Integrand size = 726, antiderivative size = 36 \[ \int \frac {-2+2 x+20 x^3+30 x^4-80 x^6-100 x^7-225 x^8+160 x^9-40 x^{10}-150 x^{11}-160 x^{12}+240 x^{13}+64 x^{15}-64 x^{16}+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{40/x} \left (-2 x^{10}+2 x^{11}\right )+e^{28/x} \left (240 x^7-240 x^8-160 x^{10}+160 x^{11}\right )+e^{20/x} \left (504 x^5-504 x^6-1920 x^8+1020 x^9+480 x^{11}-480 x^{12}\right )+e^{32/x} \left (-90 x^8+90 x^9+20 x^{11}-20 x^{12}\right )+e^{24/x} \left (-420 x^6+420 x^7+720 x^9-550 x^{10}-80 x^{12}+80 x^{13}\right )+e^{12/x} \left (240 x^3-240 x^4-2720 x^6+520 x^7+3520 x^9-1360 x^{10}-640 x^{12}+640 x^{13}\right )+e^{4/x} \left (20 x-20 x^2-320 x^4-100 x^5+1120 x^7+880 x^8+250 x^9-1280 x^{10}+560 x^{11}+320 x^{13}-320 x^{14}\right )+e^{16/x} \left (-420 x^4+420 x^5+3000 x^7-1050 x^8-1840 x^{10}+1180 x^{11}+160 x^{13}-160 x^{14}\right )+e^{8/x} \left (-90 x^2+90 x^3+1360 x^5-10 x^6-3120 x^8-200 x^9-25 x^{10}+1600 x^{11}-1000 x^{12}-160 x^{14}+160 x^{15}\right )}{1-10 x^3+40 x^6-80 x^9-10 e^{36/x} x^9+e^{40/x} x^{10}+80 x^{12}-32 x^{15}+e^{28/x} \left (-120 x^7+80 x^{10}\right )+e^{20/x} \left (-252 x^5+560 x^8-240 x^{11}\right )+e^{32/x} \left (45 x^8-10 x^{11}\right )+e^{24/x} \left (210 x^6-280 x^9+40 x^{12}\right )+e^{12/x} \left (-120 x^3+560 x^6-800 x^9+320 x^{12}\right )+e^{4/x} \left (-10 x+80 x^4-240 x^7+320 x^{10}-160 x^{13}\right )+e^{16/x} \left (210 x^4-700 x^7+600 x^{10}-80 x^{13}\right )+e^{8/x} \left (45 x^2-280 x^5+600 x^8-480 x^{11}+80 x^{14}\right )} \, dx=x \left (-1+x-\left (1-\frac {5}{\left (-\left (e^{4/x}-\frac {1}{x}\right )^2+2 x\right )^2}\right )^2\right ) \]
Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(36)=72\).
Time = 0.38 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.14 \[ \int \frac {-2+2 x+20 x^3+30 x^4-80 x^6-100 x^7-225 x^8+160 x^9-40 x^{10}-150 x^{11}-160 x^{12}+240 x^{13}+64 x^{15}-64 x^{16}+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{40/x} \left (-2 x^{10}+2 x^{11}\right )+e^{28/x} \left (240 x^7-240 x^8-160 x^{10}+160 x^{11}\right )+e^{20/x} \left (504 x^5-504 x^6-1920 x^8+1020 x^9+480 x^{11}-480 x^{12}\right )+e^{32/x} \left (-90 x^8+90 x^9+20 x^{11}-20 x^{12}\right )+e^{24/x} \left (-420 x^6+420 x^7+720 x^9-550 x^{10}-80 x^{12}+80 x^{13}\right )+e^{12/x} \left (240 x^3-240 x^4-2720 x^6+520 x^7+3520 x^9-1360 x^{10}-640 x^{12}+640 x^{13}\right )+e^{4/x} \left (20 x-20 x^2-320 x^4-100 x^5+1120 x^7+880 x^8+250 x^9-1280 x^{10}+560 x^{11}+320 x^{13}-320 x^{14}\right )+e^{16/x} \left (-420 x^4+420 x^5+3000 x^7-1050 x^8-1840 x^{10}+1180 x^{11}+160 x^{13}-160 x^{14}\right )+e^{8/x} \left (-90 x^2+90 x^3+1360 x^5-10 x^6-3120 x^8-200 x^9-25 x^{10}+1600 x^{11}-1000 x^{12}-160 x^{14}+160 x^{15}\right )}{1-10 x^3+40 x^6-80 x^9-10 e^{36/x} x^9+e^{40/x} x^{10}+80 x^{12}-32 x^{15}+e^{28/x} \left (-120 x^7+80 x^{10}\right )+e^{20/x} \left (-252 x^5+560 x^8-240 x^{11}\right )+e^{32/x} \left (45 x^8-10 x^{11}\right )+e^{24/x} \left (210 x^6-280 x^9+40 x^{12}\right )+e^{12/x} \left (-120 x^3+560 x^6-800 x^9+320 x^{12}\right )+e^{4/x} \left (-10 x+80 x^4-240 x^7+320 x^{10}-160 x^{13}\right )+e^{16/x} \left (210 x^4-700 x^7+600 x^{10}-80 x^{13}\right )+e^{8/x} \left (45 x^2-280 x^5+600 x^8-480 x^{11}+80 x^{14}\right )} \, dx=-2 x+x^2-\frac {25 x^9}{\left (1-2 e^{4/x} x+e^{8/x} x^2-2 x^3\right )^4}+\frac {10 x^5}{\left (1-2 e^{4/x} x+e^{8/x} x^2-2 x^3\right )^2} \]
Integrate[(-2 + 2*x + 20*x^3 + 30*x^4 - 80*x^6 - 100*x^7 - 225*x^8 + 160*x ^9 - 40*x^10 - 150*x^11 - 160*x^12 + 240*x^13 + 64*x^15 - 64*x^16 + E^(36/ x)*(20*x^9 - 20*x^10) + E^(40/x)*(-2*x^10 + 2*x^11) + E^(28/x)*(240*x^7 - 240*x^8 - 160*x^10 + 160*x^11) + E^(20/x)*(504*x^5 - 504*x^6 - 1920*x^8 + 1020*x^9 + 480*x^11 - 480*x^12) + E^(32/x)*(-90*x^8 + 90*x^9 + 20*x^11 - 2 0*x^12) + E^(24/x)*(-420*x^6 + 420*x^7 + 720*x^9 - 550*x^10 - 80*x^12 + 80 *x^13) + E^(12/x)*(240*x^3 - 240*x^4 - 2720*x^6 + 520*x^7 + 3520*x^9 - 136 0*x^10 - 640*x^12 + 640*x^13) + E^(4/x)*(20*x - 20*x^2 - 320*x^4 - 100*x^5 + 1120*x^7 + 880*x^8 + 250*x^9 - 1280*x^10 + 560*x^11 + 320*x^13 - 320*x^ 14) + E^(16/x)*(-420*x^4 + 420*x^5 + 3000*x^7 - 1050*x^8 - 1840*x^10 + 118 0*x^11 + 160*x^13 - 160*x^14) + E^(8/x)*(-90*x^2 + 90*x^3 + 1360*x^5 - 10* x^6 - 3120*x^8 - 200*x^9 - 25*x^10 + 1600*x^11 - 1000*x^12 - 160*x^14 + 16 0*x^15))/(1 - 10*x^3 + 40*x^6 - 80*x^9 - 10*E^(36/x)*x^9 + E^(40/x)*x^10 + 80*x^12 - 32*x^15 + E^(28/x)*(-120*x^7 + 80*x^10) + E^(20/x)*(-252*x^5 + 560*x^8 - 240*x^11) + E^(32/x)*(45*x^8 - 10*x^11) + E^(24/x)*(210*x^6 - 28 0*x^9 + 40*x^12) + E^(12/x)*(-120*x^3 + 560*x^6 - 800*x^9 + 320*x^12) + E^ (4/x)*(-10*x + 80*x^4 - 240*x^7 + 320*x^10 - 160*x^13) + E^(16/x)*(210*x^4 - 700*x^7 + 600*x^10 - 80*x^13) + E^(8/x)*(45*x^2 - 280*x^5 + 600*x^8 - 4 80*x^11 + 80*x^14)),x]
-2*x + x^2 - (25*x^9)/(1 - 2*E^(4/x)*x + E^(8/x)*x^2 - 2*x^3)^4 + (10*x^5) /(1 - 2*E^(4/x)*x + E^(8/x)*x^2 - 2*x^3)^2
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.
