left (2\right )^{4} {\mathrm e}^{2 x} x^{4}-128 \ln \left (2\right )^{5} {\mathrm e}^{x} x^{4}+128 \ln \left (2\right )^{4} {\mathrm e}^{x} x^{5}}{4 x^{2} \left (x^{2}-12 x +36\right )}\) | \(675\) |
| default | \(\text {Expression too large to display}\) | \(751\) |
| parts | \(\text {Expression too large to display}\) | \(751\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(1686\) |
Input:
int(((4*(2*x^4-24*x^3+72*x^2)*ln(2)^2+2*x^5-24*x^4+72*x^3)*ln(2/exp(5/(x^2 -6*x)))^2+((16*(-2*x^4+24*x^3-72*x^2)*ln(2)^4+4*(-4*x^5+44*x^4-96*x^3-144* x^2)*ln(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24*x^3-72*x^2+ 20*x-60)*ln(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*ln(2)^2-6*x^6+72*x ^5-216*x^4+20*x^3-60*x^2)*ln(2/exp(5/(x^2-6*x)))+(16*(2*x^4-24*x^3+72*x^2) *ln(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*ln(2)^2+2*x^6-22*x^5+48*x^4+72*x^ 3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*ln(2)^4+4*(4*x^6-40*x ^5+48*x^4+288*x^3-40*x^2+120*x)*ln(2)^2+2*x^7-18*x^6+216*x^4-20*x^3+60*x^2 )*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*ln(2)^4+4*(6*x^6-72*x^5+216* x^4-40*x^3+120*x^2)*ln(2)^2+4*x^7-48*x^6+144*x^5-20*x^4+60*x^3)/(x^4-12*x^ 3+36*x^2),x,method=_RETURNVERBOSE)
Output:
(8*x*ln(2)^2+x^2)*ln(exp(5/x/(-6+x)))^2+(96*x^2*ln(2)^3+32*x^3*ln(2)^4-192 *x^2*ln(2)^4-96*x^3*ln(2)^2+12*x^3*ln(2)-2*x^4*ln(2)+2*exp(x)*x^4-12*exp(x )*x^3+16*x^4*ln(2)^2+160*ln(2)^4-12*x^4+2*x^5+16*ln(2)^2*exp(x)*x^3-96*ln( 2)^2*exp(x)*x^2-192*ln(2)^4*exp(x)*x+32*ln(2)^4*exp(x)*x^2-16*x^3*ln(2)^3) /x/(-6+x)*ln(exp(5/x/(-6+x)))+1/4*(-8*exp(x)*ln(2)*x^6+96*exp(x)*ln(2)*x^5 +8*x^7*exp(x)+96*x^6*ln(2)+64*x^6*ln(2)^4-736*x^5*ln(2)^4+1152*x^3*ln(2)^4 -288*x^5*ln(2)+1536*ln(2)^5*x^4+144*exp(2*x)*x^4+1104*x^5*ln(2)^2-2304*x^4 *ln(2)^3-8*x^7*ln(2)-96*x^6*exp(x)+768*ln(2)^3*x^5-4608*ln(2)^5*x^3+3840*l n(2)^5*x+144*x^4*ln(2)^2-1600*ln(2)^4+4*x^8+288*x^5*exp(x)+144*x^6-48*x^7- 768*ln(2)^2*exp(x)*x^5+2304*ln(2)^2*exp(x)*x^4-288*ln(2)*exp(x)*x^4-128*ln (2)^5*x^5+4608*ln(2)^4*exp(x)*x^3-1536*ln(2)^4*exp(x)*x^4-64*ln(2)^3*x^6+3 2*ln(2)^2*x^7-768*ln(2)^4*exp(2*x)*x^3-380*ln(2)^2*x^6+1920*x^4*ln(2)^4-23 04*ln(2)^3*exp(x)*x^3-384*exp(2*x)*ln(2)^2*x^4-64*ln(2)^3*exp(x)*x^5+768*l n(2)^3*exp(x)*x^4+4*x^6*exp(2*x)-48*x^5*exp(2*x)+1152*ln(2)^2*exp(2*x)*x^3 -640*x^2*ln(2)^5+1536*ln(2)^5*x^3*exp(x)-4608*ln(2)^5*x^2*exp(x)+2304*ln(2 )^4*exp(2*x)*x^2+32*exp(2*x)*ln(2)^2*x^5+64*ln(2)^2*exp(x)*x^6+64*ln(2)^4* exp(2*x)*x^4-128*ln(2)^5*exp(x)*x^4+128*ln(2)^4*exp(x)*x^5)/x^2/(x^2-12*x+ 36)
Leaf count of result is larger than twice the leaf count of optimal. 412 vs. \(2 (33) = 66\).
