3.9.86 \(\int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20})+e^{16} (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20})+e^{20} (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20})+e^4 (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20})+e^{12} (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20})}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20})+e^{16} (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20})+e^{20} (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20})+e^4 (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20})+e^{12} (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20})} \, dx\)
Optimal. Leaf size=24 \[ x+\frac {16}{\left (x+(-4+x) x^2 \left (-x+e^4 x\right )\right )^4} \]
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Rubi [F] time = 180.01, 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[(-64 - 768*x^2 + 256*x^3 + x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 12
90*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x^11 -
1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) + E^
16*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1024*x^
15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(768*x^2 - 256*x^3 - 20*x^7 + 5*x^8 - 320*x^9 + 1
60*x^10 - 1940*x^11 + 1440*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x
^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160*x^15 + 13120*x^16 - 6420*x^17 + 160
0*x^18 - 200*x^19 + 10*x^20))/(x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 12
90*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x^11 -
1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) + E^
16*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1024*x^
15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(-20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 1940*x^11
+ 1440*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x^19 + 5*x^20) + E^1
2*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160*x^15 + 13120*x^16 - 6420*x^17 + 1600*x^18 - 200*x^19 +
10*x^20)),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [F] time = 0.16, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Integrate[(-64 - 768*x^2 + 256*x^3 + x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^1
3 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x
^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20
) + E^16*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1
024*x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(768*x^2 - 256*x^3 - 20*x^7 + 5*x^8 - 320*x
^9 + 160*x^10 - 1940*x^11 + 1440*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 -
100*x^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160*x^15 + 13120*x^16 - 6420*x^17
+ 1600*x^18 - 200*x^19 + 10*x^20))/(x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^1
3 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x
^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20
) + E^16*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1
024*x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(-20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 194
0*x^11 + 1440*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x^19 + 5*x^20)
+ E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160*x^15 + 13120*x^16 - 6420*x^17 + 1600*x^18 - 200*
x^19 + 10*x^20)),x]
[Out]
Integrate[(-64 - 768*x^2 + 256*x^3 + x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^1
3 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x
^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20
) + E^16*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1
024*x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(768*x^2 - 256*x^3 - 20*x^7 + 5*x^8 - 320*x
^9 + 160*x^10 - 1940*x^11 + 1440*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 -
100*x^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160*x^15 + 13120*x^16 - 6420*x^17
+ 1600*x^18 - 200*x^19 + 10*x^20))/(x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^1
3 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x
^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20
) + E^16*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1
024*x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(-20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 194
0*x^11 + 1440*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x^19 + 5*x^20)
+ E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160*x^15 + 13120*x^16 - 6420*x^17 + 1600*x^18 - 200*
x^19 + 10*x^20)), x]