| \(\displaystyle \int \frac {-64 x^{16}+64 x^{15}+240 x^{13}-160 x^{12}-150 x^{11}-40 x^{10}+160 x^9-225 x^8-100 x^7-80 x^6+30 x^4+20 x^3+e^{40/x} \left (2 x^{11}-2 x^{10}\right )+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{32/x} \left (-20 x^{12}+20 x^{11}+90 x^9-90 x^8\right )+e^{28/x} \left (160 x^{11}-160 x^{10}-240 x^8+240 x^7\right )+e^{24/x} \left (80 x^{13}-80 x^{12}-550 x^{10}+720 x^9+420 x^7-420 x^6\right )+e^{20/x} \left (-480 x^{12}+480 x^{11}+1020 x^9-1920 x^8-504 x^6+504 x^5\right )+e^{16/x} \left (-160 x^{14}+160 x^{13}+1180 x^{11}-1840 x^{10}-1050 x^8+3000 x^7+420 x^5-420 x^4\right )+e^{12/x} \left (640 x^{13}-640 x^{12}-1360 x^{10}+3520 x^9+520 x^7-2720 x^6-240 x^4+240 x^3\right )+2 x+e^{4/x} \left (-320 x^{14}+320 x^{13}+560 x^{11}-1280 x^{10}+250 x^9+880 x^8+1120 x^7-100 x^5-320 x^4-20 x^2+20 x\right )+e^{8/x} \left (160 x^{15}-160 x^{14}-1000 x^{12}+1600 x^{11}-25 x^{10}-200 x^9-3120 x^8-10 x^6+1360 x^5+90 x^3-90 x^2\right )-2}{-32 x^{15}+80 x^{12}+e^{40/x} x^{10}-10 e^{36/x} x^9-80 x^9+40 x^6-10 x^3+e^{32/x} \left (45 x^8-10 x^{11}\right )+e^{28/x} \left (80 x^{10}-120 x^7\right )+e^{24/x} \left (40 x^{12}-280 x^9+210 x^6\right )+e^{20/x} \left (-240 x^{11}+560 x^8-252 x^5\right )+e^{4/x} \left (-160 x^{13}+320 x^{10}-240 x^7+80 x^4-10 x\right )+e^{16/x} \left (-80 x^{13}+600 x^{10}-700 x^7+210 x^4\right )+e^{12/x} \left (320 x^{12}-800 x^9+560 x^6-120 x^3\right )+e^{8/x} \left (80 x^{14}-480 x^{11}+600 x^8-280 x^5+45 x^2\right )+1} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-64 x^{16}+64 x^{15}+240 x^{13}-160 x^{12}-150 x^{11}-40 x^{10}+160 x^9-225 x^8-100 x^7-80 x^6+30 x^4+20 x^3+e^{40/x} \left (2 x^{11}-2 x^{10}\right )+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{32/x} \left (-20 x^{12}+20 x^{11}+90 x^9-90 x^8\right )+e^{28/x} \left (160 x^{11}-160 x^{10}-240 x^8+240 x^7\right )+e^{24/x} \left (80 x^{13}-80 x^{12}-550 x^{10}+720 x^9+420 x^7-420 x^6\right )+e^{20/x} \left (-480 x^{12}+480 x^{11}+1020 x^9-1920 x^8-504 x^6+504 x^5\right )+e^{16/x} \left (-160 x^{14}+160 x^{13}+1180 x^{11}-1840 x^{10}-1050 x^8+3000 x^7+420 x^5-420 x^4\right )+e^{12/x} \left (640 x^{13}-640 x^{12}-1360 x^{10}+3520 x^9+520 x^7-2720 x^6-240 x^4+240 x^3\right )+2 x+e^{4/x} \left (-320 x^{14}+320 x^{13}+560 x^{11}-1280 x^{10}+250 x^9+880 x^8+1120 x^7-100 x^5-320 x^4-20 x^2+20 x\right )+e^{8/x} \left (160 x^{15}-160 x^{14}-1000 x^{12}+1600 x^{11}-25 x^{10}-200 x^9-3120 x^8-10 x^6+1360 x^5+90 x^3-90 x^2\right )-2}{\left (-2 x^3+e^{8/x} x^2-2 e^{4/x} x+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {10 (x+16) x^3}{\left (2 x^3-e^{8/x} x^2+2 e^{4/x} x-1\right )^2}-\frac {25 (x+32) x^7}{\left (2 x^3-e^{8/x} x^2+2 e^{4/x} x-1\right )^4}-\frac {40 \left (x^4+8 x^3-e^{4/x} x^2+4 e^{4/x} x+x-4\right ) x^3}{\left (2 x^3-e^{8/x} x^2+2 e^{4/x} x-1\right )^3}+\frac {200 \left (x^4+8 x^3-e^{4/x} x^2+4 e^{4/x} x+x-4\right ) x^7}{\left (2 x^3-e^{8/x} x^2+2 e^{4/x} x-1\right )^5}+2 (x-1)\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {10 (x+16) x^3}{\left (2 x^3-e^{8/x} x^2+2 e^{4/x} x-1\right )^2}-\frac {25 (x+32) x^7}{\left (2 x^3-e^{8/x} x^2+2 e^{4/x} x-1\right )^4}-\frac {40 \left (x^4+8 x^3-e^{4/x} x^2+4 e^{4/x} x+x-4\right ) x^3}{\left (2 x^3-e^{8/x} x^2+2 e^{4/x} x-1\right )^3}+\frac {200 \left (x^4+8 x^3-e^{4/x} x^2+4 e^{4/x} x+x-4\right ) x^7}{\left (2 x^3-e^{8/x} x^2+2 e^{4/x} x-1\right )^5}+2 (x-1)\right )dx\) |
Int[(-2 + 2*x + 20*x^3 + 30*x^4 - 80*x^6 - 100*x^7 - 225*x^8 + 160*x^9 - 4 0*x^10 - 150*x^11 - 160*x^12 + 240*x^13 + 64*x^15 - 64*x^16 + E^(36/x)*(20 *x^9 - 20*x^10) + E^(40/x)*(-2*x^10 + 2*x^11) + E^(28/x)*(240*x^7 - 240*x^ 8 - 160*x^10 + 160*x^11) + E^(20/x)*(504*x^5 - 504*x^6 - 1920*x^8 + 1020*x ^9 + 480*x^11 - 480*x^12) + E^(32/x)*(-90*x^8 + 90*x^9 + 20*x^11 - 20*x^12 ) + E^(24/x)*(-420*x^6 + 420*x^7 + 720*x^9 - 550*x^10 - 80*x^12 + 80*x^13) + E^(12/x)*(240*x^3 - 240*x^4 - 2720*x^6 + 520*x^7 + 3520*x^9 - 1360*x^10 - 640*x^12 + 640*x^13) + E^(4/x)*(20*x - 20*x^2 - 320*x^4 - 100*x^5 + 112 0*x^7 + 880*x^8 + 250*x^9 - 1280*x^10 + 560*x^11 + 320*x^13 - 320*x^14) + E^(16/x)*(-420*x^4 + 420*x^5 + 3000*x^7 - 1050*x^8 - 1840*x^10 + 1180*x^11 + 160*x^13 - 160*x^14) + E^(8/x)*(-90*x^2 + 90*x^3 + 1360*x^5 - 10*x^6 - 3120*x^8 - 200*x^9 - 25*x^10 + 1600*x^11 - 1000*x^12 - 160*x^14 + 160*x^15 ))/(1 - 10*x^3 + 40*x^6 - 80*x^9 - 10*E^(36/x)*x^9 + E^(40/x)*x^10 + 80*x^ 12 - 32*x^15 + E^(28/x)*(-120*x^7 + 80*x^10) + E^(20/x)*(-252*x^5 + 560*x^ 8 - 240*x^11) + E^(32/x)*(45*x^8 - 10*x^11) + E^(24/x)*(210*x^6 - 280*x^9 + 40*x^12) + E^(12/x)*(-120*x^3 + 560*x^6 - 800*x^9 + 320*x^12) + E^(4/x)* (-10*x + 80*x^4 - 240*x^7 + 320*x^10 - 160*x^13) + E^(16/x)*(210*x^4 - 700 *x^7 + 600*x^10 - 80*x^13) + E^(8/x)*(45*x^2 - 280*x^5 + 600*x^8 - 480*x^1 1 + 80*x^14)),x]
3.26.45.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(132\) vs. \(2(35)=70\).