Time = 0.12 (sec) , antiderivative size = 412, normalized size of antiderivative = 11.77 \[ \int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx=\frac {x^{8} - 12 \, x^{7} + 36 \, x^{6} - 32 \, {\left (x^{5} - 12 \, x^{4} + 36 \, x^{3} + 5 \, x^{2} - 30 \, x\right )} \log \left (2\right )^{5} + 10 \, x^{5} + 8 \, {\left (2 \, x^{6} - 23 \, x^{5} + 60 \, x^{4} + 56 \, x^{3} - 120 \, x^{2} + 50\right )} \log \left (2\right )^{4} - 120 \, x^{4} - 16 \, {\left (x^{6} - 12 \, x^{5} + 36 \, x^{4} + 5 \, x^{3} - 30 \, x^{2}\right )} \log \left (2\right )^{3} + 720 \, x^{3} + {\left (8 \, x^{7} - 95 \, x^{6} + 276 \, x^{5} + 36 \, x^{4} + 480 \, x^{3} - 2880 \, x^{2} + 200 \, x\right )} \log \left (2\right )^{2} - 2135 \, x^{2} + {\left (x^{6} - 12 \, x^{5} + 16 \, {\left (x^{4} - 12 \, x^{3} + 36 \, x^{2}\right )} \log \left (2\right )^{4} + 36 \, x^{4} + 8 \, {\left (x^{5} - 12 \, x^{4} + 36 \, x^{3}\right )} \log \left (2\right )^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{7} - 12 \, x^{6} - 16 \, {\left (x^{4} - 12 \, x^{3} + 36 \, x^{2}\right )} \log \left (2\right )^{5} + 36 \, x^{5} + 16 \, {\left (x^{5} - 12 \, x^{4} + 36 \, x^{3} + 5 \, x^{2} - 30 \, x\right )} \log \left (2\right )^{4} + 5 \, x^{4} - 8 \, {\left (x^{5} - 12 \, x^{4} + 36 \, x^{3}\right )} \log \left (2\right )^{3} - 30 \, x^{3} + 8 \, {\left (x^{6} - 12 \, x^{5} + 36 \, x^{4} + 5 \, x^{3} - 30 \, x^{2}\right )} \log \left (2\right )^{2} - {\left (x^{6} - 12 \, x^{5} + 36 \, x^{4}\right )} \log \left (2\right )\right )} e^{x} - 2 \, {\left (x^{7} - 12 \, x^{6} + 36 \, x^{5} + 30 \, x^{3} - 180 \, x^{2}\right )} \log \left (2\right )}{x^{4} - 12 \, x^{3} + 36 \, x^{2}} \] Input:
integrate(((4*(2*x^4-24*x^3+72*x^2)*log(2)^2+2*x^5-24*x^4+72*x^3)*log(2/ex p(5/(x^2-6*x)))^2+((16*(-2*x^4+24*x^3-72*x^2)*log(2)^4+4*(-4*x^5+44*x^4-96 *x^3-144*x^2)*log(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24*x ^3-72*x^2+20*x-60)*log(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*log(2)^ 2-6*x^6+72*x^5-216*x^4+20*x^3-60*x^2)*log(2/exp(5/(x^2-6*x)))+(16*(2*x^4-2 4*x^3+72*x^2)*log(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*log(2)^2+2*x^6-22*x ^5+48*x^4+72*x^3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*log(2) ^4+4*(4*x^6-40*x^5+48*x^4+288*x^3-40*x^2+120*x)*log(2)^2+2*x^7-18*x^6+216* x^4-20*x^3+60*x^2)*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*log(2)^4+4* (6*x^6-72*x^5+216*x^4-40*x^3+120*x^2)*log(2)^2+4*x^7-48*x^6+144*x^5-20*x^4 +60*x^3)/(x^4-12*x^3+36*x^2),x, algorithm="fricas")
Output:
(x^8 - 12*x^7 + 36*x^6 - 32*(x^5 - 12*x^4 + 36*x^3 + 5*x^2 - 30*x)*log(2)^ 5 + 10*x^5 + 8*(2*x^6 - 23*x^5 + 60*x^4 + 56*x^3 - 120*x^2 + 50)*log(2)^4 - 120*x^4 - 16*(x^6 - 12*x^5 + 36*x^4 + 5*x^3 - 30*x^2)*log(2)^3 + 720*x^3 + (8*x^7 - 95*x^6 + 276*x^5 + 36*x^4 + 480*x^3 - 2880*x^2 + 200*x)*log(2) ^2 - 2135*x^2 + (x^6 - 12*x^5 + 16*(x^4 - 12*x^3 + 36*x^2)*log(2)^4 + 36*x ^4 + 8*(x^5 - 12*x^4 + 36*x^3)*log(2)^2)*e^(2*x) + 2*(x^7 - 12*x^6 - 16*(x ^4 - 12*x^3 + 36*x^2)*log(2)^5 + 36*x^5 + 16*(x^5 - 12*x^4 + 36*x^3 + 5*x^ 2 - 30*x)*log(2)^4 + 5*x^4 - 8*(x^5 - 12*x^4 + 36*x^3)*log(2)^3 - 30*x^3 + 8*(x^6 - 12*x^5 + 36*x^4 + 5*x^3 - 30*x^2)*log(2)^2 - (x^6 - 12*x^5 + 36* x^4)*log(2))*e^x - 2*(x^7 - 12*x^6 + 36*x^5 + 30*x^3 - 180*x^2)*log(2))/(x ^4 - 12*x^3 + 36*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 350 vs. \(2 (27) = 54\).