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fricas [B] time = 1.16, size = 460, normalized size = 19.17 \begin {gather*} \frac {x^{17} - 16 \, x^{16} + 96 \, x^{15} - 260 \, x^{14} + 304 \, x^{13} - 192 \, x^{12} + 262 \, x^{11} - 48 \, x^{10} + 96 \, x^{9} - 4 \, x^{8} + 16 \, x^{7} + x^{5} + {\left (x^{17} - 16 \, x^{16} + 96 \, x^{15} - 256 \, x^{14} + 256 \, x^{13}\right )} e^{16} - 4 \, {\left (x^{17} - 16 \, x^{16} + 96 \, x^{15} - 257 \, x^{14} + 268 \, x^{13} - 48 \, x^{12} + 64 \, x^{11}\right )} e^{12} + 6 \, {\left (x^{17} - 16 \, x^{16} + 96 \, x^{15} - 258 \, x^{14} + 280 \, x^{13} - 96 \, x^{12} + 129 \, x^{11} - 8 \, x^{10} + 16 \, x^{9}\right )} e^{8} - 4 \, {\left (x^{17} - 16 \, x^{16} + 96 \, x^{15} - 259 \, x^{14} + 292 \, x^{13} - 144 \, x^{12} + 195 \, x^{11} - 24 \, x^{10} + 48 \, x^{9} - x^{8} + 4 \, x^{7}\right )} e^{4} + 16}{x^{16} - 16 \, x^{15} + 96 \, x^{14} - 260 \, x^{13} + 304 \, x^{12} - 192 \, x^{11} + 262 \, x^{10} - 48 \, x^{9} + 96 \, x^{8} - 4 \, x^{7} + 16 \, x^{6} + x^{4} + {\left (x^{16} - 16 \, x^{15} + 96 \, x^{14} - 256 \, x^{13} + 256 \, x^{12}\right )} e^{16} - 4 \, {\left (x^{16} - 16 \, x^{15} + 96 \, x^{14} - 257 \, x^{13} + 268 \, x^{12} - 48 \, x^{11} + 64 \, x^{10}\right )} e^{12} + 6 \, {\left (x^{16} - 16 \, x^{15} + 96 \, x^{14} - 258 \, x^{13} + 280 \, x^{12} - 96 \, x^{11} + 129 \, x^{10} - 8 \, x^{9} + 16 \, x^{8}\right )} e^{8} - 4 \, {\left (x^{16} - 16 \, x^{15} + 96 \, x^{14} - 259 \, x^{13} + 292 \, x^{12} - 144 \, x^{11} + 195 \, x^{10} - 24 \, x^{9} + 48 \, x^{8} - x^{7} + 4 \, x^{6}\right )} e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-
6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+
5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7
710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16
-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7-256*x^3+768*x^2)*exp(4)-x^20+
20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x
^7+x^5+256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-80
0*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120
*x^16-12160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*
x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-32
20*x^17+6720*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7)*exp(4)-x^20
+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*
x^7+x^5),x, algorithm="fricas")
[Out]
(x^17 - 16*x^16 + 96*x^15 - 260*x^14 + 304*x^13 - 192*x^12 + 262*x^11 - 48*x^10 + 96*x^9 - 4*x^8 + 16*x^7 + x^
5 + (x^17 - 16*x^16 + 96*x^15 - 256*x^14 + 256*x^13)*e^16 - 4*(x^17 - 16*x^16 + 96*x^15 - 257*x^14 + 268*x^13
- 48*x^12 + 64*x^11)*e^12 + 6*(x^17 - 16*x^16 + 96*x^15 - 258*x^14 + 280*x^13 - 96*x^12 + 129*x^11 - 8*x^10 +
16*x^9)*e^8 - 4*(x^17 - 16*x^16 + 96*x^15 - 259*x^14 + 292*x^13 - 144*x^12 + 195*x^11 - 24*x^10 + 48*x^9 - x^8
+ 4*x^7)*e^4 + 16)/(x^16 - 16*x^15 + 96*x^14 - 260*x^13 + 304*x^12 - 192*x^11 + 262*x^10 - 48*x^9 + 96*x^8 -
4*x^7 + 16*x^6 + x^4 + (x^16 - 16*x^15 + 96*x^14 - 256*x^13 + 256*x^12)*e^16 - 4*(x^16 - 16*x^15 + 96*x^14 - 2
57*x^13 + 268*x^12 - 48*x^11 + 64*x^10)*e^12 + 6*(x^16 - 16*x^15 + 96*x^14 - 258*x^13 + 280*x^12 - 96*x^11 + 1
29*x^10 - 8*x^9 + 16*x^8)*e^8 - 4*(x^16 - 16*x^15 + 96*x^14 - 259*x^13 + 292*x^12 - 144*x^11 + 195*x^10 - 24*x
^9 + 48*x^8 - x^7 + 4*x^6)*e^4)
________________________________________________________________________________________
giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-
6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+
5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7
710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16
-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7-256*x^3+768*x^2)*exp(4)-x^20+
20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x
^7+x^5+256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-80
0*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120
*x^16-12160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*
x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-32
20*x^17+6720*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7)*exp(4)-x^20
+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*
x^7+x^5),x, algorithm="giac")
[Out]
Timed out