Time = 4.35 (sec) , antiderivative size = 133, normalized size of antiderivative = 3.69
| method | result | size |
| risch | \(x^{2}-2 x +\frac {5 \left (2 \,{\mathrm e}^{\frac {16}{x}} x^{4}-8 \,{\mathrm e}^{\frac {8}{x}} x^{5}+8 x^{6}-8 \,{\mathrm e}^{\frac {12}{x}} x^{3}+16 \,{\mathrm e}^{\frac {4}{x}} x^{4}-5 x^{4}+12 \,{\mathrm e}^{\frac {8}{x}} x^{2}-8 x^{3}-8 x \,{\mathrm e}^{\frac {4}{x}}+2\right ) x^{5}}{\left (-{\mathrm e}^{\frac {8}{x}} x^{2}+2 x^{3}+2 x \,{\mathrm e}^{\frac {4}{x}}-1\right )^{4}}\) | \(133\) |
| parallelrisch | \(\frac {-16 x +128 x^{2} {\mathrm e}^{\frac {4}{x}}+64 x^{11}-256 x^{13}+128 x^{14}-384 x^{7}-128 x^{8}+512 x^{10}-200 x^{9}+16 x^{5}+128 x^{4}+8 x^{2}-64 \,{\mathrm e}^{\frac {4}{x}} x^{3}-128 \,{\mathrm e}^{\frac {4}{x}} x^{9}+1536 \,{\mathrm e}^{\frac {4}{x}} x^{8}+64 \,{\mathrm e}^{\frac {4}{x}} x^{6}-768 \,{\mathrm e}^{\frac {4}{x}} x^{5}+512 \,{\mathrm e}^{\frac {4}{x}} x^{12}-1024 \,{\mathrm e}^{\frac {4}{x}} x^{11}+560 \,{\mathrm e}^{\frac {16}{x}} x^{6}-448 \,{\mathrm e}^{\frac {12}{x}} x^{5}+224 \,{\mathrm e}^{\frac {8}{x}} x^{4}+512 \,{\mathrm e}^{\frac {8}{x}} x^{12}-384 \,{\mathrm e}^{\frac {16}{x}} x^{11}+128 \,{\mathrm e}^{\frac {24}{x}} x^{10}+1536 \,{\mathrm e}^{\frac {12}{x}} x^{10}+832 \,{\mathrm e}^{\frac {8}{x}} x^{10}-16 \,{\mathrm e}^{\frac {32}{x}} x^{9}-768 \,{\mathrm e}^{\frac {20}{x}} x^{9}-2304 \,{\mathrm e}^{\frac {8}{x}} x^{9}+128 \,{\mathrm e}^{\frac {28}{x}} x^{8}+1920 \,{\mathrm e}^{\frac {16}{x}} x^{8}-448 \,{\mathrm e}^{\frac {24}{x}} x^{7}-2560 \,{\mathrm e}^{\frac {12}{x}} x^{7}+1920 \,{\mathrm e}^{\frac {8}{x}} x^{6}-1120 \,{\mathrm e}^{\frac {16}{x}} x^{5}+896 \,{\mathrm e}^{\frac {12}{x}} x^{4}-448 \,{\mathrm e}^{\frac {8}{x}} x^{3}+896 \,{\mathrm e}^{\frac {20}{x}} x^{6}-256 \,{\mathrm e}^{\frac {8}{x}} x^{13}+192 \,{\mathrm e}^{\frac {16}{x}} x^{12}-64 \,{\mathrm e}^{\frac {24}{x}} x^{11}-768 \,{\mathrm e}^{\frac {12}{x}} x^{11}+8 \,{\mathrm e}^{\frac {32}{x}} x^{10}+384 \,{\mathrm e}^{\frac {20}{x}} x^{10}-64 \,{\mathrm e}^{\frac {28}{x}} x^{9}-880 \,{\mathrm e}^{\frac {16}{x}} x^{9}+224 \,{\mathrm e}^{\frac {24}{x}} x^{8}+960 \,{\mathrm e}^{\frac {12}{x}} x^{8}-448 \,{\mathrm e}^{\frac {20}{x}} x^{7}-480 \,{\mathrm e}^{\frac {8}{x}} x^{7}}{8-64 x \,{\mathrm e}^{\frac {4}{x}}+128 x^{12}-256 x^{9}+192 x^{6}-64 x^{3}-448 \,{\mathrm e}^{\frac {20}{x}} x^{5}+384 \,{\mathrm e}^{\frac {4}{x}} x^{4}-768 \,{\mathrm e}^{\frac {4}{x}} x^{7}+512 \,{\mathrm e}^{\frac {4}{x}} x^{10}-256 \,{\mathrm e}^{\frac {8}{x}} x^{11}+192 \,{\mathrm e}^{\frac {16}{x}} x^{10}-64 \,{\mathrm e}^{\frac {24}{x}} x^{9}-768 \,{\mathrm e}^{\frac {12}{x}} x^{9}+8 \,{\mathrm e}^{\frac {32}{x}} x^{8}+384 \,{\mathrm e}^{\frac {20}{x}} x^{8}+1152 \,{\mathrm e}^{\frac {8}{x}} x^{8}-64 \,{\mathrm e}^{\frac {28}{x}} x^{7}-960 \,{\mathrm e}^{\frac {16}{x}} x^{7}+224 \,{\mathrm e}^{\frac {24}{x}} x^{6}+1280 \,{\mathrm e}^{\frac {12}{x}} x^{6}-960 \,{\mathrm e}^{\frac {8}{x}} x^{5}+560 \,{\mathrm e}^{\frac {16}{x}} x^{4}-448 \,{\mathrm e}^{\frac {12}{x}} x^{3}+224 \,{\mathrm e}^{\frac {8}{x}} x^{2}}\) | \(834\) |