Time = 3.63 (sec) , antiderivative size = 350, normalized size of antiderivative = 10.00 \[ \int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx=x^{4} + x^{3} \left (- 2 \log {\left (2 \right )} + 8 \log {\left (2 \right )}^{2}\right ) + x^{2} \left (- 16 \log {\left (2 \right )}^{3} + \log {\left (2 \right )}^{2} + 16 \log {\left (2 \right )}^{4}\right ) + x \left (- 32 \log {\left (2 \right )}^{5} + 8 \log {\left (2 \right )}^{4} + 10\right ) + \frac {x^{3} \left (- 60 \log {\left (2 \right )} - 80 \log {\left (2 \right )}^{3} + 160 \log {\left (2 \right )}^{4} + 480 \log {\left (2 \right )}^{2} + 360\right ) + x^{2} \left (-2135 - 2880 \log {\left (2 \right )}^{2} - 960 \log {\left (2 \right )}^{4} - 160 \log {\left (2 \right )}^{5} + 480 \log {\left (2 \right )}^{3} + 360 \log {\left (2 \right )}\right ) + x \left (200 \log {\left (2 \right )}^{2} + 960 \log {\left (2 \right )}^{5}\right ) + 400 \log {\left (2 \right )}^{4}}{x^{4} - 12 x^{3} + 36 x^{2}} + \frac {\left (x^{4} - 6 x^{3} + 8 x^{3} \log {\left (2 \right )}^{2} - 48 x^{2} \log {\left (2 \right )}^{2} + 16 x^{2} \log {\left (2 \right )}^{4} - 96 x \log {\left (2 \right )}^{4}\right ) e^{2 x} + \left (2 x^{5} - 12 x^{4} - 2 x^{4} \log {\left (2 \right )} + 16 x^{4} \log {\left (2 \right )}^{2} - 96 x^{3} \log {\left (2 \right )}^{2} - 16 x^{3} \log {\left (2 \right )}^{3} + 32 x^{3} \log {\left (2 \right )}^{4} + 12 x^{3} \log {\left (2 \right )} - 192 x^{2} \log {\left (2 \right )}^{4} - 32 x^{2} \log {\left (2 \right )}^{5} + 10 x^{2} + 96 x^{2} \log {\left (2 \right )}^{3} + 192 x \log {\left (2 \right )}^{5} + 80 x \log {\left (2 \right )}^{2} + 160 \log {\left (2 \right )}^{4}\right ) e^{x}}{x^{2} - 6 x} \] Input:
integrate(((4*(2*x**4-24*x**3+72*x**2)*ln(2)**2+2*x**5-24*x**4+72*x**3)*ln (2/exp(5/(x**2-6*x)))**2+((16*(-2*x**4+24*x**3-72*x**2)*ln(2)**4+4*(-4*x** 5+44*x**4-96*x**3-144*x**2)*ln(2)**2-2*x**6+20*x**5-24*x**4-144*x**3)*exp( x)+16*(-2*x**4+24*x**3-72*x**2+20*x-60)*ln(2)**4+4*(-8*x**5+96*x**4-288*x* *3+40*x**2-120*x)*ln(2)**2-6*x**6+72*x**5-216*x**4+20*x**3-60*x**2)*ln(2/e xp(5/(x**2-6*x)))+(16*(2*x**4-24*x**3+72*x**2)*ln(2)**4+4*(4*x**5-46*x**4+ 120*x**3+72*x**2)*ln(2)**2+2*x**6-22*x**5+48*x**4+72*x**3)*exp(x)**2+(16*( 2*x**5-22*x**4+48*x**3+72*x**2-20*x+60)*ln(2)**4+4*(4*x**6-40*x**5+48*x**4 +288*x**3-40*x**2+120*x)*ln(2)**2+2*x**7-18*x**6+216*x**4-20*x**3+60*x**2) *exp(x)+16*(2*x**5-24*x**4+72*x**3-20*x**2+60*x)*ln(2)**4+4*(6*x**6-72*x** 5+216*x**4-40*x**3+120*x**2)*ln(2)**2+4*x**7-48*x**6+144*x**5-20*x**4+60*x **3)/(x**4-12*x**3+36*x**2),x)