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maple [F] time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right ) {\mathrm e}^{20}+\left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right ) {\mathrm e}^{16}+\left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right ) {\mathrm e}^{12}+\left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^{9}\right ) {\mathrm e}^{8}+\left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^{9}+5 x^{8}-20 x^{7}-256 x^{3}+768 x^{2}\right ) {\mathrm e}^{4}-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^{9}-5 x^{8}+20 x^{7}+x^{5}+256 x^{3}-768 x^{2}-64}{\left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right ) {\mathrm e}^{20}+\left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right ) {\mathrm e}^{16}+\left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right ) {\mathrm e}^{12}+\left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^{9}\right ) {\mathrm e}^{8}+\left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^{9}+5 x^{8}-20 x^{7}\right ) {\mathrm e}^{4}-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^{9}-5 x^{8}+20 x^{7}+x^{5}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x
^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+5130*x
^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^
14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-7040*
x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7-256*x^3+768*x^2)*exp(4)-x^20+20*x^1
9-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5
+256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18
+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-
12160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+1
3120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^1
7+6720*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7)*exp(4)-x^20+20*x^
19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^
5),x)
[Out]
int(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x
^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+5130*x
^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^
14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-7040*
x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7-256*x^3+768*x^2)*exp(4)-x^20+20*x^1
9-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5
+256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18
+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-
12160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+1
3120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^1
7+6720*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7)*exp(4)-x^20+20*x^
19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^
5),x)
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maxima [B] time = 0.48, size = 198, normalized size = 8.25 \begin {gather*} x + \frac {16}{x^{16} {\left (e^{16} - 4 \, e^{12} + 6 \, e^{8} - 4 \, e^{4} + 1\right )} - 16 \, x^{15} {\left (e^{16} - 4 \, e^{12} + 6 \, e^{8} - 4 \, e^{4} + 1\right )} + 96 \, x^{14} {\left (e^{16} - 4 \, e^{12} + 6 \, e^{8} - 4 \, e^{4} + 1\right )} - 4 \, x^{13} {\left (64 \, e^{16} - 257 \, e^{12} + 387 \, e^{8} - 259 \, e^{4} + 65\right )} + 16 \, x^{12} {\left (16 \, e^{16} - 67 \, e^{12} + 105 \, e^{8} - 73 \, e^{4} + 19\right )} + 192 \, x^{11} {\left (e^{12} - 3 \, e^{8} + 3 \, e^{4} - 1\right )} - 2 \, x^{10} {\left (128 \, e^{12} - 387 \, e^{8} + 390 \, e^{4} - 131\right )} - 48 \, x^{9} {\left (e^{8} - 2 \, e^{4} + 1\right )} + 96 \, x^{8} {\left (e^{8} - 2 \, e^{4} + 1\right )} + 4 \, x^{7} {\left (e^{4} - 1\right )} - 16 \, x^{6} {\left (e^{4} - 1\right )} + x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-
6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+
5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7
710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16
-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7-256*x^3+768*x^2)*exp(4)-x^20+
20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x
^7+x^5+256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^20+100*x^19-80
0*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120
*x^16-12160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430*x^17-13280*
x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-32
20*x^17+6720*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7)*exp(4)-x^20
+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*
x^7+x^5),x, algorithm="maxima")
[Out]
x + 16/(x^16*(e^16 - 4*e^12 + 6*e^8 - 4*e^4 + 1) - 16*x^15*(e^16 - 4*e^12 + 6*e^8 - 4*e^4 + 1) + 96*x^14*(e^16
- 4*e^12 + 6*e^8 - 4*e^4 + 1) - 4*x^13*(64*e^16 - 257*e^12 + 387*e^8 - 259*e^4 + 65) + 16*x^12*(16*e^16 - 67*
e^12 + 105*e^8 - 73*e^4 + 19) + 192*x^11*(e^12 - 3*e^8 + 3*e^4 - 1) - 2*x^10*(128*e^12 - 387*e^8 + 390*e^4 - 1
31) - 48*x^9*(e^8 - 2*e^4 + 1) + 96*x^8*(e^8 - 2*e^4 + 1) + 4*x^7*(e^4 - 1) - 16*x^6*(e^4 - 1) + x^4)
