Integrand size = 525, antiderivative size = 30 \[ \int \frac {e^{\frac {\left (256-256 x+96 x^2-16 x^3+x^4\right ) \log ^2\left (\frac {x}{5+x}\right )}{256+e^{4 x}+768 x+608 x^2-144 x^3-255 x^4+36 x^5+38 x^6-12 x^7+x^8+e^{3 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (96+144 x+6 x^2-36 x^3+6 x^4\right )+e^x \left (-256-576 x-240 x^2+180 x^3+60 x^4-36 x^5+4 x^6\right )}} \left (\left (-10240+2560 x+6400 x^2-4800 x^3+1400 x^4-190 x^5+10 x^6+e^x \left (2560-2560 x+960 x^2-160 x^3+10 x^4\right )\right ) \log \left (\frac {x}{5+x}\right )+\left (20480 x-21504 x^2+7680 x^3-640 x^4-240 x^5+60 x^6-4 x^7+e^x \left (-6400 x+4800 x^2-944 x^3-92 x^4+48 x^5-4 x^6\right )\right ) \log ^2\left (\frac {x}{5+x}\right )\right )}{-5120 x-20224 x^2-26240 x^3-6880 x^4+9820 x^5+4445 x^6-2098 x^7-665 x^8+320 x^9-5 x^{10}-10 x^{11}+x^{12}+e^{5 x} \left (5 x+x^2\right )+e^{4 x} \left (-100 x-95 x^2+10 x^3+5 x^4\right )+e^{3 x} \left (800 x+1360 x^2+290 x^3-290 x^4-10 x^5+10 x^6\right )+e^{2 x} \left (-3200 x-7840 x^2-4440 x^3+1650 x^4+1200 x^5-300 x^6-40 x^7+10 x^8\right )+e^x \left (6400 x+20480 x^2+19040 x^3-560 x^4-7095 x^5-375 x^6+1130 x^7-110 x^8-35 x^9+5 x^{10}\right )} \, dx=e^{\frac {\log ^2\left (\frac {x}{5+x}\right )}{\left (1-\frac {e^x}{4-x}+x\right )^4}} \]
Time = 0.33 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03 \[ \int \frac {e^{\frac {\left (256-256 x+96 x^2-16 x^3+x^4\right ) \log ^2\left (\frac {x}{5+x}\right )}{256+e^{4 x}+768 x+608 x^2-144 x^3-255 x^4+36 x^5+38 x^6-12 x^7+x^8+e^{3 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (96+144 x+6 x^2-36 x^3+6 x^4\right )+e^x \left (-256-576 x-240 x^2+180 x^3+60 x^4-36 x^5+4 x^6\right )}} \left (\left (-10240+2560 x+6400 x^2-4800 x^3+1400 x^4-190 x^5+10 x^6+e^x \left (2560-2560 x+960 x^2-160 x^3+10 x^4\right )\right ) \log \left (\frac {x}{5+x}\right )+\left (20480 x-21504 x^2+7680 x^3-640 x^4-240 x^5+60 x^6-4 x^7+e^x \left (-6400 x+4800 x^2-944 x^3-92 x^4+48 x^5-4 x^6\right )\right ) \log ^2\left (\frac {x}{5+x}\right )\right )}{-5120 x-20224 x^2-26240 x^3-6880 x^4+9820 x^5+4445 x^6-2098 x^7-665 x^8+320 x^9-5 x^{10}-10 x^{11}+x^{12}+e^{5 x} \left (5 x+x^2\right )+e^{4 x} \left (-100 x-95 x^2+10 x^3+5 x^4\right )+e^{3 x} \left (800 x+1360 x^2+290 x^3-290 x^4-10 x^5+10 x^6\right )+e^{2 x} \left (-3200 x-7840 x^2-4440 x^3+1650 x^4+1200 x^5-300 x^6-40 x^7+10 x^8\right )+e^x \left (6400 x+20480 x^2+19040 x^3-560 x^4-7095 x^5-375 x^6+1130 x^7-110 x^8-35 x^9+5 x^{10}\right )} \, dx=e^{\frac {(-4+x)^4 \log ^2\left (\frac {x}{5+x}\right )}{\left (-4+e^x-3 x+x^2\right )^4}} \]
Integrate[(E^(((256 - 256*x + 96*x^2 - 16*x^3 + x^4)*Log[x/(5 + x)]^2)/(25 6 + E^(4*x) + 768*x + 608*x^2 - 144*x^3 - 255*x^4 + 36*x^5 + 38*x^6 - 12*x ^7 + x^8 + E^(3*x)*(-16 - 12*x + 4*x^2) + E^(2*x)*(96 + 144*x + 6*x^2 - 36 *x^3 + 6*x^4) + E^x*(-256 - 576*x - 240*x^2 + 180*x^3 + 60*x^4 - 36*x^5 + 4*x^6)))*((-10240 + 2560*x + 6400*x^2 - 4800*x^3 + 1400*x^4 - 190*x^5 + 10 *x^6 + E^x*(2560 - 2560*x + 960*x^2 - 160*x^3 + 10*x^4))*Log[x/(5 + x)] + (20480*x - 21504*x^2 + 7680*x^3 - 640*x^4 - 240*x^5 + 60*x^6 - 4*x^7 + E^x *(-6400*x + 4800*x^2 - 944*x^3 - 92*x^4 + 48*x^5 - 4*x^6))*Log[x/(5 + x)]^ 2))/(-5120*x - 20224*x^2 - 26240*x^3 - 6880*x^4 + 9820*x^5 + 4445*x^6 - 20 98*x^7 - 665*x^8 + 320*x^9 - 5*x^10 - 10*x^11 + x^12 + E^(5*x)*(5*x + x^2) + E^(4*x)*(-100*x - 95*x^2 + 10*x^3 + 5*x^4) + E^(3*x)*(800*x + 1360*x^2 + 290*x^3 - 290*x^4 - 10*x^5 + 10*x^6) + E^(2*x)*(-3200*x - 7840*x^2 - 444 0*x^3 + 1650*x^4 + 1200*x^5 - 300*x^6 - 40*x^7 + 10*x^8) + E^x*(6400*x + 2 0480*x^2 + 19040*x^3 - 560*x^4 - 7095*x^5 - 375*x^6 + 1130*x^7 - 110*x^8 - 35*x^9 + 5*x^10)),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.
