Integrand size = 718, antiderivative size = 24 \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=x+\frac {16}{\left (x+(-4+x) x^2 \left (-x+e^4 x\right )\right )^4} \]
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Timed out. \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
\[ \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=\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 \]
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Timed out.
\[\int \frac {\left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right ) {\mathrm e}^{20}+\left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right ) {\mathrm e}^{16}+\left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right ) {\mathrm e}^{12}+\left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^{9}\right ) {\mathrm e}^{8}+\left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^{9}+5 x^{8}-20 x^{7}-256 x^{3}+768 x^{2}\right ) {\mathrm e}^{4}-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^{9}-5 x^{8}+20 x^{7}+x^{5}+256 x^{3}-768 x^{2}-64}{\left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right ) {\mathrm e}^{20}+\left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right ) {\mathrm e}^{16}+\left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right ) {\mathrm e}^{12}+\left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^{9}\right ) {\mathrm e}^{8}+\left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^{9}+5 x^{8}-20 x^{7}\right ) {\mathrm e}^{4}-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^{9}-5 x^{8}+20 x^{7}+x^{5}}d x\]
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Leaf count of result is larger than twice the leaf count of optimal. 460 vs. \(2 (23) = 46\).
Time = 0.30 (sec) , antiderivative size = 460, normalized size of antiderivative = 19.17 \[ \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=\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}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 223 vs. \(2 (19) = 38\).
Time = 58.81 (sec) , antiderivative size = 223, normalized size of antiderivative = 9.29 \[ \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=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} \cdot \left (16 - 16 e^{4}\right ) + x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 198 vs. \(2 (23) = 46\).
Time = 0.26 (sec) , antiderivative size = 198, normalized size of antiderivative = 8.25 \[ \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=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}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (23) = 46\).
Time = 0.31 (sec) , antiderivative size = 81, normalized size of antiderivative = 3.38 \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=\frac {x e^{20} - 5 \, x e^{16} + 10 \, x e^{12} - 10 \, x e^{8} + 5 \, x e^{4} - x}{e^{20} - 5 \, e^{16} + 10 \, e^{12} - 10 \, e^{8} + 5 \, e^{4} - 1} + \frac {16}{{\left (x^{4} e^{4} - x^{4} - 4 \, x^{3} e^{4} + 4 \, x^{3} + x\right )}^{4}} \]
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Timed out. \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=\text {Hanged} \]
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