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mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(exp(4)*(768*x^2 - 256*x^3 - 20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 1940*x^11 + 1440*x^12 - 5480*x^13 + 51
50*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x^19 + 5*x^20) - exp(20)*(1024*x^15 - 1280*x^16 +
640*x^17 - 160*x^18 + 20*x^19 - x^20) - exp(12)*(640*x^11 - 480*x^12 + 5240*x^13 - 5130*x^14 + 12160*x^15 - 1
3120*x^16 + 6420*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) + exp(8)*(160*x^9 - 80*x^10 + 1930*x^11 - 1440*x^12 +
8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) - 768*x^2 + 256*
x^3 + x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 1290*x^14 + 1504*x^15 - 136
0*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + exp(16)*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*
x^17 - 800*x^18 + 100*x^19 - 5*x^20) - 64)/(exp(4)*(20*x^7 - 5*x^8 + 320*x^9 - 160*x^10 + 1940*x^11 - 1440*x^1
2 + 5480*x^13 - 5150*x^14 + 7040*x^15 - 6720*x^16 + 3220*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + exp(12)*(640*x
^11 - 480*x^12 + 5240*x^13 - 5130*x^14 + 12160*x^15 - 13120*x^16 + 6420*x^17 - 1600*x^18 + 200*x^19 - 10*x^20)
+ exp(20)*(1024*x^15 - 1280*x^16 + 640*x^17 - 160*x^18 + 20*x^19 - x^20) - exp(8)*(160*x^9 - 80*x^10 + 1930*x
^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20
) - x^5 - 20*x^7 + 5*x^8 - 160*x^9 + 80*x^10 - 650*x^11 + 480*x^12 - 1400*x^13 + 1290*x^14 - 1504*x^15 + 1360*
x^16 - 645*x^17 + 160*x^18 - 20*x^19 + x^20 - exp(16)*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^
17 - 800*x^18 + 100*x^19 - 5*x^20)),x)
[Out]
\text{Hanged}
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sympy [B] time = 103.74, size = 223, normalized size = 9.29 \begin {gather*} x + \frac {16}{x^{16} \left (- 4 e^{12} - 4 e^{4} + 1 + 6 e^{8} + e^{16}\right ) + x^{15} \left (- 16 e^{16} - 96 e^{8} - 16 + 64 e^{4} + 64 e^{12}\right ) + x^{14} \left (- 384 e^{12} - 384 e^{4} + 96 + 576 e^{8} + 96 e^{16}\right ) + x^{13} \left (- 256 e^{16} - 1548 e^{8} - 260 + 1036 e^{4} + 1028 e^{12}\right ) + x^{12} \left (- 1072 e^{12} - 1168 e^{4} + 304 + 1680 e^{8} + 256 e^{16}\right ) + x^{11} \left (- 576 e^{8} - 192 + 576 e^{4} + 192 e^{12}\right ) + x^{10} \left (- 256 e^{12} - 780 e^{4} + 262 + 774 e^{8}\right ) + x^{9} \left (- 48 e^{8} - 48 + 96 e^{4}\right ) + x^{8} \left (- 192 e^{4} + 96 + 96 e^{8}\right ) + x^{7} \left (-4 + 4 e^{4}\right ) + x^{6} \left (16 - 16 e^{4}\right ) + x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x**20-20*x**19+160*x**18-640*x**17+1280*x**16-1024*x**15)*exp(4)**5+(-5*x**20+100*x**19-800*x**18+
3205*x**17-6480*x**16+5600*x**15-1280*x**14+1280*x**13)*exp(4)**4+(10*x**20-200*x**19+1600*x**18-6420*x**17+13
120*x**16-12160*x**15+5130*x**14-5240*x**13+480*x**12-640*x**11)*exp(4)**3+(-10*x**20+200*x**19-1600*x**18+643
0*x**17-13280*x**16+13120*x**15-7710*x**14+8040*x**13-1440*x**12+1930*x**11-80*x**10+160*x**9)*exp(4)**2+(5*x*
*20-100*x**19+800*x**18-3220*x**17+6720*x**16-7040*x**15+5150*x**14-5480*x**13+1440*x**12-1940*x**11+160*x**10
-320*x**9+5*x**8-20*x**7-256*x**3+768*x**2)*exp(4)-x**20+20*x**19-160*x**18+645*x**17-1360*x**16+1504*x**15-12
90*x**14+1400*x**13-480*x**12+650*x**11-80*x**10+160*x**9-5*x**8+20*x**7+x**5+256*x**3-768*x**2-64)/((x**20-20
*x**19+160*x**18-640*x**17+1280*x**16-1024*x**15)*exp(4)**5+(-5*x**20+100*x**19-800*x**18+3205*x**17-6480*x**1
6+5600*x**15-1280*x**14+1280*x**13)*exp(4)**4+(10*x**20-200*x**19+1600*x**18-6420*x**17+13120*x**16-12160*x**1
5+5130*x**14-5240*x**13+480*x**12-640*x**11)*exp(4)**3+(-10*x**20+200*x**19-1600*x**18+6430*x**17-13280*x**16+
13120*x**15-7710*x**14+8040*x**13-1440*x**12+1930*x**11-80*x**10+160*x**9)*exp(4)**2+(5*x**20-100*x**19+800*x*
*18-3220*x**17+6720*x**16-7040*x**15+5150*x**14-5480*x**13+1440*x**12-1940*x**11+160*x**10-320*x**9+5*x**8-20*
x**7)*exp(4)-x**20+20*x**19-160*x**18+645*x**17-1360*x**16+1504*x**15-1290*x**14+1400*x**13-480*x**12+650*x**1
1-80*x**10+160*x**9-5*x**8+20*x**7+x**5),x)
[Out]
x + 16/(x**16*(-4*exp(12) - 4*exp(4) + 1 + 6*exp(8) + exp(16)) + x**15*(-16*exp(16) - 96*exp(8) - 16 + 64*exp(
4) + 64*exp(12)) + x**14*(-384*exp(12) - 384*exp(4) + 96 + 576*exp(8) + 96*exp(16)) + x**13*(-256*exp(16) - 15
48*exp(8) - 260 + 1036*exp(4) + 1028*exp(12)) + x**12*(-1072*exp(12) - 1168*exp(4) + 304 + 1680*exp(8) + 256*e
xp(16)) + x**11*(-576*exp(8) - 192 + 576*exp(4) + 192*exp(12)) + x**10*(-256*exp(12) - 780*exp(4) + 262 + 774*
exp(8)) + x**9*(-48*exp(8) - 48 + 96*exp(4)) + x**8*(-192*exp(4) + 96 + 96*exp(8)) + x**7*(-4 + 4*exp(4)) + x*
*6*(16 - 16*exp(4)) + x**4)
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