Integrand size = 125, antiderivative size = 27 \[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx=\frac {16 e^{5+x} \log \left ((16+x) \left (-5+(2-x)^2 \log (2)\right )\right )}{x} \] Output:
16*ln(((2-x)^2*ln(2)-5)*(x+16))*exp(5+x)/x
Time = 0.70 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.11 \[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx=\frac {16 e^{5+x} \log \left ((16+x) \left (-5-4 x \log (2)+x^2 \log (2)+\log (16)\right )\right )}{x} \] Input:
Integrate[(E^(5 + x)*(-80*x + (-960*x + 384*x^2 + 48*x^3)*Log[2]) + E^(5 + x)*(1280 - 1200*x - 80*x^2 + (-1024 + 1984*x - 1152*x^2 + 176*x^3 + 16*x^ 4)*Log[2])*Log[-80 - 5*x + (64 - 60*x + 12*x^2 + x^3)*Log[2]])/(-80*x^2 - 5*x^3 + (64*x^2 - 60*x^3 + 12*x^4 + x^5)*Log[2]),x]
Output:
(16*E^(5 + x)*Log[(16 + x)*(-5 - 4*x*Log[2] + x^2*Log[2] + Log[16])])/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.
| \(\displaystyle \int \frac {e^{x+5} \left (\left (48 x^3+384 x^2-960 x\right ) \log (2)-80 x\right )+e^{x+5} \left (-80 x^2+\left (16 x^4+176 x^3-1152 x^2+1984 x-1024\right ) \log (2)-1200 x+1280\right ) \log \left (\left (x^3+12 x^2-60 x+64\right ) \log (2)-5 x-80\right )}{-5 x^3-80 x^2+\left (x^5+12 x^4-60 x^3+64 x^2\right ) \log (2)} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {e^{x+5} \left (\left (48 x^3+384 x^2-960 x\right ) \log (2)-80 x\right )+e^{x+5} \left (-80 x^2+\left (16 x^4+176 x^3-1152 x^2+1984 x-1024\right ) \log (2)-1200 x+1280\right ) \log \left (\left (x^3+12 x^2-60 x+64\right ) \log (2)-5 x-80\right )}{x^2 \left (x^3 \log (2)+12 x^2 \log (2)-5 x (1+\log (4096))-16 (5-4 \log (2))\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{x+5} \left (-5 x^2 \log (2) (1+\log (4096))+4 x \log (2) (5-16 \log (2)-15 \log (4096))-768 \log ^2(2)+25 (1+\log (4096))^2+960 \log (2)\right ) \left (-x^3 \log (8)+5 x^2 \left (1+\log \left (16384\ 2^{2/5}\right )\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )-24 x^2 \log (2)+75 x \left (1-\frac {124 \log (2)}{75}\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )-80 \left (1-\frac {4 \log (2)}{5}\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )+x^4 (-\log (2)) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )-11 x^3 \log (2) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )+5 x (1+\log (4096))\right )}{16 (5-\log (16))^2 \left (x^3 (-\log (2))-12 x^2 \log (2)+5 x (1+\log (4096))+16 (5-4 \log (2))\right )}+\frac {5 e^{x+5} (1+\log (4096)) \left (3 x^3 \log (2)-5 x^2 \left (1+\log \left (16384\ 2^{2/5}\right )\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )+24 x^2 \log (2)-75 x \left (1-\frac {124 \log (2)}{75}\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )+80 \left (1-\frac {4 \log (2)}{5}\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )+x^4 \log (2) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )+11 x^3 \log (2) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )-5 x (1+\log (4096))\right )}{16 x (5-\log (16))^2}+\frac {e^{x+5} \left (-3 x^3 \log (2)+5 x^2 \left (1+\log \left (16384\ 2^{2/5}\right )\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )-24 x^2 \log (2)+75 x \left (1-\frac {124 \log (2)}{75}\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )-80 \left (1-\frac {4 \log (2)}{5}\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )+x^4 (-\log (2)) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )-11 x^3 \log (2) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )+5 x (1+\log (4096))\right )}{x^2 (5-\log (16))}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {16 e^{x+5} \left (-x \left (x^2 \log (8)+24 x \log (2)-5 (1+\log (4096))\right )-\left (x^4 \log (2)+11 x^3 \log (2)-x^2 (5+\log (4)+5 \log (16384))+x (124 \log (2)-75)+80-64 \log (2)\right ) \log \left ((x+16) \left (x^2 \log (2)-4 x \log (2)-5+\log (16)\right )\right )\right )}{x^2 \left (x^3 (-\log (2))-12 x^2 \log (2)+5 x (1+\log (4096))+16 (5-4 \log (2))\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 16 \int -\frac {e^{x+5} \left (x \left (\log (8) x^2+24 \log (2) x-5 (1+\log (4096))\right )-\left (-\log (2) x^4-11 \log (2) x^3+(5+\log (4)+5 \log (16384)) x^2+(75-124 \log (2)) x-16 (5-4 \log (2))\right ) \log \left (-\left ((x+16) \left (-\log (2) x^2+4 \log (2) x-\log (16)+5\right )\right )\right )\right )}{x^2 \left (-\log (2) x^3-12 \log (2) x^2+5 (1+\log (4096)) x+16 (5-4 \log (2))\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -16 \int \frac {e^{x+5} \left (x \left (\log (8) x^2+24 \log (2) x-5 (1+\log (4096))\right )-\left (-\log (2) x^4-11 \log (2) x^3+(5+\log (4)+5 \log (16384)) x^2+(75-124 \log (2)) x-16 (5-4 \log (2))\right ) \log \left (-\left ((x+16) \left (-\log (2) x^2+4 \log (2) x-\log (16)+5\right )\right )\right )\right )}{x^2 \left (-\log (2) x^3-12 \log (2) x^2+5 (1+\log (4096)) x+16 (5-4 \log (2))\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -16 \int \left (\frac {e^{x+5} \left (\log (8) x^2+24 \log (2) x-5 (1+\log (4096))\right )}{x \left (-\log (2) x^3-12 \log (2) x^2+5 (1+\log (4096)) x+16 (5-4 \log (2))\right )}+\frac {e^{x+5} \left (\log (2) x^4+11 \log (2) x^3-(5+\log (4)+5 \log (16384)) x^2-(75-124 \log (2)) x+16 (5-4 \log (2))\right ) \log \left ((x+16) \left (\log (2) x^2-4 \log (2) x+\log (16)-5\right )\right )}{x^2 \left (-\log (2) x^3-12 \log (2) x^2+5 (1+\log (4096)) x+16 (5-4 \log (2))\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -16 \left (-\frac {\left (-1536 \log ^2(2)+1920 \log (2)+25 (1+\log (4096))^2\right ) \int \frac {e^{x+5}}{\log (2) x^3+12 \log (2) x^2-5 (1+\log (4096)) x-16 (5-4 \log (2))}dx}{16 (5-\log (16))}+\frac {\log (2) (45-16 \log (8)-15 \log (4096)) \int \frac {e^{x+5} x}{-\log (2) x^3-12 \log (2) x^2+5 (1+\log (4096)) x+16 (5-4 \log (2))}dx}{4 (5-\log (16))}-\frac {5 \log (2) (1+\log (4096)) \int \frac {e^{x+5} x^2}{-\log (2) x^3-12 \log (2) x^2+5 (1+\log (4096)) x+16 (5-4 \log (2))}dx}{16 (5-\log (16))}-\frac {\operatorname {ExpIntegralEi}(x+16)}{16 e^{11}}+\frac {e^{7-\frac {\sqrt {\log (32)}}{\log (2)}} \left (2560 \log ^3(2)+\log (2) \left (25+\log ^2(16)\right )+8 \log ^2(2) \left (390-79 \log (16)+160 \sqrt {\log (32)}\right )+\left (\log ^2(16)-4 \log (32)\right ) \sqrt {\log (32)}-\log (8) (5-\log (16))^2\right ) \operatorname {ExpIntegralEi}\left (\frac {2 \log (2) x+2 \sqrt {\log (32)}-\log (16)}{2 \log (2)}\right )}{2 (5-\log (16)) (5-320 \log (2)-\log (16)) \sqrt {\log (32)}}-\frac {e^{7+\frac {\sqrt {\log (32)}}{\log (2)}} \left (4 \log ^{\frac {3}{2}}(32)+2560 \log ^3(2)+8 \log ^2(2) \left (390-79 \log (16)-160 \sqrt {\log (32)}\right )+\log (2) \left (25+\log ^2(16)-4 \log (16) \sqrt {\log (32)}\right )-\log (8) (5-\log (16))^2\right ) \operatorname {ExpIntegralEi}\left (\frac {\log (2) x-\sqrt {\log (32)}-\log (4)}{\log (2)}\right )}{2 (5-\log (16)) (5-320 \log (2)-\log (16)) \sqrt {\log (32)}}-\frac {5 e^5 (1+\log (4096)) \operatorname {ExpIntegralEi}(x)}{16 (5-\log (16))}+\frac {e^5 (5+64 \log (2)-\log (16)) \operatorname {ExpIntegralEi}(x)}{16 (5-\log (16))}-\frac {e^{x+5} \log \left (-\left ((x+16) \left (x^2 (-\log (2))+4 x \log (2)+5-\log (16)\right )\right )\right )}{x}\right )\) |
Input:
Int[(E^(5 + x)*(-80*x + (-960*x + 384*x^2 + 48*x^3)*Log[2]) + E^(5 + x)*(1 280 - 1200*x - 80*x^2 + (-1024 + 1984*x - 1152*x^2 + 176*x^3 + 16*x^4)*Log [2])*Log[-80 - 5*x + (64 - 60*x + 12*x^2 + x^3)*Log[2]])/(-80*x^2 - 5*x^3 + (64*x^2 - 60*x^3 + 12*x^4 + x^5)*Log[2]),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(104\) vs. \(2(26)=52\).
Time = 3.92 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.89
| method | result | size |
| parallelrisch | \(\frac {65536 \ln \left (2\right )^{2} {\mathrm e}^{5+x} \ln \left (\left (x^{3}+12 x^{2}-60 x +64\right ) \ln \left (2\right )-5 x -80\right )-163840 \ln \left (2\right ) {\mathrm e}^{5+x} \ln \left (\left (x^{3}+12 x^{2}-60 x +64\right ) \ln \left (2\right )-5 x -80\right )+102400 \,{\mathrm e}^{5+x} \ln \left (\left (x^{3}+12 x^{2}-60 x +64\right ) \ln \left (2\right )-5 x -80\right )}{256 x \left (4 \ln \left (2\right )-5\right )^{2}}\) | \(105\) |