Output:
x**4 + x**3*(-2*log(2) + 8*log(2)**2) + x**2*(-16*log(2)**3 + log(2)**2 + 16*log(2)**4) + x*(-32*log(2)**5 + 8*log(2)**4 + 10) + (x**3*(-60*log(2) - 80*log(2)**3 + 160*log(2)**4 + 480*log(2)**2 + 360) + x**2*(-2135 - 2880* log(2)**2 - 960*log(2)**4 - 160*log(2)**5 + 480*log(2)**3 + 360*log(2)) + x*(200*log(2)**2 + 960*log(2)**5) + 400*log(2)**4)/(x**4 - 12*x**3 + 36*x* *2) + ((x**4 - 6*x**3 + 8*x**3*log(2)**2 - 48*x**2*log(2)**2 + 16*x**2*log (2)**4 - 96*x*log(2)**4)*exp(2*x) + (2*x**5 - 12*x**4 - 2*x**4*log(2) + 16 *x**4*log(2)**2 - 96*x**3*log(2)**2 - 16*x**3*log(2)**3 + 32*x**3*log(2)** 4 + 12*x**3*log(2) - 192*x**2*log(2)**4 - 32*x**2*log(2)**5 + 10*x**2 + 96 *x**2*log(2)**3 + 192*x*log(2)**5 + 80*x*log(2)**2 + 160*log(2)**4)*exp(x) )/(x**2 - 6*x)
Leaf count of result is larger than twice the leaf count of optimal. 663 vs. \(2 (33) = 66\).
Time = 0.23 (sec) , antiderivative size = 663, normalized size of antiderivative = 18.94 \[ \int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx=\text {Too large to display} \] Input:
integrate(((4*(2*x^4-24*x^3+72*x^2)*log(2)^2+2*x^5-24*x^4+72*x^3)*log(2/ex p(5/(x^2-6*x)))^2+((16*(-2*x^4+24*x^3-72*x^2)*log(2)^4+4*(-4*x^5+44*x^4-96 *x^3-144*x^2)*log(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24*x ^3-72*x^2+20*x-60)*log(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*log(2)^ 2-6*x^6+72*x^5-216*x^4+20*x^3-60*x^2)*log(2/exp(5/(x^2-6*x)))+(16*(2*x^4-2 4*x^3+72*x^2)*log(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*log(2)^2+2*x^6-22*x ^5+48*x^4+72*x^3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*log(2) ^4+4*(4*x^6-40*x^5+48*x^4+288*x^3-40*x^2+120*x)*log(2)^2+2*x^7-18*x^6+216* x^4-20*x^3+60*x^2)*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*log(2)^4+4* (6*x^6-72*x^5+216*x^4-40*x^3+120*x^2)*log(2)^2+4*x^7-48*x^6+144*x^5-20*x^4 +60*x^3)/(x^4-12*x^3+36*x^2),x, algorithm="maxima")
Output:
16*(x^2 + 24*x - 432/(x - 6) + 216*log(x - 6))*log(2)^4 - 384*(x - 36/(x - 6) + 12*log(x - 6))*log(2)^4 - 80/3*(6/(x - 6) + log(x - 6) - log(x))*log (2)^4 - 1152*(6/(x - 6) - log(x - 6))*log(2)^4 - 80/3*log(2)^4*log(x) + x^ 4 + 8*(x^3 + 18*x^2 + 324*x - 3888/(x - 6) + 2592*log(x - 6))*log(2)^2 - 1 44*(x^2 + 24*x - 432/(x - 6) + 216*log(x - 6))*log(2)^2 + 864*(x - 36/(x - 6) + 12*log(x - 6))*log(2)^2 + 160*(6/(x - 6) - log(x - 6))*log(2)^2 + 32 0*log(2)^4/(x - 6) + 20/3*(4*log(2)^4 + 24*log(2)^2 + 27)*log(x - 6) - 20* x - 480*log(2)^2/(x - 6) - (2*x^7*log(2) + (16*log(2)^3 - log(2)^2 - 24*lo g(2))*x^6 + 2*(16*log(2)^5 - 4*log(2)^4 - 96*log(2)^3 + 6*log(2)^2 + 36*lo g(2) - 15)*x^5 - 12*(32*log(2)^5 - 8*log(2)^4 - 48*log(2)^3 + 3*log(2)^2 - 30)*x^4 + 4*(288*log(2)^5 - 72*log(2)^4 + 20*log(2)^3 + 15*log(2) - 270)* x^3 - 400*log(2)^4 + 5*(32*log(2)^5 - 96*log(2)^3 - 72*log(2) - 5)*x^2 - 4 0*(24*log(2)^5 + 5*log(2)^2)*x - (4*(2*log(2)^2 - 3)*x^5 + x^6 + 576*x^2*l og(2)^4 + 4*(4*log(2)^4 - 24*log(2)^2 + 9)*x^4 - 96*(2*log(2)^4 - 3*log(2) ^2)*x^3)*e^(2*x) - 2*((8*log(2)^2 - log(2) - 12)*x^6 + x^7 + 4*(4*log(2)^4 - 2*log(2)^3 - 24*log(2)^2 + 3*log(2) + 9)*x^5 - (16*log(2)^5 + 192*log(2 )^4 - 96*log(2)^3 - 288*log(2)^2 + 36*log(2) - 5)*x^4 - 480*x*log(2)^4 + 2 *(96*log(2)^5 + 288*log(2)^4 - 144*log(2)^3 + 20*log(2)^2 - 15)*x^3 - 16*( 36*log(2)^5 - 5*log(2)^4 + 15*log(2)^2)*x^2)*e^x)/(x^4 - 12*x^3 + 36*x^2) + 360/(x - 6) - 180*log(x - 6)
Leaf count of result is larger than twice the leaf count of optimal. 626 vs. \(2 (33) = 66\).
Time = 0.16 (sec) , antiderivative size = 626, normalized size of antiderivative = 17.89 \[ \int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx =\text {Too large to display} \] Input:
integrate(((4*(2*x^4-24*x^3+72*x^2)*log(2)^2+2*x^5-24*x^4+72*x^3)*log(2/ex p(5/(x^2-6*x)))^2+((16*(-2*x^4+24*x^3-72*x^2)*log(2)^4+4*(-4*x^5+44*x^4-96 *x^3-144*x^2)*log(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24*x ^3-72*x^2+20*x-60)*log(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*log(2)^ 2-6*x^6+72*x^5-216*x^4+20*x^3-60*x^2)*log(2/exp(5/(x^2-6*x)))+(16*(2*x^4-2 4*x^3+72*x^2)*log(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*log(2)^2+2*x^6-22*x ^5+48*x^4+72*x^3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*log(2) ^4+4*(4*x^6-40*x^5+48*x^4+288*x^3-40*x^2+120*x)*log(2)^2+2*x^7-18*x^6+216* x^4-20*x^3+60*x^2)*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*log(2)^4+4* (6*x^6-72*x^5+216*x^4-40*x^3+120*x^2)*log(2)^2+4*x^7-48*x^6+144*x^5-20*x^4 +60*x^3)/(x^4-12*x^3+36*x^2),x, algorithm="giac")
Output:
(16*x^6*log(2)^4 + 32*x^5*e^x*log(2)^4 - 32*x^5*log(2)^5 - 32*x^4*e^x*log( 2)^5 + 8*x^7*log(2)^2 + 16*x^6*e^x*log(2)^2 - 16*x^6*log(2)^3 - 16*x^5*e^x *log(2)^3 - 184*x^5*log(2)^4 + 16*x^4*e^(2*x)*log(2)^4 - 384*x^4*e^x*log(2 )^4 + 384*x^4*log(2)^5 + 384*x^3*e^x*log(2)^5 + x^8 + 2*x^7*e^x - 2*x^7*lo g(2) - 2*x^6*e^x*log(2) - 95*x^6*log(2)^2 + 8*x^5*e^(2*x)*log(2)^2 - 192*x ^5*e^x*log(2)^2 + 192*x^5*log(2)^3 + 192*x^4*e^x*log(2)^3 + 480*x^4*log(2) ^4 - 192*x^3*e^(2*x)*log(2)^4 + 1152*x^3*e^x*log(2)^4 - 1152*x^3*log(2)^5 - 1152*x^2*e^x*log(2)^5 - 12*x^7 + x^6*e^(2*x) - 24*x^6*e^x + 24*x^6*log(2 ) + 24*x^5*e^x*log(2) + 276*x^5*log(2)^2 - 96*x^4*e^(2*x)*log(2)^2 + 576*x ^4*e^x*log(2)^2 - 576*x^4*log(2)^3 - 576*x^3*e^x*log(2)^3 + 448*x^3*log(2) ^4 + 576*x^2*e^(2*x)*log(2)^4 + 160*x^2*e^x*log(2)^4 - 160*x^2*log(2)^5 + 36*x^6 - 12*x^5*e^(2*x) + 72*x^5*e^x - 72*x^5*log(2) - 72*x^4*e^x*log(2) + 36*x^4*log(2)^2 + 288*x^3*e^(2*x)*log(2)^2 + 80*x^3*e^x*log(2)^2 - 80*x^3 *log(2)^3 - 960*x^2*log(2)^4 - 960*x*e^x*log(2)^4 + 960*x*log(2)^5 + 10*x^ 5 + 36*x^4*e^(2*x) + 10*x^4*e^x + 480*x^3*log(2)^2 - 480*x^2*e^x*log(2)^2 + 480*x^2*log(2)^3 - 120*x^4 - 60*x^3*e^x - 60*x^3*log(2) - 2880*x^2*log(2 )^2 + 400*log(2)^4 + 720*x^3 + 360*x^2*log(2) + 200*x*log(2)^2 - 2135*x^2) /(x^4 - 12*x^3 + 36*x^2)
Time = 4.60 (sec) , antiderivative size = 291, normalized size of antiderivative = 8.31 \[ \int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx=\frac {\left (480\,{\ln \left (2\right )}^2-60\,\ln \left (2\right )-80\,{\ln \left (2\right )}^3+160\,{\ln \left (2\right )}^4+360\right )\,x^3+\left (360\,\ln \left (2\right )-2880\,{\ln \left (2\right )}^2+480\,{\ln \left (2\right )}^3-960\,{\ln \left (2\right )}^4-160\,{\ln \left (2\right )}^5-2135\right )\,x^2+\left (200\,{\ln \left (2\right )}^2+960\,{\ln \left (2\right )}^5\right )\,x+400\,{\ln \left (2\right )}^4}{x^4-12\,x^3+36\,x^2}-x^3\,\left (2\,\ln \left (2\right )-8\,{\ln \left (2\right )}^2\right )+x\,\left (8\,{\ln \left (2\right )}^4-32\,{\ln \left (2\right )}^5+10\right )+{\mathrm {e}}^{2\,x}\,\left (x^2+8\,{\ln \left (2\right )}^2\,x+16\,{\ln \left (2\right )}^4\right )+x^2\,\left ({\ln \left (2\right )}^2-16\,{\ln \left (2\right )}^3+16\,{\ln \left (2\right )}^4\right )+x^4-\frac {{\mathrm {e}}^x\,\left (2\,x^5+\left (16\,{\ln \left (2\right )}^2-2\,\ln \left (2\right )-12\right )\,x^4+\left (12\,\ln \left (2\right )-96\,{\ln \left (2\right )}^2-16\,{\ln \left (2\right )}^3+32\,{\ln \left (2\right )}^4\right )\,x^3+\left (96\,{\ln \left (2\right )}^3-192\,{\ln \left (2\right )}^4-32\,{\ln \left (2\right )}^5+10\right )\,x^2+\left (80\,{\ln \left (2\right )}^2+192\,{\ln \left (2\right )}^5\right )\,x+160\,{\ln \left (2\right )}^4\right )}{6\,x-x^2} \] Input:
int((16*log(2)^4*(60*x - 20*x^2 + 72*x^3 - 24*x^4 + 2*x^5) + log(2*exp(5/( 6*x - x^2)))^2*(4*log(2)^2*(72*x^2 - 24*x^3 + 2*x^4) + 72*x^3 - 24*x^4 + 2 *x^5) + exp(x)*(16*log(2)^4*(72*x^2 - 20*x + 48*x^3 - 22*x^4 + 2*x^5 + 60) + 4*log(2)^2*(120*x - 40*x^2 + 288*x^3 + 48*x^4 - 40*x^5 + 4*x^6) + 60*x^ 2 - 20*x^3 + 216*x^4 - 18*x^6 + 2*x^7) + exp(2*x)*(16*log(2)^4*(72*x^2 - 2 4*x^3 + 2*x^4) + 4*log(2)^2*(72*x^2 + 120*x^3 - 46*x^4 + 4*x^5) + 72*x^3 + 48*x^4 - 22*x^5 + 2*x^6) - log(2*exp(5/(6*x - x^2)))*(16*log(2)^4*(72*x^2 - 20*x - 24*x^3 + 2*x^4 + 60) + exp(x)*(16*log(2)^4*(72*x^2 - 24*x^3 + 2* x^4) + 4*log(2)^2*(144*x^2 + 96*x^3 - 44*x^4 + 4*x^5) + 144*x^3 + 24*x^4 - 20*x^5 + 2*x^6) + 4*log(2)^2*(120*x - 40*x^2 + 288*x^3 - 96*x^4 + 8*x^5) + 60*x^2 - 20*x^3 + 216*x^4 - 72*x^5 + 6*x^6) + 4*log(2)^2*(120*x^2 - 40*x ^3 + 216*x^4 - 72*x^5 + 6*x^6) + 60*x^3 - 20*x^4 + 144*x^5 - 48*x^6 + 4*x^ 7)/(36*x^2 - 12*x^3 + x^4),x)
Output:
(x*(200*log(2)^2 + 960*log(2)^5) - x^2*(2880*log(2)^2 - 360*log(2) - 480*l og(2)^3 + 960*log(2)^4 + 160*log(2)^5 + 2135) + 400*log(2)^4 + x^3*(480*lo g(2)^2 - 60*log(2) - 80*log(2)^3 + 160*log(2)^4 + 360))/(36*x^2 - 12*x^3 + x^4) - x^3*(2*log(2) - 8*log(2)^2) + x*(8*log(2)^4 - 32*log(2)^5 + 10) + exp(2*x)*(8*x*log(2)^2 + 16*log(2)^4 + x^2) + x^2*(log(2)^2 - 16*log(2)^3 + 16*log(2)^4) + x^4 - (exp(x)*(x^2*(96*log(2)^3 - 192*log(2)^4 - 32*log(2 )^5 + 10) - x^4*(2*log(2) - 16*log(2)^2 + 12) + x*(80*log(2)^2 + 192*log(2 )^5) + 160*log(2)^4 + 2*x^5 + x^3*(12*log(2) - 96*log(2)^2 - 16*log(2)^3 + 32*log(2)^4)))/(6*x - x^2)
\[ \int \frac {60 x^3-20 x^4+144 x^5-48 x^6+4 x^7+\left (120 x^2-40 x^3+216 x^4-72 x^5+6 x^6\right ) \log ^2(4)+\left (60 x-20 x^2+72 x^3-24 x^4+2 x^5\right ) \log ^4(4)+e^{2 x} \left (72 x^3+48 x^4-22 x^5+2 x^6+\left (72 x^2+120 x^3-46 x^4+4 x^5\right ) \log ^2(4)+\left (72 x^2-24 x^3+2 x^4\right ) \log ^4(4)\right )+e^x \left (60 x^2-20 x^3+216 x^4-18 x^6+2 x^7+\left (120 x-40 x^2+288 x^3+48 x^4-40 x^5+4 x^6\right ) \log ^2(4)+\left (60-20 x+72 x^2+48 x^3-22 x^4+2 x^5\right ) \log ^4(4)\right )+\left (-60 x^2+20 x^3-216 x^4+72 x^5-6 x^6+\left (-120 x+40 x^2-288 x^3+96 x^4-8 x^5\right ) \log ^2(4)+\left (-60+20 x-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)+e^x \left (-144 x^3-24 x^4+20 x^5-2 x^6+\left (-144 x^2-96 x^3+44 x^4-4 x^5\right ) \log ^2(4)+\left (-72 x^2+24 x^3-2 x^4\right ) \log ^4(4)\right )\right ) \log \left (2 e^{-\frac {5}{-6 x+x^2}}\right )+\left (72 x^3-24 x^4+2 x^5+\left (72 x^2-24 x^3+2 x^4\right ) \log ^2(4)\right ) \log ^2\left (2 e^{-\frac {5}{-6 x+x^2}}\right )}{36 x^2-12 x^3+x^4} \, dx=\text {too large to display} \] Input:
int(((4*(2*x^4-24*x^3+72*x^2)*log(2)^2+2*x^5-24*x^4+72*x^3)*log(2/exp(5/(x ^2-6*x)))^2+((16*(-2*x^4+24*x^3-72*x^2)*log(2)^4+4*(-4*x^5+44*x^4-96*x^3-1 44*x^2)*log(2)^2-2*x^6+20*x^5-24*x^4-144*x^3)*exp(x)+16*(-2*x^4+24*x^3-72* x^2+20*x-60)*log(2)^4+4*(-8*x^5+96*x^4-288*x^3+40*x^2-120*x)*log(2)^2-6*x^ 6+72*x^5-216*x^4+20*x^3-60*x^2)*log(2/exp(5/(x^2-6*x)))+(16*(2*x^4-24*x^3+ 72*x^2)*log(2)^4+4*(4*x^5-46*x^4+120*x^3+72*x^2)*log(2)^2+2*x^6-22*x^5+48* x^4+72*x^3)*exp(x)^2+(16*(2*x^5-22*x^4+48*x^3+72*x^2-20*x+60)*log(2)^4+4*( 4*x^6-40*x^5+48*x^4+288*x^3-40*x^2+120*x)*log(2)^2+2*x^7-18*x^6+216*x^4-20 *x^3+60*x^2)*exp(x)+16*(2*x^5-24*x^4+72*x^3-20*x^2+60*x)*log(2)^4+4*(6*x^6 -72*x^5+216*x^4-40*x^3+120*x^2)*log(2)^2+4*x^7-48*x^6+144*x^5-20*x^4+60*x^ 3)/(x^4-12*x^3+36*x^2),x)
Output:
(336*e**(2*x)*log(2)**4*x**2 - 2016*e**(2*x)*log(2)**4*x + 168*e**(2*x)*lo g(2)**2*x**3 - 1008*e**(2*x)*log(2)**2*x**2 + 21*e**(2*x)*x**4 - 126*e**(2 *x)*x**3 + 672*e**x*log(2)**4*x**3 - 4032*e**x*log(2)**4*x**2 + 3456*e**x* log(2)**4*x + 3360*e**x*log(2)**4 + 336*e**x*log(2)**2*x**4 - 2016*e**x*lo g(2)**2*x**3 + 42*e**x*x**5 - 252*e**x*x**4 + 6048*int(log(2/e**(5/(x**2 - 6*x)))**2/(x**2 - 12*x + 36),x)*log(2)**2*x**2 - 36288*int(log(2/e**(5/(x **2 - 6*x)))**2/(x**2 - 12*x + 36),x)*log(2)**2*x + 20160*int(e**x/(x**3 - 12*x**2 + 36*x),x)*log(2)**4*x**2 - 120960*int(e**x/(x**3 - 12*x**2 + 36* x),x)*log(2)**4*x + 10080*int(e**x/(x**3 - 12*x**2 + 36*x),x)*log(2)**2*x* *2 - 60480*int(e**x/(x**3 - 12*x**2 + 36*x),x)*log(2)**2*x + 20832*int(e** x/(x**2 - 12*x + 36),x)*log(2)**4*x**2 - 124992*int(e**x/(x**2 - 12*x + 36 ),x)*log(2)**4*x - 3360*int(e**x/(x**2 - 12*x + 36),x)*log(2)**2*x**2 + 20 160*int(e**x/(x**2 - 12*x + 36),x)*log(2)**2*x + 1260*int(e**x/(x**2 - 12* x + 36),x)*x**2 - 7560*int(e**x/(x**2 - 12*x + 36),x)*x - 20160*int(log(2/ e**(5/(x**2 - 6*x)))/(x**4 - 12*x**3 + 36*x**2),x)*log(2)**4*x**2 + 120960 *int(log(2/e**(5/(x**2 - 6*x)))/(x**4 - 12*x**3 + 36*x**2),x)*log(2)**4*x + 6720*int(log(2/e**(5/(x**2 - 6*x)))/(x**3 - 12*x**2 + 36*x),x)*log(2)**4 *x**2 - 40320*int(log(2/e**(5/(x**2 - 6*x)))/(x**3 - 12*x**2 + 36*x),x)*lo g(2)**4*x - 10080*int(log(2/e**(5/(x**2 - 6*x)))/(x**3 - 12*x**2 + 36*x),x )*log(2)**2*x**2 + 60480*int(log(2/e**(5/(x**2 - 6*x)))/(x**3 - 12*x**2...