3.74.24 \(\int \frac {e^{\frac {(256-256 x+96 x^2-16 x^3+x^4) \log ^2(\frac {x}{5+x})}{256+e^{4 x}+768 x+608 x^2-144 x^3-255 x^4+36 x^5+38 x^6-12 x^7+x^8+e^{3 x} (-16-12 x+4 x^2)+e^{2 x} (96+144 x+6 x^2-36 x^3+6 x^4)+e^x (-256-576 x-240 x^2+180 x^3+60 x^4-36 x^5+4 x^6)}} ((-10240+2560 x+6400 x^2-4800 x^3+1400 x^4-190 x^5+10 x^6+e^x (2560-2560 x+960 x^2-160 x^3+10 x^4)) \log (\frac {x}{5+x})+(20480 x-21504 x^2+7680 x^3-640 x^4-240 x^5+60 x^6-4 x^7+e^x (-6400 x+4800 x^2-944 x^3-92 x^4+48 x^5-4 x^6)) \log ^2(\frac {x}{5+x}))}{-5120 x-20224 x^2-26240 x^3-6880 x^4+9820 x^5+4445 x^6-2098 x^7-665 x^8+320 x^9-5 x^{10}-10 x^{11}+x^{12}+e^{5 x} (5 x+x^2)+e^{4 x} (-100 x-95 x^2+10 x^3+5 x^4)+e^{3 x} (800 x+1360 x^2+290 x^3-290 x^4-10 x^5+10 x^6)+e^{2 x} (-3200 x-7840 x^2-4440 x^3+1650 x^4+1200 x^5-300 x^6-40 x^7+10 x^8)+e^x (6400 x+20480 x^2+19040 x^3-560 x^4-7095 x^5-375 x^6+1130 x^7-110 x^8-35 x^9+5 x^{10})} \, dx\)
Optimal. Leaf size=30 \[ e^{\frac {\log ^2\left (\frac {x}{5+x}\right )}{\left (1-\frac {e^x}{4-x}+x\right )^4}} \]
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Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
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)] + (2
0480*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 - 4
440*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 - 7
095*x^5 - 375*x^6 + 1130*x^7 - 110*x^8 - 35*x^9 + 5*x^10)),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [A] time = 0.32, size = 31, normalized size = 1.03 \begin {gather*} e^{\frac {(-4+x)^4 \log ^2\left (\frac {x}{5+x}\right )}{\left (-4+e^x-3 x+x^2\right )^4}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(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*(-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 - 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]
[Out]
E^(((-4 + x)^4*Log[x/(5 + x)]^2)/(-4 + E^x - 3*x + x^2)^4)
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fricas [B] time = 0.77, size = 142, normalized size = 4.73 \begin {gather*} 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 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
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^4-160*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)*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)*ex
p(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^2-3200*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, algo
rithm="fricas")
[Out]
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))
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
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^4-160*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)*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)*ex
p(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^2-3200*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, algo
rithm="giac")
[Out]
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 - 12
00*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 - 20224*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 - 51
20*x), x)
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maple [C] time = 0.80, size = 262, normalized size = 8.73
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result |
size |
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\({\mathrm e}^{\frac {\left (x -4\right )^{4} \left (i \pi \mathrm {csgn}\left (\frac {i x}{5+x}\right )^{3}-i \pi \mathrm {csgn}\left (\frac {i x}{5+x}\right )^{2} \mathrm {csgn}\left (i x \right )-i \pi \mathrm {csgn}\left (\frac {i x}{5+x}\right )^{2} \mathrm {csgn}\left (\frac {i}{5+x}\right )+i \pi \,\mathrm {csgn}\left (\frac {i x}{5+x}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{5+x}\right )-2 \ln \relax (x )+2 \ln \left (5+x \right )\right )^{2}}{1024+3072 x +4 \,{\mathrm e}^{4 x}-144 x^{5} {\mathrm e}^{x}-64 \,{\mathrm e}^{3 x}+384 \,{\mathrm e}^{2 x}-48 x^{7}+4 x^{8}+152 x^{6}+144 x^{5}-1020 x^{4}-576 x^{3}+2432 x^{2}-1024 \,{\mathrm e}^{x}+16 x^{2} {\mathrm e}^{3 x}-144 \,{\mathrm e}^{2 x} x^{3}-48 x \,{\mathrm e}^{3 x}+24 \,{\mathrm e}^{2 x} x^{2}+576 x \,{\mathrm e}^{2 x}+16 x^{6} {\mathrm e}^{x}+240 \,{\mathrm e}^{x} x^{4}-960 \,{\mathrm e}^{x} x^{2}+720 \,{\mathrm e}^{x} x^{3}-2304 \,{\mathrm e}^{x} x +24 \,{\mathrm e}^{2 x} x^{4}}}\) |