| \(\displaystyle \int \frac {\left (\left (10 x^6-190 x^5+1400 x^4-4800 x^3+6400 x^2+e^x \left (10 x^4-160 x^3+960 x^2-2560 x+2560\right )+2560 x-10240\right ) \log \left (\frac {x}{x+5}\right )+\left (-4 x^7+60 x^6-240 x^5-640 x^4+7680 x^3-21504 x^2+e^x \left (-4 x^6+48 x^5-92 x^4-944 x^3+4800 x^2-6400 x\right )+20480 x\right ) \log ^2\left (\frac {x}{x+5}\right )\right ) \exp \left (\frac {\left (x^4-16 x^3+96 x^2-256 x+256\right ) \log ^2\left (\frac {x}{x+5}\right )}{x^8-12 x^7+38 x^6+36 x^5-255 x^4-144 x^3+608 x^2+e^{3 x} \left (4 x^2-12 x-16\right )+e^{2 x} \left (6 x^4-36 x^3+6 x^2+144 x+96\right )+e^x \left (4 x^6-36 x^5+60 x^4+180 x^3-240 x^2-576 x-256\right )+768 x+e^{4 x}+256}\right )}{x^{12}-10 x^{11}-5 x^{10}+320 x^9-665 x^8-2098 x^7+4445 x^6+9820 x^5-6880 x^4-26240 x^3-20224 x^2+e^{5 x} \left (x^2+5 x\right )+e^{4 x} \left (5 x^4+10 x^3-95 x^2-100 x\right )+e^{3 x} \left (10 x^6-10 x^5-290 x^4+290 x^3+1360 x^2+800 x\right )+e^{2 x} \left (10 x^8-40 x^7-300 x^6+1200 x^5+1650 x^4-4440 x^3-7840 x^2-3200 x\right )+e^x \left (5 x^{10}-35 x^9-110 x^8+1130 x^7-375 x^6-7095 x^5-560 x^4+19040 x^3+20480 x^2+6400 x\right )-5120 x} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 (4-x)^3 \log \left (\frac {x}{x+5}\right ) \left (5 (x-4) \left (x^2-3 x+e^x-4\right )-2 \left ((x-4)^2+e^x (x-5)\right ) x (x+5) \log \left (\frac {x}{x+5}\right )\right ) \exp \left (\frac {(x-4)^4 \log ^2\left (\frac {x}{x+5}\right )}{\left (x^2-3 x+e^x-4\right )^4}\right )}{x (x+5) \left (-x^2+3 x-e^x+4\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {\exp \left (\frac {(4-x)^4 \log ^2\left (\frac {x}{x+5}\right )}{\left (-x^2+3 x-e^x+4\right )^4}\right ) (4-x)^3 \log \left (\frac {x}{x+5}\right ) \left (5 (4-x) \left (-x^2+3 x-e^x+4\right )+2 \left (e^x (5-x)-(x-4)^2\right ) x (x+5) \log \left (\frac {x}{x+5}\right )\right )}{x (x+5) \left (-x^2+3 x-e^x+4\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \exp \left (\frac {(4-x)^4 \log ^2\left (\frac {x}{x+5}\right )}{\left (-x^2+3 x-e^x+4\right )^4}\right ) (x-4)^4 \left (x^2-5 x-1\right ) \log ^2\left (\frac {x}{x+5}\right )}{\left (x^2-3 x+e^x-4\right )^5}-\frac {\exp \left (\frac {(4-x)^4 \log ^2\left (\frac {x}{x+5}\right )}{\left (-x^2+3 x-e^x+4\right )^4}\right ) (x-4)^3 \log \left (\frac {x}{x+5}\right ) \left (2 \log \left (\frac {x}{x+5}\right ) x^3-50 \log \left (\frac {x}{x+5}\right ) x-5 x+20\right )}{x (x+5) \left (x^2-3 x+e^x-4\right )^4}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \exp \left (\frac {(x-4)^4 \log ^2\left (\frac {x}{x+5}\right )}{\left (x^2-3 x+e^x-4\right )^4}\right ) (x-4)^4 \left (x^2-5 x-1\right ) \log ^2\left (\frac {x}{x+5}\right )}{\left (x^2-3 x+e^x-4\right )^5}-\frac {\exp \left (\frac {(x-4)^4 \log ^2\left (\frac {x}{x+5}\right )}{\left (x^2-3 x+e^x-4\right )^4}\right ) (x-4)^3 \log \left (\frac {x}{x+5}\right ) \left (2 \log \left (\frac {x}{x+5}\right ) x^3-50 \log \left (\frac {x}{x+5}\right ) x-5 x+20\right )}{x (x+5) \left (x^2-3 x+e^x-4\right )^4}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle 2 \int \left (\frac {2 \exp \left (\frac {(x-4)^4 \log ^2\left (\frac {x}{x+5}\right )}{\left (x^2-3 x+e^x-4\right )^4}\right ) (x-4)^4 \left (x^2-5 x-1\right ) \log ^2\left (\frac {x}{x+5}\right )}{\left (x^2-3 x+e^x-4\right )^5}-\frac {\exp \left (\frac {(x-4)^4 \log ^2\left (\frac {x}{x+5}\right )}{\left (x^2-3 x+e^x-4\right )^4}\right ) (x-4)^3 \log \left (\frac {x}{x+5}\right ) \left (2 \log \left (\frac {x}{x+5}\right ) x^3-50 \log \left (\frac {x}{x+5}\right ) x-5 x+20\right )}{x (x+5) \left (x^2-3 x+e^x-4\right )^4}\right )dx\) |