| risch | \(\frac {16 \,{\mathrm e}^{5+x} \ln \left (-5+\left (x^{2}-4 x +4\right ) \ln \left (2\right )\right )}{x}+\frac {8 \,{\mathrm e}^{5+x} \left (-i \pi \,\operatorname {csgn}\left (i \left (-5+\left (x^{2}-4 x +4\right ) \ln \left (2\right )\right )\right ) \operatorname {csgn}\left (i \left (x +16\right )\right ) \operatorname {csgn}\left (i \left (-5+\left (x^{2}-4 x +4\right ) \ln \left (2\right )\right ) \left (x +16\right )\right )+i \pi \,\operatorname {csgn}\left (i \left (-5+\left (x^{2}-4 x +4\right ) \ln \left (2\right )\right )\right ) {\operatorname {csgn}\left (i \left (-5+\left (x^{2}-4 x +4\right ) \ln \left (2\right )\right ) \left (x +16\right )\right )}^{2}+i \pi \,\operatorname {csgn}\left (i \left (x +16\right )\right ) {\operatorname {csgn}\left (i \left (-5+\left (x^{2}-4 x +4\right ) \ln \left (2\right )\right ) \left (x +16\right )\right )}^{2}-i \pi {\operatorname {csgn}\left (i \left (-5+\left (x^{2}-4 x +4\right ) \ln \left (2\right )\right ) \left (x +16\right )\right )}^{3}+2 \ln \left (x +16\right )\right )}{x}\) | \(191\) |
Input:
int((((16*x^4+176*x^3-1152*x^2+1984*x-1024)*ln(2)-80*x^2-1200*x+1280)*exp( 5+x)*ln((x^3+12*x^2-60*x+64)*ln(2)-5*x-80)+((48*x^3+384*x^2-960*x)*ln(2)-8 0*x)*exp(5+x))/((x^5+12*x^4-60*x^3+64*x^2)*ln(2)-5*x^3-80*x^2),x,method=_R ETURNVERBOSE)
Output:
1/256*(65536*ln(2)^2*exp(5+x)*ln((x^3+12*x^2-60*x+64)*ln(2)-5*x-80)-163840 *ln(2)*exp(5+x)*ln((x^3+12*x^2-60*x+64)*ln(2)-5*x-80)+102400*exp(5+x)*ln(( x^3+12*x^2-60*x+64)*ln(2)-5*x-80))/x/(4*ln(2)-5)^2
Time = 0.08 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx=\frac {16 \, e^{\left (x + 5\right )} \log \left ({\left (x^{3} + 12 \, x^{2} - 60 \, x + 64\right )} \log \left (2\right ) - 5 \, x - 80\right )}{x} \] Input:
integrate((((16*x^4+176*x^3-1152*x^2+1984*x-1024)*log(2)-80*x^2-1200*x+128 0)*exp(5+x)*log((x^3+12*x^2-60*x+64)*log(2)-5*x-80)+((48*x^3+384*x^2-960*x )*log(2)-80*x)*exp(5+x))/((x^5+12*x^4-60*x^3+64*x^2)*log(2)-5*x^3-80*x^2), x, algorithm="fricas")
Output:
16*e^(x + 5)*log((x^3 + 12*x^2 - 60*x + 64)*log(2) - 5*x - 80)/x
Time = 0.19 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx=\frac {16 e^{x + 5} \log {\left (- 5 x + \left (x^{3} + 12 x^{2} - 60 x + 64\right ) \log {\left (2 \right )} - 80 \right )}}{x} \] Input:
integrate((((16*x**4+176*x**3-1152*x**2+1984*x-1024)*ln(2)-80*x**2-1200*x+ 1280)*exp(5+x)*ln((x**3+12*x**2-60*x+64)*ln(2)-5*x-80)+((48*x**3+384*x**2- 960*x)*ln(2)-80*x)*exp(5+x))/((x**5+12*x**4-60*x**3+64*x**2)*ln(2)-5*x**3- 80*x**2),x)
Output:
16*exp(x + 5)*log(-5*x + (x**3 + 12*x**2 - 60*x + 64)*log(2) - 80)/x
Time = 0.28 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.41 \[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx=\frac {16 \, {\left (e^{\left (x + 5\right )} \log \left (x^{2} \log \left (2\right ) - 4 \, x \log \left (2\right ) + 4 \, \log \left (2\right ) - 5\right ) + e^{\left (x + 5\right )} \log \left (x + 16\right )\right )}}{x} \] Input:
integrate((((16*x^4+176*x^3-1152*x^2+1984*x-1024)*log(2)-80*x^2-1200*x+128 0)*exp(5+x)*log((x^3+12*x^2-60*x+64)*log(2)-5*x-80)+((48*x^3+384*x^2-960*x )*log(2)-80*x)*exp(5+x))/((x^5+12*x^4-60*x^3+64*x^2)*log(2)-5*x^3-80*x^2), x, algorithm="maxima")
Output:
16*(e^(x + 5)*log(x^2*log(2) - 4*x*log(2) + 4*log(2) - 5) + e^(x + 5)*log( x + 16))/x
Time = 0.20 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.37 \[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx=\frac {16 \, e^{\left (x + 5\right )} \log \left (x^{3} \log \left (2\right ) + 12 \, x^{2} \log \left (2\right ) - 60 \, x \log \left (2\right ) - 5 \, x + 64 \, \log \left (2\right ) - 80\right )}{x} \] Input:
integrate((((16*x^4+176*x^3-1152*x^2+1984*x-1024)*log(2)-80*x^2-1200*x+128 0)*exp(5+x)*log((x^3+12*x^2-60*x+64)*log(2)-5*x-80)+((48*x^3+384*x^2-960*x )*log(2)-80*x)*exp(5+x))/((x^5+12*x^4-60*x^3+64*x^2)*log(2)-5*x^3-80*x^2), x, algorithm="giac")
Output:
16*e^(x + 5)*log(x^3*log(2) + 12*x^2*log(2) - 60*x*log(2) - 5*x + 64*log(2 ) - 80)/x
Timed out. \[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx=\int \frac {{\mathrm {e}}^{x+5}\,\left (80\,x-\ln \left (2\right )\,\left (48\,x^3+384\,x^2-960\,x\right )\right )+{\mathrm {e}}^{x+5}\,\ln \left (\ln \left (2\right )\,\left (x^3+12\,x^2-60\,x+64\right )-5\,x-80\right )\,\left (1200\,x-\ln \left (2\right )\,\left (16\,x^4+176\,x^3-1152\,x^2+1984\,x-1024\right )+80\,x^2-1280\right )}{80\,x^2-\ln \left (2\right )\,\left (x^5+12\,x^4-60\,x^3+64\,x^2\right )+5\,x^3} \,d x \] Input:
int((exp(x + 5)*(80*x - log(2)*(384*x^2 - 960*x + 48*x^3)) + exp(x + 5)*lo g(log(2)*(12*x^2 - 60*x + x^3 + 64) - 5*x - 80)*(1200*x - log(2)*(1984*x - 1152*x^2 + 176*x^3 + 16*x^4 - 1024) + 80*x^2 - 1280))/(80*x^2 - log(2)*(6 4*x^2 - 60*x^3 + 12*x^4 + x^5) + 5*x^3),x)
Output:
int((exp(x + 5)*(80*x - log(2)*(384*x^2 - 960*x + 48*x^3)) + exp(x + 5)*lo g(log(2)*(12*x^2 - 60*x + x^3 + 64) - 5*x - 80)*(1200*x - log(2)*(1984*x - 1152*x^2 + 176*x^3 + 16*x^4 - 1024) + 80*x^2 - 1280))/(80*x^2 - log(2)*(6 4*x^2 - 60*x^3 + 12*x^4 + x^5) + 5*x^3), x)
Time = 0.20 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.44 \[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx=\frac {16 e^{x} \mathrm {log}\left (\mathrm {log}\left (2\right ) x^{3}+12 \,\mathrm {log}\left (2\right ) x^{2}-60 \,\mathrm {log}\left (2\right ) x +64 \,\mathrm {log}\left (2\right )-5 x -80\right ) e^{5}}{x} \] Input:
int((((16*x^4+176*x^3-1152*x^2+1984*x-1024)*log(2)-80*x^2-1200*x+1280)*exp (5+x)*log((x^3+12*x^2-60*x+64)*log(2)-5*x-80)+((48*x^3+384*x^2-960*x)*log( 2)-80*x)*exp(5+x))/((x^5+12*x^4-60*x^3+64*x^2)*log(2)-5*x^3-80*x^2),x)
Output:
(16*e**x*log(log(2)*x**3 + 12*log(2)*x**2 - 60*log(2)*x + 64*log(2) - 5*x - 80)*e**5)/x