int(((2*x^11-2*x^10)*exp(4/x)^10+(-20*x^10+20*x^9)*exp(4/x)^9+(-20*x^12+20 *x^11+90*x^9-90*x^8)*exp(4/x)^8+(160*x^11-160*x^10-240*x^8+240*x^7)*exp(4/ x)^7+(80*x^13-80*x^12-550*x^10+720*x^9+420*x^7-420*x^6)*exp(4/x)^6+(-480*x ^12+480*x^11+1020*x^9-1920*x^8-504*x^6+504*x^5)*exp(4/x)^5+(-160*x^14+160* x^13+1180*x^11-1840*x^10-1050*x^8+3000*x^7+420*x^5-420*x^4)*exp(4/x)^4+(64 0*x^13-640*x^12-1360*x^10+3520*x^9+520*x^7-2720*x^6-240*x^4+240*x^3)*exp(4 /x)^3+(160*x^15-160*x^14-1000*x^12+1600*x^11-25*x^10-200*x^9-3120*x^8-10*x ^6+1360*x^5+90*x^3-90*x^2)*exp(4/x)^2+(-320*x^14+320*x^13+560*x^11-1280*x^ 10+250*x^9+880*x^8+1120*x^7-100*x^5-320*x^4-20*x^2+20*x)*exp(4/x)-64*x^16+ 64*x^15+240*x^13-160*x^12-150*x^11-40*x^10+160*x^9-225*x^8-100*x^7-80*x^6+ 30*x^4+20*x^3+2*x-2)/(x^10*exp(4/x)^10-10*x^9*exp(4/x)^9+(-10*x^11+45*x^8) *exp(4/x)^8+(80*x^10-120*x^7)*exp(4/x)^7+(40*x^12-280*x^9+210*x^6)*exp(4/x )^6+(-240*x^11+560*x^8-252*x^5)*exp(4/x)^5+(-80*x^13+600*x^10-700*x^7+210* x^4)*exp(4/x)^4+(320*x^12-800*x^9+560*x^6-120*x^3)*exp(4/x)^3+(80*x^14-480 *x^11+600*x^8-280*x^5+45*x^2)*exp(4/x)^2+(-160*x^13+320*x^10-240*x^7+80*x^ 4-10*x)*exp(4/x)-32*x^15+80*x^12-80*x^9+40*x^6-10*x^3+1),x,method=_RETURNV ERBOSE)
x^2-2*x+5*(2*x^4*exp(4/x)^4-8*exp(4/x)^2*x^5+8*x^6-8*x^3*exp(4/x)^3+16*exp (4/x)*x^4-5*x^4+12*x^2*exp(4/x)^2-8*x^3-8*x*exp(4/x)+2)*x^5/(-x^2*exp(4/x) ^2+2*x^3+2*x*exp(4/x)-1)^4
Leaf count of result is larger than twice the leaf count of optimal. 505 vs. \(2 (34) = 68\).
Time = 0.31 (sec) , antiderivative size = 505, normalized size of antiderivative = 14.03 \[ \int \frac {-2+2 x+20 x^3+30 x^4-80 x^6-100 x^7-225 x^8+160 x^9-40 x^{10}-150 x^{11}-160 x^{12}+240 x^{13}+64 x^{15}-64 x^{16}+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{40/x} \left (-2 x^{10}+2 x^{11}\right )+e^{28/x} \left (240 x^7-240 x^8-160 x^{10}+160 x^{11}\right )+e^{20/x} \left (504 x^5-504 x^6-1920 x^8+1020 x^9+480 x^{11}-480 x^{12}\right )+e^{32/x} \left (-90 x^8+90 x^9+20 x^{11}-20 x^{12}\right )+e^{24/x} \left (-420 x^6+420 x^7+720 x^9-550 x^{10}-80 x^{12}+80 x^{13}\right )+e^{12/x} \left (240 x^3-240 x^4-2720 x^6+520 x^7+3520 x^9-1360 x^{10}-640 x^{12}+640 x^{13}\right )+e^{4/x} \left (20 x-20 x^2-320 x^4-100 x^5+1120 x^7+880 x^8+250 x^9-1280 x^{10}+560 x^{11}+320 x^{13}-320 x^{14}\right )+e^{16/x} \left (-420 x^4+420 x^5+3000 x^7-1050 x^8-1840 x^{10}+1180 x^{11}+160 x^{13}-160 x^{14}\right )+e^{8/x} \left (-90 x^2+90 x^3+1360 x^5-10 x^6-3120 x^8-200 x^9-25 x^{10}+1600 x^{11}-1000 x^{12}-160 x^{14}+160 x^{15}\right )}{1-10 x^3+40 x^6-80 x^9-10 e^{36/x} x^9+e^{40/x} x^{10}+80 x^{12}-32 x^{15}+e^{28/x} \left (-120 x^7+80 x^{10}\right )+e^{20/x} \left (-252 x^5+560 x^8-240 x^{11}\right )+e^{32/x} \left (45 x^8-10 x^{11}\right )+e^{24/x} \left (210 x^6-280 x^9+40 x^{12}\right )+e^{12/x} \left (-120 x^3+560 x^6-800 x^9+320 x^{12}\right )+e^{4/x} \left (-10 x+80 x^4-240 x^7+320 x^{10}-160 x^{13}\right )+e^{16/x} \left (210 x^4-700 x^7+600 x^{10}-80 x^{13}\right )+e^{8/x} \left (45 x^2-280 x^5+600 x^8-480 x^{11}+80 x^{14}\right )} \, dx=\frac {16 \, x^{14} - 32 \, x^{13} + 8 \, x^{11} + 64 \, x^{10} - 25 \, x^{9} - 16 \, x^{8} - 48 \, x^{7} + 2 \, x^{5} + 16 \, x^{4} + x^{2} + {\left (x^{10} - 2 \, x^{9}\right )} e^{\frac {32}{x}} - 8 \, {\left (x^{9} - 2 \, x^{8}\right )} e^{\frac {28}{x}} - 4 \, {\left (2 \, x^{11} - 4 \, x^{10} - 7 \, x^{8} + 14 \, x^{7}\right )} e^{\frac {24}{x}} + 8 \, {\left (6 \, x^{10} - 12 \, x^{9} - 7 \, x^{7} + 14 \, x^{6}\right )} e^{\frac {20}{x}} + 2 \, {\left (12 \, x^{12} - 24 \, x^{11} - 55 \, x^{9} + 120 \, x^{8} + 35 \, x^{6} - 70 \, x^{5}\right )} e^{\frac {16}{x}} - 8 \, {\left (12 \, x^{11} - 24 \, x^{10} - 15 \, x^{8} + 40 \, x^{7} + 7 \, x^{5} - 14 \, x^{4}\right )} e^{\frac {12}{x}} - 4 \, {\left (8 \, x^{13} - 16 \, x^{12} - 26 \, x^{10} + 72 \, x^{9} + 15 \, x^{7} - 60 \, x^{6} - 7 \, x^{4} + 14 \, x^{3}\right )} e^{\frac {8}{x}} + 8 \, {\left (8 \, x^{12} - 16 \, x^{11} - 2 \, x^{9} + 24 \, x^{8} + x^{6} - 12 \, x^{5} - x^{3} + 2 \, x^{2}\right )} e^{\frac {4}{x}} - 2 \, x}{16 \, x^{12} - 32 \, x^{9} + x^{8} e^{\frac {32}{x}} - 8 \, x^{7} e^{\frac {28}{x}} + 24 \, x^{6} - 8 \, x^{3} - 4 \, {\left (2 \, x^{9} - 7 \, x^{6}\right )} e^{\frac {24}{x}} + 8 \, {\left (6 \, x^{8} - 7 \, x^{5}\right )} e^{\frac {20}{x}} + 2 \, {\left (12 \, x^{10} - 60 \, x^{7} + 35 \, x^{4}\right )} e^{\frac {16}{x}} - 8 \, {\left (12 \, x^{9} - 20 \, x^{6} + 7 \, x^{3}\right )} e^{\frac {12}{x}} - 4 \, {\left (8 \, x^{11} - 36 \, x^{8} + 30 \, x^{5} - 7 \, x^{2}\right )} e^{\frac {8}{x}} + 8 \, {\left (8 \, x^{10} - 12 \, x^{7} + 6 \, x^{4} - x\right )} e^{\frac {4}{x}} + 1} \]
integrate(((2*x^11-2*x^10)*exp(4/x)^10+(-20*x^10+20*x^9)*exp(4/x)^9+(-20*x ^12+20*x^11+90*x^9-90*x^8)*exp(4/x)^8+(160*x^11-160*x^10-240*x^8+240*x^7)* exp(4/x)^7+(80*x^13-80*x^12-550*x^10+720*x^9+420*x^7-420*x^6)*exp(4/x)^6+( -480*x^12+480*x^11+1020*x^9-1920*x^8-504*x^6+504*x^5)*exp(4/x)^5+(-160*x^1 4+160*x^13+1180*x^11-1840*x^10-1050*x^8+3000*x^7+420*x^5-420*x^4)*exp(4/x) ^4+(640*x^13-640*x^12-1360*x^10+3520*x^9+520*x^7-2720*x^6-240*x^4+240*x^3) *exp(4/x)^3+(160*x^15-160*x^14-1000*x^12+1600*x^11-25*x^10-200*x^9-3120*x^ 8-10*x^6+1360*x^5+90*x^3-90*x^2)*exp(4/x)^2+(-320*x^14+320*x^13+560*x^11-1 280*x^10+250*x^9+880*x^8+1120*x^7-100*x^5-320*x^4-20*x^2+20*x)*exp(4/x)-64 *x^16+64*x^15+240*x^13-160*x^12-150*x^11-40*x^10+160*x^9-225*x^8-100*x^7-8 0*x^6+30*x^4+20*x^3+2*x-2)/(x^10*exp(4/x)^10-10*x^9*exp(4/x)^9+(-10*x^11+4 5*x^8)*exp(4/x)^8+(80*x^10-120*x^7)*exp(4/x)^7+(40*x^12-280*x^9+210*x^6)*e xp(4/x)^6+(-240*x^11+560*x^8-252*x^5)*exp(4/x)^5+(-80*x^13+600*x^10-700*x^ 7+210*x^4)*exp(4/x)^4+(320*x^12-800*x^9+560*x^6-120*x^3)*exp(4/x)^3+(80*x^ 14-480*x^11+600*x^8-280*x^5+45*x^2)*exp(4/x)^2+(-160*x^13+320*x^10-240*x^7 +80*x^4-10*x)*exp(4/x)-32*x^15+80*x^12-80*x^9+40*x^6-10*x^3+1),x, algorith m=\
(16*x^14 - 32*x^13 + 8*x^11 + 64*x^10 - 25*x^9 - 16*x^8 - 48*x^7 + 2*x^5 + 16*x^4 + x^2 + (x^10 - 2*x^9)*e^(32/x) - 8*(x^9 - 2*x^8)*e^(28/x) - 4*(2* x^11 - 4*x^10 - 7*x^8 + 14*x^7)*e^(24/x) + 8*(6*x^10 - 12*x^9 - 7*x^7 + 14 *x^6)*e^(20/x) + 2*(12*x^12 - 24*x^11 - 55*x^9 + 120*x^8 + 35*x^6 - 70*x^5 )*e^(16/x) - 8*(12*x^11 - 24*x^10 - 15*x^8 + 40*x^7 + 7*x^5 - 14*x^4)*e^(1 2/x) - 4*(8*x^13 - 16*x^12 - 26*x^10 + 72*x^9 + 15*x^7 - 60*x^6 - 7*x^4 + 14*x^3)*e^(8/x) + 8*(8*x^12 - 16*x^11 - 2*x^9 + 24*x^8 + x^6 - 12*x^5 - x^ 3 + 2*x^2)*e^(4/x) - 2*x)/(16*x^12 - 32*x^9 + x^8*e^(32/x) - 8*x^7*e^(28/x ) + 24*x^6 - 8*x^3 - 4*(2*x^9 - 7*x^6)*e^(24/x) + 8*(6*x^8 - 7*x^5)*e^(20/ x) + 2*(12*x^10 - 60*x^7 + 35*x^4)*e^(16/x) - 8*(12*x^9 - 20*x^6 + 7*x^3)* e^(12/x) - 4*(8*x^11 - 36*x^8 + 30*x^5 - 7*x^2)*e^(8/x) + 8*(8*x^10 - 12*x ^7 + 6*x^4 - x)*e^(4/x) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 238 vs. \(2 (24) = 48\).