Int[(E^(((256 - 256*x + 96*x^2 - 16*x^3 + x^4)*Log[x/(5 + x)]^2)/(256 + E^ (4*x) + 768*x + 608*x^2 - 144*x^3 - 255*x^4 + 36*x^5 + 38*x^6 - 12*x^7 + x ^8 + E^(3*x)*(-16 - 12*x + 4*x^2) + E^(2*x)*(96 + 144*x + 6*x^2 - 36*x^3 + 6*x^4) + E^x*(-256 - 576*x - 240*x^2 + 180*x^3 + 60*x^4 - 36*x^5 + 4*x^6) ))*((-10240 + 2560*x + 6400*x^2 - 4800*x^3 + 1400*x^4 - 190*x^5 + 10*x^6 + E^x*(2560 - 2560*x + 960*x^2 - 160*x^3 + 10*x^4))*Log[x/(5 + x)] + (20480 *x - 21504*x^2 + 7680*x^3 - 640*x^4 - 240*x^5 + 60*x^6 - 4*x^7 + E^x*(-640 0*x + 4800*x^2 - 944*x^3 - 92*x^4 + 48*x^5 - 4*x^6))*Log[x/(5 + x)]^2))/(- 5120*x - 20224*x^2 - 26240*x^3 - 6880*x^4 + 9820*x^5 + 4445*x^6 - 2098*x^7 - 665*x^8 + 320*x^9 - 5*x^10 - 10*x^11 + x^12 + E^(5*x)*(5*x + x^2) + E^( 4*x)*(-100*x - 95*x^2 + 10*x^3 + 5*x^4) + E^(3*x)*(800*x + 1360*x^2 + 290* x^3 - 290*x^4 - 10*x^5 + 10*x^6) + E^(2*x)*(-3200*x - 7840*x^2 - 4440*x^3 + 1650*x^4 + 1200*x^5 - 300*x^6 - 40*x^7 + 10*x^8) + E^x*(6400*x + 20480*x ^2 + 19040*x^3 - 560*x^4 - 7095*x^5 - 375*x^6 + 1130*x^7 - 110*x^8 - 35*x^ 9 + 5*x^10)),x]
3.14.24.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 4.57 (sec) , antiderivative size = 262, normalized size of antiderivative = 8.73
\[{\mathrm e}^{\frac {\left (x -4\right )^{4} \left (i \pi \operatorname {csgn}\left (\frac {i x}{5+x}\right )^{3}-i \pi \operatorname {csgn}\left (\frac {i x}{5+x}\right )^{2} \operatorname {csgn}\left (i x \right )-i \pi \operatorname {csgn}\left (\frac {i x}{5+x}\right )^{2} \operatorname {csgn}\left (\frac {i}{5+x}\right )+i \pi \,\operatorname {csgn}\left (\frac {i x}{5+x}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i}{5+x}\right )-2 \ln \left (x \right )+2 \ln \left (5+x \right )\right )^{2}}{1024+3072 x +24 \,{\mathrm e}^{2 x} x^{4}+16 x^{2} {\mathrm e}^{3 x}-144 \,{\mathrm e}^{2 x} x^{3}-48 x \,{\mathrm e}^{3 x}+24 \,{\mathrm e}^{2 x} x^{2}+576 x \,{\mathrm e}^{2 x}+16 x^{6} {\mathrm e}^{x}+240 \,{\mathrm e}^{x} x^{4}-960 \,{\mathrm e}^{x} x^{2}+720 \,{\mathrm e}^{x} x^{3}-2304 \,{\mathrm e}^{x} x +4 \,{\mathrm e}^{4 x}-144 x^{5} {\mathrm e}^{x}-64 \,{\mathrm e}^{3 x}+384 \,{\mathrm e}^{2 x}-48 x^{7}+4 x^{8}+152 x^{6}+144 x^{5}-1020 x^{4}-576 x^{3}+2432 x^{2}-1024 \,{\mathrm e}^{x}}}\]
int((((-4*x^6+48*x^5-92*x^4-944*x^3+4800*x^2-6400*x)*exp(x)-4*x^7+60*x^6-2 40*x^5-640*x^4+7680*x^3-21504*x^2+20480*x)*ln(x/(5+x))^2+((10*x^4-160*x^3+ 960*x^2-2560*x+2560)*exp(x)+10*x^6-190*x^5+1400*x^4-4800*x^3+6400*x^2+2560 *x-10240)*ln(x/(5+x)))*exp((x^4-16*x^3+96*x^2-256*x+256)*ln(x/(5+x))^2/(ex p(x)^4+(4*x^2-12*x-16)*exp(x)^3+(6*x^4-36*x^3+6*x^2+144*x+96)*exp(x)^2+(4* x^6-36*x^5+60*x^4+180*x^3-240*x^2-576*x-256)*exp(x)+x^8-12*x^7+38*x^6+36*x ^5-255*x^4-144*x^3+608*x^2+768*x+256))/((x^2+5*x)*exp(x)^5+(5*x^4+10*x^3-9 5*x^2-100*x)*exp(x)^4+(10*x^6-10*x^5-290*x^4+290*x^3+1360*x^2+800*x)*exp(x )^3+(10*x^8-40*x^7-300*x^6+1200*x^5+1650*x^4-4440*x^3-7840*x^2-3200*x)*exp (x)^2+(5*x^10-35*x^9-110*x^8+1130*x^7-375*x^6-7095*x^5-560*x^4+19040*x^3+2 0480*x^2+6400*x)*exp(x)+x^12-10*x^11-5*x^10+320*x^9-665*x^8-2098*x^7+4445* x^6+9820*x^5-6880*x^4-26240*x^3-20224*x^2-5120*x),x)
exp(1/4*(x-4)^4*(I*Pi*csgn(I*x/(5+x))^3-I*Pi*csgn(I*x/(5+x))^2*csgn(I*x)-I *Pi*csgn(I*x/(5+x))^2*csgn(I/(5+x))+I*Pi*csgn(I*x/(5+x))*csgn(I*x)*csgn(I/ (5+x))-2*ln(x)+2*ln(5+x))^2/(256+768*x+6*exp(2*x)*x^4+4*x^2*exp(3*x)-36*ex p(2*x)*x^3-12*x*exp(3*x)+6*exp(2*x)*x^2+144*x*exp(2*x)+4*x^6*exp(x)+60*exp (x)*x^4-240*exp(x)*x^2+180*exp(x)*x^3-576*exp(x)*x+exp(4*x)-36*x^5*exp(x)- 16*exp(3*x)+96*exp(2*x)-12*x^7+x^8+38*x^6+36*x^5-255*x^4-144*x^3+608*x^2-2 56*exp(x)))