\(262\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
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^6-240*x^5-640*x^4+7680*x^3-21504*x^2+20
480*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+25
60*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^4-36*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^2-3200*
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^12-1
0*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,method=_RETURN
VERBOSE)
[Out]
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+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^2-256*exp(x)+4*x^2*exp(3*x)-36*exp(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+6
*exp(2*x)*x^4))
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maxima [B] time = 29.51, size = 2629, normalized size = 87.63 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
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^4-160*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)*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)*ex
p(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^2-3200*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, algo
rithm="maxima")
[Out]
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 + 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) - 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 + 6
08*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) - 125*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) - 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 + 1
6)*e^x - 144*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 + 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) - 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)*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) - 2*e^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 - 144*x + e^(
3*x) - 64) + 250*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) + 20*x*log(x + 5)*log(x)/(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 - 144*x + e^(3*x) - 64) - 2*e^(2*x)*log(x + 5)*lo
g(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) + 130*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) + 4*e^x*log(x + 5)*log(x)/(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 - 144*x + e^(3*x) - 64) - 125*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) - 10*x*lo
g(x)^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 - 144*x + e^(3*x) - 64) + e^(2*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 - 6
0*x^2 - 144*x - 64)*e^x + 768*x + e^(4*x) + 256) - 65*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) - 2*e^x*log(x)^2/(x^6 - 9*x^5 + 15*x^4 + 4
5*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 - 144*x + e^(3*x) - 64) + 5
00*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*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 - 144*x + e^(3*x) - 64) + log(x + 5)^2/(x^4 - 6*x^3 + x^2 + 2*(x^2 - 3*x - 4)
*e^x + 24*x + e^(2*x) + 16) - 1000*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) - 130*log(x + 5)*log(x)/(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 - 144*x + e^(3*x) - 64) - 2*log(x
+ 5)*log(x)/(x^4 - 6*x^3 + x^2 + 2*(x^2 - 3*x - 4)*e^x + 24*x + e^(2*x) + 16) + 500*log(x)^2/(x^8 - 12*x^7 + 3
8*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*log(x)^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 - 14
4*x + e^(3*x) - 64) + log(x)^2/(x^4 - 6*x^3 + x^2 + 2*(x^2 - 3*x - 4)*e^x + 24*x + e^(2*x) + 16))