Time = 0.70 (sec) , antiderivative size = 238, normalized size of antiderivative = 6.61 \[ \int \frac {-2+2 x+20 x^3+30 x^4-80 x^6-100 x^7-225 x^8+160 x^9-40 x^{10}-150 x^{11}-160 x^{12}+240 x^{13}+64 x^{15}-64 x^{16}+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{40/x} \left (-2 x^{10}+2 x^{11}\right )+e^{28/x} \left (240 x^7-240 x^8-160 x^{10}+160 x^{11}\right )+e^{20/x} \left (504 x^5-504 x^6-1920 x^8+1020 x^9+480 x^{11}-480 x^{12}\right )+e^{32/x} \left (-90 x^8+90 x^9+20 x^{11}-20 x^{12}\right )+e^{24/x} \left (-420 x^6+420 x^7+720 x^9-550 x^{10}-80 x^{12}+80 x^{13}\right )+e^{12/x} \left (240 x^3-240 x^4-2720 x^6+520 x^7+3520 x^9-1360 x^{10}-640 x^{12}+640 x^{13}\right )+e^{4/x} \left (20 x-20 x^2-320 x^4-100 x^5+1120 x^7+880 x^8+250 x^9-1280 x^{10}+560 x^{11}+320 x^{13}-320 x^{14}\right )+e^{16/x} \left (-420 x^4+420 x^5+3000 x^7-1050 x^8-1840 x^{10}+1180 x^{11}+160 x^{13}-160 x^{14}\right )+e^{8/x} \left (-90 x^2+90 x^3+1360 x^5-10 x^6-3120 x^8-200 x^9-25 x^{10}+1600 x^{11}-1000 x^{12}-160 x^{14}+160 x^{15}\right )}{1-10 x^3+40 x^6-80 x^9-10 e^{36/x} x^9+e^{40/x} x^{10}+80 x^{12}-32 x^{15}+e^{28/x} \left (-120 x^7+80 x^{10}\right )+e^{20/x} \left (-252 x^5+560 x^8-240 x^{11}\right )+e^{32/x} \left (45 x^8-10 x^{11}\right )+e^{24/x} \left (210 x^6-280 x^9+40 x^{12}\right )+e^{12/x} \left (-120 x^3+560 x^6-800 x^9+320 x^{12}\right )+e^{4/x} \left (-10 x+80 x^4-240 x^7+320 x^{10}-160 x^{13}\right )+e^{16/x} \left (210 x^4-700 x^7+600 x^{10}-80 x^{13}\right )+e^{8/x} \left (45 x^2-280 x^5+600 x^8-480 x^{11}+80 x^{14}\right )} \, dx=x^{2} - 2 x + \frac {40 x^{11} + 10 x^{9} e^{\frac {16}{x}} - 25 x^{9} - 40 x^{8} e^{\frac {12}{x}} - 40 x^{8} + 10 x^{5} + \left (80 x^{9} - 40 x^{6}\right ) e^{\frac {4}{x}} + \left (- 40 x^{10} + 60 x^{7}\right ) e^{\frac {8}{x}}}{16 x^{12} - 32 x^{9} + x^{8} e^{\frac {32}{x}} - 8 x^{7} e^{\frac {28}{x}} + 24 x^{6} - 8 x^{3} + \left (48 x^{8} - 56 x^{5}\right ) e^{\frac {20}{x}} + \left (- 8 x^{9} + 28 x^{6}\right ) e^{\frac {24}{x}} + \left (- 96 x^{9} + 160 x^{6} - 56 x^{3}\right ) e^{\frac {12}{x}} + \left (24 x^{10} - 120 x^{7} + 70 x^{4}\right ) e^{\frac {16}{x}} + \left (64 x^{10} - 96 x^{7} + 48 x^{4} - 8 x\right ) e^{\frac {4}{x}} + \left (- 32 x^{11} + 144 x^{8} - 120 x^{5} + 28 x^{2}\right ) e^{\frac {8}{x}} + 1} \]
integrate(((2*x**11-2*x**10)*exp(4/x)**10+(-20*x**10+20*x**9)*exp(4/x)**9+ (-20*x**12+20*x**11+90*x**9-90*x**8)*exp(4/x)**8+(160*x**11-160*x**10-240* x**8+240*x**7)*exp(4/x)**7+(80*x**13-80*x**12-550*x**10+720*x**9+420*x**7- 420*x**6)*exp(4/x)**6+(-480*x**12+480*x**11+1020*x**9-1920*x**8-504*x**6+5 04*x**5)*exp(4/x)**5+(-160*x**14+160*x**13+1180*x**11-1840*x**10-1050*x**8 +3000*x**7+420*x**5-420*x**4)*exp(4/x)**4+(640*x**13-640*x**12-1360*x**10+ 3520*x**9+520*x**7-2720*x**6-240*x**4+240*x**3)*exp(4/x)**3+(160*x**15-160 *x**14-1000*x**12+1600*x**11-25*x**10-200*x**9-3120*x**8-10*x**6+1360*x**5 +90*x**3-90*x**2)*exp(4/x)**2+(-320*x**14+320*x**13+560*x**11-1280*x**10+2 50*x**9+880*x**8+1120*x**7-100*x**5-320*x**4-20*x**2+20*x)*exp(4/x)-64*x** 16+64*x**15+240*x**13-160*x**12-150*x**11-40*x**10+160*x**9-225*x**8-100*x **7-80*x**6+30*x**4+20*x**3+2*x-2)/(x**10*exp(4/x)**10-10*x**9*exp(4/x)**9 +(-10*x**11+45*x**8)*exp(4/x)**8+(80*x**10-120*x**7)*exp(4/x)**7+(40*x**12 -280*x**9+210*x**6)*exp(4/x)**6+(-240*x**11+560*x**8-252*x**5)*exp(4/x)**5 +(-80*x**13+600*x**10-700*x**7+210*x**4)*exp(4/x)**4+(320*x**12-800*x**9+5 60*x**6-120*x**3)*exp(4/x)**3+(80*x**14-480*x**11+600*x**8-280*x**5+45*x** 2)*exp(4/x)**2+(-160*x**13+320*x**10-240*x**7+80*x**4-10*x)*exp(4/x)-32*x* *15+80*x**12-80*x**9+40*x**6-10*x**3+1),x)
x**2 - 2*x + (40*x**11 + 10*x**9*exp(16/x) - 25*x**9 - 40*x**8*exp(12/x) - 40*x**8 + 10*x**5 + (80*x**9 - 40*x**6)*exp(4/x) + (-40*x**10 + 60*x**7)* exp(8/x))/(16*x**12 - 32*x**9 + x**8*exp(32/x) - 8*x**7*exp(28/x) + 24*x** 6 - 8*x**3 + (48*x**8 - 56*x**5)*exp(20/x) + (-8*x**9 + 28*x**6)*exp(24/x) + (-96*x**9 + 160*x**6 - 56*x**3)*exp(12/x) + (24*x**10 - 120*x**7 + 70*x **4)*exp(16/x) + (64*x**10 - 96*x**7 + 48*x**4 - 8*x)*exp(4/x) + (-32*x**1 1 + 144*x**8 - 120*x**5 + 28*x**2)*exp(8/x) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 505 vs. \(2 (34) = 68\).