Leaf count of result is larger than twice the leaf count of optimal. 142 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 142, normalized size of antiderivative = 4.73 \[ \int \frac {e^{\frac {\left (256-256 x+96 x^2-16 x^3+x^4\right ) \log ^2\left (\frac {x}{5+x}\right )}{256+e^{4 x}+768 x+608 x^2-144 x^3-255 x^4+36 x^5+38 x^6-12 x^7+x^8+e^{3 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (96+144 x+6 x^2-36 x^3+6 x^4\right )+e^x \left (-256-576 x-240 x^2+180 x^3+60 x^4-36 x^5+4 x^6\right )}} \left (\left (-10240+2560 x+6400 x^2-4800 x^3+1400 x^4-190 x^5+10 x^6+e^x \left (2560-2560 x+960 x^2-160 x^3+10 x^4\right )\right ) \log \left (\frac {x}{5+x}\right )+\left (20480 x-21504 x^2+7680 x^3-640 x^4-240 x^5+60 x^6-4 x^7+e^x \left (-6400 x+4800 x^2-944 x^3-92 x^4+48 x^5-4 x^6\right )\right ) \log ^2\left (\frac {x}{5+x}\right )\right )}{-5120 x-20224 x^2-26240 x^3-6880 x^4+9820 x^5+4445 x^6-2098 x^7-665 x^8+320 x^9-5 x^{10}-10 x^{11}+x^{12}+e^{5 x} \left (5 x+x^2\right )+e^{4 x} \left (-100 x-95 x^2+10 x^3+5 x^4\right )+e^{3 x} \left (800 x+1360 x^2+290 x^3-290 x^4-10 x^5+10 x^6\right )+e^{2 x} \left (-3200 x-7840 x^2-4440 x^3+1650 x^4+1200 x^5-300 x^6-40 x^7+10 x^8\right )+e^x \left (6400 x+20480 x^2+19040 x^3-560 x^4-7095 x^5-375 x^6+1130 x^7-110 x^8-35 x^9+5 x^{10}\right )} \, dx=e^{\left (\frac {{\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} - 256 \, x + 256\right )} \log \left (\frac {x}{x + 5}\right )^{2}}{x^{8} - 12 \, x^{7} + 38 \, x^{6} + 36 \, x^{5} - 255 \, x^{4} - 144 \, x^{3} + 608 \, x^{2} + 4 \, {\left (x^{2} - 3 \, x - 4\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 6 \, x^{3} + x^{2} + 24 \, x + 16\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{6} - 9 \, x^{5} + 15 \, x^{4} + 45 \, x^{3} - 60 \, x^{2} - 144 \, x - 64\right )} e^{x} + 768 \, x + e^{\left (4 \, x\right )} + 256}\right )} \]
integrate((((-4*x^6+48*x^5-92*x^4-944*x^3+4800*x^2-6400*x)*exp(x)-4*x^7+60 *x^6-240*x^5-640*x^4+7680*x^3-21504*x^2+20480*x)*log(x/(5+x))^2+((10*x^4-1 60*x^3+960*x^2-2560*x+2560)*exp(x)+10*x^6-190*x^5+1400*x^4-4800*x^3+6400*x ^2+2560*x-10240)*log(x/(5+x)))*exp((x^4-16*x^3+96*x^2-256*x+256)*log(x/(5+ x))^2/(exp(x)^4+(4*x^2-12*x-16)*exp(x)^3+(6*x^4-36*x^3+6*x^2+144*x+96)*exp (x)^2+(4*x^6-36*x^5+60*x^4+180*x^3-240*x^2-576*x-256)*exp(x)+x^8-12*x^7+38 *x^6+36*x^5-255*x^4-144*x^3+608*x^2+768*x+256))/((x^2+5*x)*exp(x)^5+(5*x^4 +10*x^3-95*x^2-100*x)*exp(x)^4+(10*x^6-10*x^5-290*x^4+290*x^3+1360*x^2+800 *x)*exp(x)^3+(10*x^8-40*x^7-300*x^6+1200*x^5+1650*x^4-4440*x^3-7840*x^2-32 00*x)*exp(x)^2+(5*x^10-35*x^9-110*x^8+1130*x^7-375*x^6-7095*x^5-560*x^4+19 040*x^3+20480*x^2+6400*x)*exp(x)+x^12-10*x^11-5*x^10+320*x^9-665*x^8-2098* x^7+4445*x^6+9820*x^5-6880*x^4-26240*x^3-20224*x^2-5120*x),x, algorithm=\
e^((x^4 - 16*x^3 + 96*x^2 - 256*x + 256)*log(x/(x + 5))^2/(x^8 - 12*x^7 + 38*x^6 + 36*x^5 - 255*x^4 - 144*x^3 + 608*x^2 + 4*(x^2 - 3*x - 4)*e^(3*x) + 6*(x^4 - 6*x^3 + x^2 + 24*x + 16)*e^(2*x) + 4*(x^6 - 9*x^5 + 15*x^4 + 45 *x^3 - 60*x^2 - 144*x - 64)*e^x + 768*x + e^(4*x) + 256))
Leaf count of result is larger than twice the leaf count of optimal. 146 vs. \(2 (20) = 40\).
Time = 20.50 (sec) , antiderivative size = 146, normalized size of antiderivative = 4.87 \[ \int \frac {e^{\frac {\left (256-256 x+96 x^2-16 x^3+x^4\right ) \log ^2\left (\frac {x}{5+x}\right )}{256+e^{4 x}+768 x+608 x^2-144 x^3-255 x^4+36 x^5+38 x^6-12 x^7+x^8+e^{3 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (96+144 x+6 x^2-36 x^3+6 x^4\right )+e^x \left (-256-576 x-240 x^2+180 x^3+60 x^4-36 x^5+4 x^6\right )}} \left (\left (-10240+2560 x+6400 x^2-4800 x^3+1400 x^4-190 x^5+10 x^6+e^x \left (2560-2560 x+960 x^2-160 x^3+10 x^4\right )\right ) \log \left (\frac {x}{5+x}\right )+\left (20480 x-21504 x^2+7680 x^3-640 x^4-240 x^5+60 x^6-4 x^7+e^x \left (-6400 x+4800 x^2-944 x^3-92 x^4+48 x^5-4 x^6\right )\right ) \log ^2\left (\frac {x}{5+x}\right )\right )}{-5120 x-20224 x^2-26240 x^3-6880 x^4+9820 x^5+4445 x^6-2098 x^7-665 x^8+320 x^9-5 x^{10}-10 x^{11}+x^{12}+e^{5 x} \left (5 x+x^2\right )+e^{4 x} \left (-100 x-95 x^2+10 x^3+5 x^4\right )+e^{3 x} \left (800 x+1360 x^2+290 x^3-290 x^4-10 x^5+10 x^6\right )+e^{2 x} \left (-3200 x-7840 x^2-4440 x^3+1650 x^4+1200 x^5-300 x^6-40 x^7+10 x^8\right )+e^x \left (6400 x+20480 x^2+19040 x^3-560 x^4-7095 x^5-375 x^6+1130 x^7-110 x^8-35 x^9+5 x^{10}\right )} \, dx=e^{\frac {\left (x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256\right ) \log {\left (\frac {x}{x + 5} \right )}^{2}}{x^{8} - 12 x^{7} + 38 x^{6} + 36 x^{5} - 255 x^{4} - 144 x^{3} + 608 x^{2} + 768 x + \left (4 x^{2} - 12 x - 16\right ) e^{3 x} + \left (6 x^{4} - 36 x^{3} + 6 x^{2} + 144 x + 96\right ) e^{2 x} + \left (4 x^{6} - 36 x^{5} + 60 x^{4} + 180 x^{3} - 240 x^{2} - 576 x - 256\right ) e^{x} + e^{4 x} + 256}} \]
integrate((((-4*x**6+48*x**5-92*x**4-944*x**3+4800*x**2-6400*x)*exp(x)-4*x **7+60*x**6-240*x**5-640*x**4+7680*x**3-21504*x**2+20480*x)*ln(x/(5+x))**2 +((10*x**4-160*x**3+960*x**2-2560*x+2560)*exp(x)+10*x**6-190*x**5+1400*x** 4-4800*x**3+6400*x**2+2560*x-10240)*ln(x/(5+x)))*exp((x**4-16*x**3+96*x**2 -256*x+256)*ln(x/(5+x))**2/(exp(x)**4+(4*x**2-12*x-16)*exp(x)**3+(6*x**4-3 6*x**3+6*x**2+144*x+96)*exp(x)**2+(4*x**6-36*x**5+60*x**4+180*x**3-240*x** 2-576*x-256)*exp(x)+x**8-12*x**7+38*x**6+36*x**5-255*x**4-144*x**3+608*x** 2+768*x+256))/((x**2+5*x)*exp(x)**5+(5*x**4+10*x**3-95*x**2-100*x)*exp(x)* *4+(10*x**6-10*x**5-290*x**4+290*x**3+1360*x**2+800*x)*exp(x)**3+(10*x**8- 40*x**7-300*x**6+1200*x**5+1650*x**4-4440*x**3-7840*x**2-3200*x)*exp(x)**2 +(5*x**10-35*x**9-110*x**8+1130*x**7-375*x**6-7095*x**5-560*x**4+19040*x** 3+20480*x**2+6400*x)*exp(x)+x**12-10*x**11-5*x**10+320*x**9-665*x**8-2098* x**7+4445*x**6+9820*x**5-6880*x**4-26240*x**3-20224*x**2-5120*x),x)
exp((x**4 - 16*x**3 + 96*x**2 - 256*x + 256)*log(x/(x + 5))**2/(x**8 - 12* x**7 + 38*x**6 + 36*x**5 - 255*x**4 - 144*x**3 + 608*x**2 + 768*x + (4*x** 2 - 12*x - 16)*exp(3*x) + (6*x**4 - 36*x**3 + 6*x**2 + 144*x + 96)*exp(2*x ) + (4*x**6 - 36*x**5 + 60*x**4 + 180*x**3 - 240*x**2 - 576*x - 256)*exp(x ) + exp(4*x) + 256))
Leaf count of result is larger than twice the leaf count of optimal. 2629 vs. \(2 (25) = 50\).
Time = 24.27 (sec) , antiderivative size = 2629, normalized size of antiderivative = 87.63 \[ \int \frac {e^{\frac {\left (256-256 x+96 x^2-16 x^3+x^4\right ) \log ^2\left (\frac {x}{5+x}\right )}{256+e^{4 x}+768 x+608 x^2-144 x^3-255 x^4+36 x^5+38 x^6-12 x^7+x^8+e^{3 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (96+144 x+6 x^2-36 x^3+6 x^4\right )+e^x \left (-256-576 x-240 x^2+180 x^3+60 x^4-36 x^5+4 x^6\right )}} \left (\left (-10240+2560 x+6400 x^2-4800 x^3+1400 x^4-190 x^5+10 x^6+e^x \left (2560-2560 x+960 x^2-160 x^3+10 x^4\right )\right ) \log \left (\frac {x}{5+x}\right )+\left (20480 x-21504 x^2+7680 x^3-640 x^4-240 x^5+60 x^6-4 x^7+e^x \left (-6400 x+4800 x^2-944 x^3-92 x^4+48 x^5-4 x^6\right )\right ) \log ^2\left (\frac {x}{5+x}\right )\right )}{-5120 x-20224 x^2-26240 x^3-6880 x^4+9820 x^5+4445 x^6-2098 x^7-665 x^8+320 x^9-5 x^{10}-10 x^{11}+x^{12}+e^{5 x} \left (5 x+x^2\right )+e^{4 x} \left (-100 x-95 x^2+10 x^3+5 x^4\right )+e^{3 x} \left (800 x+1360 x^2+290 x^3-290 x^4-10 x^5+10 x^6\right )+e^{2 x} \left (-3200 x-7840 x^2-4440 x^3+1650 x^4+1200 x^5-300 x^6-40 x^7+10 x^8\right )+e^x \left (6400 x+20480 x^2+19040 x^3-560 x^4-7095 x^5-375 x^6+1130 x^7-110 x^8-35 x^9+5 x^{10}\right )} \, dx=\text {Too large to display} \]