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mupad [B] time = 6.14, size = 825, normalized size = 27.50 \begin {gather*} {\mathrm {e}}^{\frac {256\,{\ln \left (\frac {x}{x+5}\right )}^2}{768\,x+96\,{\mathrm {e}}^{2\,x}-16\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{4\,x}-256\,{\mathrm {e}}^x+144\,x\,{\mathrm {e}}^{2\,x}-12\,x\,{\mathrm {e}}^{3\,x}-240\,x^2\,{\mathrm {e}}^x+180\,x^3\,{\mathrm {e}}^x+60\,x^4\,{\mathrm {e}}^x-36\,x^5\,{\mathrm {e}}^x+4\,x^6\,{\mathrm {e}}^x+6\,x^2\,{\mathrm {e}}^{2\,x}+4\,x^2\,{\mathrm {e}}^{3\,x}-36\,x^3\,{\mathrm {e}}^{2\,x}+6\,x^4\,{\mathrm {e}}^{2\,x}-576\,x\,{\mathrm {e}}^x+608\,x^2-144\,x^3-255\,x^4+36\,x^5+38\,x^6-12\,x^7+x^8+256}}\,{\mathrm {e}}^{-\frac {256\,x\,{\ln \left (\frac {x}{x+5}\right )}^2}{768\,x+96\,{\mathrm {e}}^{2\,x}-16\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{4\,x}-256\,{\mathrm {e}}^x+144\,x\,{\mathrm {e}}^{2\,x}-12\,x\,{\mathrm {e}}^{3\,x}-240\,x^2\,{\mathrm {e}}^x+180\,x^3\,{\mathrm {e}}^x+60\,x^4\,{\mathrm {e}}^x-36\,x^5\,{\mathrm {e}}^x+4\,x^6\,{\mathrm {e}}^x+6\,x^2\,{\mathrm {e}}^{2\,x}+4\,x^2\,{\mathrm {e}}^{3\,x}-36\,x^3\,{\mathrm {e}}^{2\,x}+6\,x^4\,{\mathrm {e}}^{2\,x}-576\,x\,{\mathrm {e}}^x+608\,x^2-144\,x^3-255\,x^4+36\,x^5+38\,x^6-12\,x^7+x^8+256}}\,{\mathrm {e}}^{\frac {x^4\,{\ln \left (\frac {x}{x+5}\right )}^2}{768\,x+96\,{\mathrm {e}}^{2\,x}-16\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{4\,x}-256\,{\mathrm {e}}^x+144\,x\,{\mathrm {e}}^{2\,x}-12\,x\,{\mathrm {e}}^{3\,x}-240\,x^2\,{\mathrm {e}}^x+180\,x^3\,{\mathrm {e}}^x+60\,x^4\,{\mathrm {e}}^x-36\,x^5\,{\mathrm {e}}^x+4\,x^6\,{\mathrm {e}}^x+6\,x^2\,{\mathrm {e}}^{2\,x}+4\,x^2\,{\mathrm {e}}^{3\,x}-36\,x^3\,{\mathrm {e}}^{2\,x}+6\,x^4\,{\mathrm {e}}^{2\,x}-576\,x\,{\mathrm {e}}^x+608\,x^2-144\,x^3-255\,x^4+36\,x^5+38\,x^6-12\,x^7+x^8+256}}\,{\mathrm {e}}^{-\frac {16\,x^3\,{\ln \left (\frac {x}{x+5}\right )}^2}{768\,x+96\,{\mathrm {e}}^{2\,x}-16\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{4\,x}-256\,{\mathrm {e}}^x+144\,x\,{\mathrm {e}}^{2\,x}-12\,x\,{\mathrm {e}}^{3\,x}-240\,x^2\,{\mathrm {e}}^x+180\,x^3\,{\mathrm {e}}^x+60\,x^4\,{\mathrm {e}}^x-36\,x^5\,{\mathrm {e}}^x+4\,x^6\,{\mathrm {e}}^x+6\,x^2\,{\mathrm {e}}^{2\,x}+4\,x^2\,{\mathrm {e}}^{3\,x}-36\,x^3\,{\mathrm {e}}^{2\,x}+6\,x^4\,{\mathrm {e}}^{2\,x}-576\,x\,{\mathrm {e}}^x+608\,x^2-144\,x^3-255\,x^4+36\,x^5+38\,x^6-12\,x^7+x^8+256}}\,{\mathrm {e}}^{\frac {96\,x^2\,{\ln \left (\frac {x}{x+5}\right )}^2}{768\,x+96\,{\mathrm {e}}^{2\,x}-16\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{4\,x}-256\,{\mathrm {e}}^x+144\,x\,{\mathrm {e}}^{2\,x}-12\,x\,{\mathrm {e}}^{3\,x}-240\,x^2\,{\mathrm {e}}^x+180\,x^3\,{\mathrm {e}}^x+60\,x^4\,{\mathrm {e}}^x-36\,x^5\,{\mathrm {e}}^x+4\,x^6\,{\mathrm {e}}^x+6\,x^2\,{\mathrm {e}}^{2\,x}+4\,x^2\,{\mathrm {e}}^{3\,x}-36\,x^3\,{\mathrm {e}}^{2\,x}+6\,x^4\,{\mathrm {e}}^{2\,x}-576\,x\,{\mathrm {e}}^x+608\,x^2-144\,x^3-255\,x^4+36\,x^5+38\,x^6-12\,x^7+x^8+256}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
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 - 102
40) - 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 - 320*x^9 + 5*x^10 + 10*x^11 - x
^12 - exp(3*x)*(800*x + 1360*x^2 + 290*x^3 - 290*x^4 - 10*x^5 + 10*x^6)),x)
[Out]
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*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(-(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 - 255*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*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
((96*x^2*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))
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sympy [B] time = 45.08, size = 146, normalized size = 4.87 \begin {gather*} 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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
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**4-36*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**2-3200*x)*exp(x)**2+(5*x**10-35*x**9-110*x**8+113
0*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)
[Out]
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))
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