Time = 0.53 (sec) , antiderivative size = 505, normalized size of antiderivative = 14.03 \[ \int \frac {-2+2 x+20 x^3+30 x^4-80 x^6-100 x^7-225 x^8+160 x^9-40 x^{10}-150 x^{11}-160 x^{12}+240 x^{13}+64 x^{15}-64 x^{16}+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{40/x} \left (-2 x^{10}+2 x^{11}\right )+e^{28/x} \left (240 x^7-240 x^8-160 x^{10}+160 x^{11}\right )+e^{20/x} \left (504 x^5-504 x^6-1920 x^8+1020 x^9+480 x^{11}-480 x^{12}\right )+e^{32/x} \left (-90 x^8+90 x^9+20 x^{11}-20 x^{12}\right )+e^{24/x} \left (-420 x^6+420 x^7+720 x^9-550 x^{10}-80 x^{12}+80 x^{13}\right )+e^{12/x} \left (240 x^3-240 x^4-2720 x^6+520 x^7+3520 x^9-1360 x^{10}-640 x^{12}+640 x^{13}\right )+e^{4/x} \left (20 x-20 x^2-320 x^4-100 x^5+1120 x^7+880 x^8+250 x^9-1280 x^{10}+560 x^{11}+320 x^{13}-320 x^{14}\right )+e^{16/x} \left (-420 x^4+420 x^5+3000 x^7-1050 x^8-1840 x^{10}+1180 x^{11}+160 x^{13}-160 x^{14}\right )+e^{8/x} \left (-90 x^2+90 x^3+1360 x^5-10 x^6-3120 x^8-200 x^9-25 x^{10}+1600 x^{11}-1000 x^{12}-160 x^{14}+160 x^{15}\right )}{1-10 x^3+40 x^6-80 x^9-10 e^{36/x} x^9+e^{40/x} x^{10}+80 x^{12}-32 x^{15}+e^{28/x} \left (-120 x^7+80 x^{10}\right )+e^{20/x} \left (-252 x^5+560 x^8-240 x^{11}\right )+e^{32/x} \left (45 x^8-10 x^{11}\right )+e^{24/x} \left (210 x^6-280 x^9+40 x^{12}\right )+e^{12/x} \left (-120 x^3+560 x^6-800 x^9+320 x^{12}\right )+e^{4/x} \left (-10 x+80 x^4-240 x^7+320 x^{10}-160 x^{13}\right )+e^{16/x} \left (210 x^4-700 x^7+600 x^{10}-80 x^{13}\right )+e^{8/x} \left (45 x^2-280 x^5+600 x^8-480 x^{11}+80 x^{14}\right )} \, dx=\frac {16 \, x^{14} - 32 \, x^{13} + 8 \, x^{11} + 64 \, x^{10} - 25 \, x^{9} - 16 \, x^{8} - 48 \, x^{7} + 2 \, x^{5} + 16 \, x^{4} + x^{2} + {\left (x^{10} - 2 \, x^{9}\right )} e^{\frac {32}{x}} - 8 \, {\left (x^{9} - 2 \, x^{8}\right )} e^{\frac {28}{x}} - 4 \, {\left (2 \, x^{11} - 4 \, x^{10} - 7 \, x^{8} + 14 \, x^{7}\right )} e^{\frac {24}{x}} + 8 \, {\left (6 \, x^{10} - 12 \, x^{9} - 7 \, x^{7} + 14 \, x^{6}\right )} e^{\frac {20}{x}} + 2 \, {\left (12 \, x^{12} - 24 \, x^{11} - 55 \, x^{9} + 120 \, x^{8} + 35 \, x^{6} - 70 \, x^{5}\right )} e^{\frac {16}{x}} - 8 \, {\left (12 \, x^{11} - 24 \, x^{10} - 15 \, x^{8} + 40 \, x^{7} + 7 \, x^{5} - 14 \, x^{4}\right )} e^{\frac {12}{x}} - 4 \, {\left (8 \, x^{13} - 16 \, x^{12} - 26 \, x^{10} + 72 \, x^{9} + 15 \, x^{7} - 60 \, x^{6} - 7 \, x^{4} + 14 \, x^{3}\right )} e^{\frac {8}{x}} + 8 \, {\left (8 \, x^{12} - 16 \, x^{11} - 2 \, x^{9} + 24 \, x^{8} + x^{6} - 12 \, x^{5} - x^{3} + 2 \, x^{2}\right )} e^{\frac {4}{x}} - 2 \, x}{16 \, x^{12} - 32 \, x^{9} + x^{8} e^{\frac {32}{x}} - 8 \, x^{7} e^{\frac {28}{x}} + 24 \, x^{6} - 8 \, x^{3} - 4 \, {\left (2 \, x^{9} - 7 \, x^{6}\right )} e^{\frac {24}{x}} + 8 \, {\left (6 \, x^{8} - 7 \, x^{5}\right )} e^{\frac {20}{x}} + 2 \, {\left (12 \, x^{10} - 60 \, x^{7} + 35 \, x^{4}\right )} e^{\frac {16}{x}} - 8 \, {\left (12 \, x^{9} - 20 \, x^{6} + 7 \, x^{3}\right )} e^{\frac {12}{x}} - 4 \, {\left (8 \, x^{11} - 36 \, x^{8} + 30 \, x^{5} - 7 \, x^{2}\right )} e^{\frac {8}{x}} + 8 \, {\left (8 \, x^{10} - 12 \, x^{7} + 6 \, x^{4} - x\right )} e^{\frac {4}{x}} + 1} \]
integrate(((2*x^11-2*x^10)*exp(4/x)^10+(-20*x^10+20*x^9)*exp(4/x)^9+(-20*x ^12+20*x^11+90*x^9-90*x^8)*exp(4/x)^8+(160*x^11-160*x^10-240*x^8+240*x^7)* exp(4/x)^7+(80*x^13-80*x^12-550*x^10+720*x^9+420*x^7-420*x^6)*exp(4/x)^6+( -480*x^12+480*x^11+1020*x^9-1920*x^8-504*x^6+504*x^5)*exp(4/x)^5+(-160*x^1 4+160*x^13+1180*x^11-1840*x^10-1050*x^8+3000*x^7+420*x^5-420*x^4)*exp(4/x) ^4+(640*x^13-640*x^12-1360*x^10+3520*x^9+520*x^7-2720*x^6-240*x^4+240*x^3) *exp(4/x)^3+(160*x^15-160*x^14-1000*x^12+1600*x^11-25*x^10-200*x^9-3120*x^ 8-10*x^6+1360*x^5+90*x^3-90*x^2)*exp(4/x)^2+(-320*x^14+320*x^13+560*x^11-1 280*x^10+250*x^9+880*x^8+1120*x^7-100*x^5-320*x^4-20*x^2+20*x)*exp(4/x)-64 *x^16+64*x^15+240*x^13-160*x^12-150*x^11-40*x^10+160*x^9-225*x^8-100*x^7-8 0*x^6+30*x^4+20*x^3+2*x-2)/(x^10*exp(4/x)^10-10*x^9*exp(4/x)^9+(-10*x^11+4 5*x^8)*exp(4/x)^8+(80*x^10-120*x^7)*exp(4/x)^7+(40*x^12-280*x^9+210*x^6)*e xp(4/x)^6+(-240*x^11+560*x^8-252*x^5)*exp(4/x)^5+(-80*x^13+600*x^10-700*x^ 7+210*x^4)*exp(4/x)^4+(320*x^12-800*x^9+560*x^6-120*x^3)*exp(4/x)^3+(80*x^ 14-480*x^11+600*x^8-280*x^5+45*x^2)*exp(4/x)^2+(-160*x^13+320*x^10-240*x^7 +80*x^4-10*x)*exp(4/x)-32*x^15+80*x^12-80*x^9+40*x^6-10*x^3+1),x, algorith m=\
(16*x^14 - 32*x^13 + 8*x^11 + 64*x^10 - 25*x^9 - 16*x^8 - 48*x^7 + 2*x^5 + 16*x^4 + x^2 + (x^10 - 2*x^9)*e^(32/x) - 8*(x^9 - 2*x^8)*e^(28/x) - 4*(2* x^11 - 4*x^10 - 7*x^8 + 14*x^7)*e^(24/x) + 8*(6*x^10 - 12*x^9 - 7*x^7 + 14 *x^6)*e^(20/x) + 2*(12*x^12 - 24*x^11 - 55*x^9 + 120*x^8 + 35*x^6 - 70*x^5 )*e^(16/x) - 8*(12*x^11 - 24*x^10 - 15*x^8 + 40*x^7 + 7*x^5 - 14*x^4)*e^(1 2/x) - 4*(8*x^13 - 16*x^12 - 26*x^10 + 72*x^9 + 15*x^7 - 60*x^6 - 7*x^4 + 14*x^3)*e^(8/x) + 8*(8*x^12 - 16*x^11 - 2*x^9 + 24*x^8 + x^6 - 12*x^5 - x^ 3 + 2*x^2)*e^(4/x) - 2*x)/(16*x^12 - 32*x^9 + x^8*e^(32/x) - 8*x^7*e^(28/x ) + 24*x^6 - 8*x^3 - 4*(2*x^9 - 7*x^6)*e^(24/x) + 8*(6*x^8 - 7*x^5)*e^(20/ x) + 2*(12*x^10 - 60*x^7 + 35*x^4)*e^(16/x) - 8*(12*x^9 - 20*x^6 + 7*x^3)* e^(12/x) - 4*(8*x^11 - 36*x^8 + 30*x^5 - 7*x^2)*e^(8/x) + 8*(8*x^10 - 12*x ^7 + 6*x^4 - x)*e^(4/x) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 728 vs. \(2 (34) = 68\).