integrate((((-4*x^6+48*x^5-92*x^4-944*x^3+4800*x^2-6400*x)*exp(x)-4*x^7+60 *x^6-240*x^5-640*x^4+7680*x^3-21504*x^2+20480*x)*log(x/(5+x))^2+((10*x^4-1 60*x^3+960*x^2-2560*x+2560)*exp(x)+10*x^6-190*x^5+1400*x^4-4800*x^3+6400*x ^2+2560*x-10240)*log(x/(5+x)))*exp((x^4-16*x^3+96*x^2-256*x+256)*log(x/(5+ x))^2/(exp(x)^4+(4*x^2-12*x-16)*exp(x)^3+(6*x^4-36*x^3+6*x^2+144*x+96)*exp (x)^2+(4*x^6-36*x^5+60*x^4+180*x^3-240*x^2-576*x-256)*exp(x)+x^8-12*x^7+38 *x^6+36*x^5-255*x^4-144*x^3+608*x^2+768*x+256))/((x^2+5*x)*exp(x)^5+(5*x^4 +10*x^3-95*x^2-100*x)*exp(x)^4+(10*x^6-10*x^5-290*x^4+290*x^3+1360*x^2+800 *x)*exp(x)^3+(10*x^8-40*x^7-300*x^6+1200*x^5+1650*x^4-4440*x^3-7840*x^2-32 00*x)*exp(x)^2+(5*x^10-35*x^9-110*x^8+1130*x^7-375*x^6-7095*x^5-560*x^4+19 040*x^3+20480*x^2+6400*x)*exp(x)+x^12-10*x^11-5*x^10+320*x^9-665*x^8-2098* x^7+4445*x^6+9820*x^5-6880*x^4-26240*x^3-20224*x^2-5120*x),x, algorithm=\
e^(10*x*e^x*log(x + 5)^2/(x^8 - 12*x^7 + 38*x^6 + 36*x^5 - 255*x^4 - 144*x ^3 + 608*x^2 + 4*(x^2 - 3*x - 4)*e^(3*x) + 6*(x^4 - 6*x^3 + x^2 + 24*x + 1 6)*e^(2*x) + 4*(x^6 - 9*x^5 + 15*x^4 + 45*x^3 - 60*x^2 - 144*x - 64)*e^x + 768*x + e^(4*x) + 256) - 20*x*e^x*log(x + 5)*log(x)/(x^8 - 12*x^7 + 38*x^ 6 + 36*x^5 - 255*x^4 - 144*x^3 + 608*x^2 + 4*(x^2 - 3*x - 4)*e^(3*x) + 6*( x^4 - 6*x^3 + x^2 + 24*x + 16)*e^(2*x) + 4*(x^6 - 9*x^5 + 15*x^4 + 45*x^3 - 60*x^2 - 144*x - 64)*e^x + 768*x + e^(4*x) + 256) + 10*x*e^x*log(x)^2/(x ^8 - 12*x^7 + 38*x^6 + 36*x^5 - 255*x^4 - 144*x^3 + 608*x^2 + 4*(x^2 - 3*x - 4)*e^(3*x) + 6*(x^4 - 6*x^3 + x^2 + 24*x + 16)*e^(2*x) + 4*(x^6 - 9*x^5 + 15*x^4 + 45*x^3 - 60*x^2 - 144*x - 64)*e^x + 768*x + e^(4*x) + 256) - 1 25*x*log(x + 5)^2/(x^8 - 12*x^7 + 38*x^6 + 36*x^5 - 255*x^4 - 144*x^3 + 60 8*x^2 + 4*(x^2 - 3*x - 4)*e^(3*x) + 6*(x^4 - 6*x^3 + x^2 + 24*x + 16)*e^(2 *x) + 4*(x^6 - 9*x^5 + 15*x^4 + 45*x^3 - 60*x^2 - 144*x - 64)*e^x + 768*x + e^(4*x) + 256) - 10*x*log(x + 5)^2/(x^6 - 9*x^5 + 15*x^4 + 45*x^3 - 60*x ^2 + 3*(x^2 - 3*x - 4)*e^(2*x) + 3*(x^4 - 6*x^3 + x^2 + 24*x + 16)*e^x - 1 44*x + e^(3*x) - 64) + e^(2*x)*log(x + 5)^2/(x^8 - 12*x^7 + 38*x^6 + 36*x^ 5 - 255*x^4 - 144*x^3 + 608*x^2 + 4*(x^2 - 3*x - 4)*e^(3*x) + 6*(x^4 - 6*x ^3 + x^2 + 24*x + 16)*e^(2*x) + 4*(x^6 - 9*x^5 + 15*x^4 + 45*x^3 - 60*x^2 - 144*x - 64)*e^x + 768*x + e^(4*x) + 256) - 65*e^x*log(x + 5)^2/(x^8 - 12 *x^7 + 38*x^6 + 36*x^5 - 255*x^4 - 144*x^3 + 608*x^2 + 4*(x^2 - 3*x - 4...
\[ \int \frac {e^{\frac {\left (256-256 x+96 x^2-16 x^3+x^4\right ) \log ^2\left (\frac {x}{5+x}\right )}{256+e^{4 x}+768 x+608 x^2-144 x^3-255 x^4+36 x^5+38 x^6-12 x^7+x^8+e^{3 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (96+144 x+6 x^2-36 x^3+6 x^4\right )+e^x \left (-256-576 x-240 x^2+180 x^3+60 x^4-36 x^5+4 x^6\right )}} \left (\left (-10240+2560 x+6400 x^2-4800 x^3+1400 x^4-190 x^5+10 x^6+e^x \left (2560-2560 x+960 x^2-160 x^3+10 x^4\right )\right ) \log \left (\frac {x}{5+x}\right )+\left (20480 x-21504 x^2+7680 x^3-640 x^4-240 x^5+60 x^6-4 x^7+e^x \left (-6400 x+4800 x^2-944 x^3-92 x^4+48 x^5-4 x^6\right )\right ) \log ^2\left (\frac {x}{5+x}\right )\right )}{-5120 x-20224 x^2-26240 x^3-6880 x^4+9820 x^5+4445 x^6-2098 x^7-665 x^8+320 x^9-5 x^{10}-10 x^{11}+x^{12}+e^{5 x} \left (5 x+x^2\right )+e^{4 x} \left (-100 x-95 x^2+10 x^3+5 x^4\right )+e^{3 x} \left (800 x+1360 x^2+290 x^3-290 x^4-10 x^5+10 x^6\right )+e^{2 x} \left (-3200 x-7840 x^2-4440 x^3+1650 x^4+1200 x^5-300 x^6-40 x^7+10 x^8\right )+e^x \left (6400 x+20480 x^2+19040 x^3-560 x^4-7095 x^5-375 x^6+1130 x^7-110 x^8-35 x^9+5 x^{10}\right )} \, dx=\int { -\frac {2 \, {\left (2 \, {\left (x^{7} - 15 \, x^{6} + 60 \, x^{5} + 160 \, x^{4} - 1920 \, x^{3} + 5376 \, x^{2} + {\left (x^{6} - 12 \, x^{5} + 23 \, x^{4} + 236 \, x^{3} - 1200 \, x^{2} + 1600 \, x\right )} e^{x} - 5120 \, x\right )} \log \left (\frac {x}{x + 5}\right )^{2} - 5 \, {\left (x^{6} - 19 \, x^{5} + 140 \, x^{4} - 480 \, x^{3} + 640 \, x^{2} + {\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} - 256 \, x + 256\right )} e^{x} + 256 \, x - 1024\right )} \log \left (\frac {x}{x + 5}\right )\right )} e^{\left (\frac {{\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} - 256 \, x + 256\right )} \log \left (\frac {x}{x + 5}\right )^{2}}{x^{8} - 12 \, x^{7} + 38 \, x^{6} + 36 \, x^{5} - 255 \, x^{4} - 144 \, x^{3} + 608 \, x^{2} + 4 \, {\left (x^{2} - 3 \, x - 4\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 6 \, x^{3} + x^{2} + 24 \, x + 16\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{6} - 9 \, x^{5} + 15 \, x^{4} + 45 \, x^{3} - 60 \, x^{2} - 144 \, x - 64\right )} e^{x} + 768 \, x + e^{\left (4 \, x\right )} + 256}\right )}}{x^{12} - 10 \, x^{11} - 5 \, x^{10} + 320 \, x^{9} - 665 \, x^{8} - 2098 \, x^{7} + 4445 \, x^{6} + 9820 \, x^{5} - 6880 \, x^{4} - 26240 \, x^{3} - 20224 \, x^{2} + {\left (x^{2} + 5 \, x\right )} e^{\left (5 \, x\right )} + 5 \, {\left (x^{4} + 2 \, x^{3} - 19 \, x^{2} - 20 \, x\right )} e^{\left (4 \, x\right )} + 10 \, {\left (x^{6} - x^{5} - 29 \, x^{4} + 29 \, x^{3} + 136 \, x^{2} + 80 \, x\right )} e^{\left (3 \, x\right )} + 10 \, {\left (x^{8} - 4 \, x^{7} - 30 \, x^{6} + 120 \, x^{5} + 165 \, x^{4} - 444 \, x^{3} - 784 \, x^{2} - 320 \, x\right )} e^{\left (2 \, x\right )} + 5 \, {\left (x^{10} - 7 \, x^{9} - 22 \, x^{8} + 226 \, x^{7} - 75 \, x^{6} - 1419 \, x^{5} - 112 \, x^{4} + 3808 \, x^{3} + 4096 \, x^{2} + 1280 \, x\right )} e^{x} - 5120 \, x} \,d x } \]
integrate((((-4*x^6+48*x^5-92*x^4-944*x^3+4800*x^2-6400*x)*exp(x)-4*x^7+60 *x^6-240*x^5-640*x^4+7680*x^3-21504*x^2+20480*x)*log(x/(5+x))^2+((10*x^4-1 60*x^3+960*x^2-2560*x+2560)*exp(x)+10*x^6-190*x^5+1400*x^4-4800*x^3+6400*x ^2+2560*x-10240)*log(x/(5+x)))*exp((x^4-16*x^3+96*x^2-256*x+256)*log(x/(5+ x))^2/(exp(x)^4+(4*x^2-12*x-16)*exp(x)^3+(6*x^4-36*x^3+6*x^2+144*x+96)*exp (x)^2+(4*x^6-36*x^5+60*x^4+180*x^3-240*x^2-576*x-256)*exp(x)+x^8-12*x^7+38 *x^6+36*x^5-255*x^4-144*x^3+608*x^2+768*x+256))/((x^2+5*x)*exp(x)^5+(5*x^4 +10*x^3-95*x^2-100*x)*exp(x)^4+(10*x^6-10*x^5-290*x^4+290*x^3+1360*x^2+800 *x)*exp(x)^3+(10*x^8-40*x^7-300*x^6+1200*x^5+1650*x^4-4440*x^3-7840*x^2-32 00*x)*exp(x)^2+(5*x^10-35*x^9-110*x^8+1130*x^7-375*x^6-7095*x^5-560*x^4+19 040*x^3+20480*x^2+6400*x)*exp(x)+x^12-10*x^11-5*x^10+320*x^9-665*x^8-2098* x^7+4445*x^6+9820*x^5-6880*x^4-26240*x^3-20224*x^2-5120*x),x, algorithm=\
integrate(-2*(2*(x^7 - 15*x^6 + 60*x^5 + 160*x^4 - 1920*x^3 + 5376*x^2 + ( x^6 - 12*x^5 + 23*x^4 + 236*x^3 - 1200*x^2 + 1600*x)*e^x - 5120*x)*log(x/( x + 5))^2 - 5*(x^6 - 19*x^5 + 140*x^4 - 480*x^3 + 640*x^2 + (x^4 - 16*x^3 + 96*x^2 - 256*x + 256)*e^x + 256*x - 1024)*log(x/(x + 5)))*e^((x^4 - 16*x ^3 + 96*x^2 - 256*x + 256)*log(x/(x + 5))^2/(x^8 - 12*x^7 + 38*x^6 + 36*x^ 5 - 255*x^4 - 144*x^3 + 608*x^2 + 4*(x^2 - 3*x - 4)*e^(3*x) + 6*(x^4 - 6*x ^3 + x^2 + 24*x + 16)*e^(2*x) + 4*(x^6 - 9*x^5 + 15*x^4 + 45*x^3 - 60*x^2 - 144*x - 64)*e^x + 768*x + e^(4*x) + 256))/(x^12 - 10*x^11 - 5*x^10 + 320 *x^9 - 665*x^8 - 2098*x^7 + 4445*x^6 + 9820*x^5 - 6880*x^4 - 26240*x^3 - 2 0224*x^2 + (x^2 + 5*x)*e^(5*x) + 5*(x^4 + 2*x^3 - 19*x^2 - 20*x)*e^(4*x) + 10*(x^6 - x^5 - 29*x^4 + 29*x^3 + 136*x^2 + 80*x)*e^(3*x) + 10*(x^8 - 4*x ^7 - 30*x^6 + 120*x^5 + 165*x^4 - 444*x^3 - 784*x^2 - 320*x)*e^(2*x) + 5*( x^10 - 7*x^9 - 22*x^8 + 226*x^7 - 75*x^6 - 1419*x^5 - 112*x^4 + 3808*x^3 + 4096*x^2 + 1280*x)*e^x - 5120*x), x)
Time = 15.91 (sec) , antiderivative size = 825, normalized size of antiderivative = 27.50 \[ \int \frac {e^{\frac {\left (256-256 x+96 x^2-16 x^3+x^4\right ) \log ^2\left (\frac {x}{5+x}\right )}{256+e^{4 x}+768 x+608 x^2-144 x^3-255 x^4+36 x^5+38 x^6-12 x^7+x^8+e^{3 x} \left (-16-12 x+4 x^2\right )+e^{2 x} \left (96+144 x+6 x^2-36 x^3+6 x^4\right )+e^x \left (-256-576 x-240 x^2+180 x^3+60 x^4-36 x^5+4 x^6\right )}} \left (\left (-10240+2560 x+6400 x^2-4800 x^3+1400 x^4-190 x^5+10 x^6+e^x \left (2560-2560 x+960 x^2-160 x^3+10 x^4\right )\right ) \log \left (\frac {x}{5+x}\right )+\left (20480 x-21504 x^2+7680 x^3-640 x^4-240 x^5+60 x^6-4 x^7+e^x \left (-6400 x+4800 x^2-944 x^3-92 x^4+48 x^5-4 x^6\right )\right ) \log ^2\left (\frac {x}{5+x}\right )\right )}{-5120 x-20224 x^2-26240 x^3-6880 x^4+9820 x^5+4445 x^6-2098 x^7-665 x^8+320 x^9-5 x^{10}-10 x^{11}+x^{12}+e^{5 x} \left (5 x+x^2\right )+e^{4 x} \left (-100 x-95 x^2+10 x^3+5 x^4\right )+e^{3 x} \left (800 x+1360 x^2+290 x^3-290 x^4-10 x^5+10 x^6\right )+e^{2 x} \left (-3200 x-7840 x^2-4440 x^3+1650 x^4+1200 x^5-300 x^6-40 x^7+10 x^8\right )+e^x \left (6400 x+20480 x^2+19040 x^3-560 x^4-7095 x^5-375 x^6+1130 x^7-110 x^8-35 x^9+5 x^{10}\right )} \, dx =\text {Too large to display} \]
int(-(exp((log(x/(x + 5))^2*(96*x^2 - 256*x - 16*x^3 + x^4 + 256))/(768*x + exp(4*x) - exp(3*x)*(12*x - 4*x^2 + 16) + exp(2*x)*(144*x + 6*x^2 - 36*x ^3 + 6*x^4 + 96) - exp(x)*(576*x + 240*x^2 - 180*x^3 - 60*x^4 + 36*x^5 - 4 *x^6 + 256) + 608*x^2 - 144*x^3 - 255*x^4 + 36*x^5 + 38*x^6 - 12*x^7 + x^8 + 256))*(log(x/(x + 5))*(2560*x + exp(x)*(960*x^2 - 2560*x - 160*x^3 + 10 *x^4 + 2560) + 6400*x^2 - 4800*x^3 + 1400*x^4 - 190*x^5 + 10*x^6 - 10240) - log(x/(x + 5))^2*(exp(x)*(6400*x - 4800*x^2 + 944*x^3 + 92*x^4 - 48*x^5 + 4*x^6) - 20480*x + 21504*x^2 - 7680*x^3 + 640*x^4 + 240*x^5 - 60*x^6 + 4 *x^7)))/(5120*x + exp(2*x)*(3200*x + 7840*x^2 + 4440*x^3 - 1650*x^4 - 1200 *x^5 + 300*x^6 + 40*x^7 - 10*x^8) - exp(x)*(6400*x + 20480*x^2 + 19040*x^3 - 560*x^4 - 7095*x^5 - 375*x^6 + 1130*x^7 - 110*x^8 - 35*x^9 + 5*x^10) + exp(4*x)*(100*x + 95*x^2 - 10*x^3 - 5*x^4) - exp(5*x)*(5*x + x^2) + 20224* x^2 + 26240*x^3 + 6880*x^4 - 9820*x^5 - 4445*x^6 + 2098*x^7 + 665*x^8 - 32 0*x^9 + 5*x^10 + 10*x^11 - x^12 - exp(3*x)*(800*x + 1360*x^2 + 290*x^3 - 2 90*x^4 - 10*x^5 + 10*x^6)),x)
exp((256*log(x/(x + 5))^2)/(768*x + 96*exp(2*x) - 16*exp(3*x) + exp(4*x) - 256*exp(x) + 144*x*exp(2*x) - 12*x*exp(3*x) - 240*x^2*exp(x) + 180*x^3*ex p(x) + 60*x^4*exp(x) - 36*x^5*exp(x) + 4*x^6*exp(x) + 6*x^2*exp(2*x) + 4*x ^2*exp(3*x) - 36*x^3*exp(2*x) + 6*x^4*exp(2*x) - 576*x*exp(x) + 608*x^2 - 144*x^3 - 255*x^4 + 36*x^5 + 38*x^6 - 12*x^7 + x^8 + 256))*exp(-(256*x*log (x/(x + 5))^2)/(768*x + 96*exp(2*x) - 16*exp(3*x) + exp(4*x) - 256*exp(x) + 144*x*exp(2*x) - 12*x*exp(3*x) - 240*x^2*exp(x) + 180*x^3*exp(x) + 60*x^ 4*exp(x) - 36*x^5*exp(x) + 4*x^6*exp(x) + 6*x^2*exp(2*x) + 4*x^2*exp(3*x) - 36*x^3*exp(2*x) + 6*x^4*exp(2*x) - 576*x*exp(x) + 608*x^2 - 144*x^3 - 25 5*x^4 + 36*x^5 + 38*x^6 - 12*x^7 + x^8 + 256))*exp((x^4*log(x/(x + 5))^2)/ (768*x + 96*exp(2*x) - 16*exp(3*x) + exp(4*x) - 256*exp(x) + 144*x*exp(2*x ) - 12*x*exp(3*x) - 240*x^2*exp(x) + 180*x^3*exp(x) + 60*x^4*exp(x) - 36*x ^5*exp(x) + 4*x^6*exp(x) + 6*x^2*exp(2*x) + 4*x^2*exp(3*x) - 36*x^3*exp(2* x) + 6*x^4*exp(2*x) - 576*x*exp(x) + 608*x^2 - 144*x^3 - 255*x^4 + 36*x^5 + 38*x^6 - 12*x^7 + x^8 + 256))*exp(-(16*x^3*log(x/(x + 5))^2)/(768*x + 96 *exp(2*x) - 16*exp(3*x) + exp(4*x) - 256*exp(x) + 144*x*exp(2*x) - 12*x*ex p(3*x) - 240*x^2*exp(x) + 180*x^3*exp(x) + 60*x^4*exp(x) - 36*x^5*exp(x) + 4*x^6*exp(x) + 6*x^2*exp(2*x) + 4*x^2*exp(3*x) - 36*x^3*exp(2*x) + 6*x^4* exp(2*x) - 576*x*exp(x) + 608*x^2 - 144*x^3 - 255*x^4 + 36*x^5 + 38*x^6 - 12*x^7 + x^8 + 256))*exp((96*x^2*log(x/(x + 5))^2)/(768*x + 96*exp(2*x)...