Time = 67.58 (sec) , antiderivative size = 728, normalized size of antiderivative = 20.22 \[ \int \frac {-2+2 x+20 x^3+30 x^4-80 x^6-100 x^7-225 x^8+160 x^9-40 x^{10}-150 x^{11}-160 x^{12}+240 x^{13}+64 x^{15}-64 x^{16}+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{40/x} \left (-2 x^{10}+2 x^{11}\right )+e^{28/x} \left (240 x^7-240 x^8-160 x^{10}+160 x^{11}\right )+e^{20/x} \left (504 x^5-504 x^6-1920 x^8+1020 x^9+480 x^{11}-480 x^{12}\right )+e^{32/x} \left (-90 x^8+90 x^9+20 x^{11}-20 x^{12}\right )+e^{24/x} \left (-420 x^6+420 x^7+720 x^9-550 x^{10}-80 x^{12}+80 x^{13}\right )+e^{12/x} \left (240 x^3-240 x^4-2720 x^6+520 x^7+3520 x^9-1360 x^{10}-640 x^{12}+640 x^{13}\right )+e^{4/x} \left (20 x-20 x^2-320 x^4-100 x^5+1120 x^7+880 x^8+250 x^9-1280 x^{10}+560 x^{11}+320 x^{13}-320 x^{14}\right )+e^{16/x} \left (-420 x^4+420 x^5+3000 x^7-1050 x^8-1840 x^{10}+1180 x^{11}+160 x^{13}-160 x^{14}\right )+e^{8/x} \left (-90 x^2+90 x^3+1360 x^5-10 x^6-3120 x^8-200 x^9-25 x^{10}+1600 x^{11}-1000 x^{12}-160 x^{14}+160 x^{15}\right )}{1-10 x^3+40 x^6-80 x^9-10 e^{36/x} x^9+e^{40/x} x^{10}+80 x^{12}-32 x^{15}+e^{28/x} \left (-120 x^7+80 x^{10}\right )+e^{20/x} \left (-252 x^5+560 x^8-240 x^{11}\right )+e^{32/x} \left (45 x^8-10 x^{11}\right )+e^{24/x} \left (210 x^6-280 x^9+40 x^{12}\right )+e^{12/x} \left (-120 x^3+560 x^6-800 x^9+320 x^{12}\right )+e^{4/x} \left (-10 x+80 x^4-240 x^7+320 x^{10}-160 x^{13}\right )+e^{16/x} \left (210 x^4-700 x^7+600 x^{10}-80 x^{13}\right )+e^{8/x} \left (45 x^2-280 x^5+600 x^8-480 x^{11}+80 x^{14}\right )} \, dx =\text {Too large to display} \]
integrate(((2*x^11-2*x^10)*exp(4/x)^10+(-20*x^10+20*x^9)*exp(4/x)^9+(-20*x ^12+20*x^11+90*x^9-90*x^8)*exp(4/x)^8+(160*x^11-160*x^10-240*x^8+240*x^7)* exp(4/x)^7+(80*x^13-80*x^12-550*x^10+720*x^9+420*x^7-420*x^6)*exp(4/x)^6+( -480*x^12+480*x^11+1020*x^9-1920*x^8-504*x^6+504*x^5)*exp(4/x)^5+(-160*x^1 4+160*x^13+1180*x^11-1840*x^10-1050*x^8+3000*x^7+420*x^5-420*x^4)*exp(4/x) ^4+(640*x^13-640*x^12-1360*x^10+3520*x^9+520*x^7-2720*x^6-240*x^4+240*x^3) *exp(4/x)^3+(160*x^15-160*x^14-1000*x^12+1600*x^11-25*x^10-200*x^9-3120*x^ 8-10*x^6+1360*x^5+90*x^3-90*x^2)*exp(4/x)^2+(-320*x^14+320*x^13+560*x^11-1 280*x^10+250*x^9+880*x^8+1120*x^7-100*x^5-320*x^4-20*x^2+20*x)*exp(4/x)-64 *x^16+64*x^15+240*x^13-160*x^12-150*x^11-40*x^10+160*x^9-225*x^8-100*x^7-8 0*x^6+30*x^4+20*x^3+2*x-2)/(x^10*exp(4/x)^10-10*x^9*exp(4/x)^9+(-10*x^11+4 5*x^8)*exp(4/x)^8+(80*x^10-120*x^7)*exp(4/x)^7+(40*x^12-280*x^9+210*x^6)*e xp(4/x)^6+(-240*x^11+560*x^8-252*x^5)*exp(4/x)^5+(-80*x^13+600*x^10-700*x^ 7+210*x^4)*exp(4/x)^4+(320*x^12-800*x^9+560*x^6-120*x^3)*exp(4/x)^3+(80*x^ 14-480*x^11+600*x^8-280*x^5+45*x^2)*exp(4/x)^2+(-160*x^13+320*x^10-240*x^7 +80*x^4-10*x)*exp(4/x)-32*x^15+80*x^12-80*x^9+40*x^6-10*x^3+1),x, algorith m=\
-(32*e^(8/x)/x + 32/x - 24*e^(16/x)/x^2 - 64*e^(8/x)/x^2 - 64*e^(4/x)/x^2 + 8*e^(24/x)/x^3 + 48*e^(16/x)/x^3 + 96*e^(12/x)/x^3 + 128*e^(4/x)/x^3 - 4 8/x^3 - e^(32/x)/x^4 - 16*e^(24/x)/x^4 - 48*e^(20/x)/x^4 - 192*e^(12/x)/x^ 4 - 64*e^(8/x)/x^4 - 64/x^4 + 2*e^(32/x)/x^5 + 8*e^(28/x)/x^5 + 96*e^(20/x )/x^5 + 100*e^(16/x)/x^5 + 288*e^(8/x)/x^5 - 64*e^(4/x)/x^5 + 50/x^5 - 16* e^(28/x)/x^6 - 28*e^(24/x)/x^6 - 240*e^(16/x)/x^6 - 80*e^(12/x)/x^6 - 192* e^(4/x)/x^6 + 56/x^6 + 56*e^(24/x)/x^7 + 56*e^(20/x)/x^7 + 320*e^(12/x)/x^ 7 + 48/x^7 - 112*e^(20/x)/x^8 - 70*e^(16/x)/x^8 - 240*e^(8/x)/x^8 + 32*e^( 4/x)/x^8 + 140*e^(16/x)/x^9 + 56*e^(12/x)/x^9 + 96*e^(4/x)/x^9 - 12/x^9 - 112*e^(12/x)/x^10 - 28*e^(8/x)/x^10 - 16/x^10 + 56*e^(8/x)/x^11 + 8*e^(4/x )/x^11 - 16*e^(4/x)/x^12 - 1/x^12 + 2/x^13 - 16)/(16/x^2 - 32*e^(8/x)/x^3 + 24*e^(16/x)/x^4 + 64*e^(4/x)/x^4 - 8*e^(24/x)/x^5 - 96*e^(12/x)/x^5 - 32 /x^5 + e^(32/x)/x^6 + 48*e^(20/x)/x^6 + 144*e^(8/x)/x^6 - 8*e^(28/x)/x^7 - 120*e^(16/x)/x^7 - 96*e^(4/x)/x^7 + 28*e^(24/x)/x^8 + 160*e^(12/x)/x^8 + 24/x^8 - 56*e^(20/x)/x^9 - 120*e^(8/x)/x^9 + 70*e^(16/x)/x^10 + 48*e^(4/x) /x^10 - 56*e^(12/x)/x^11 - 8/x^11 + 28*e^(8/x)/x^12 - 8*e^(4/x)/x^13 + 1/x ^14)
Timed out. \[ \int \frac {-2+2 x+20 x^3+30 x^4-80 x^6-100 x^7-225 x^8+160 x^9-40 x^{10}-150 x^{11}-160 x^{12}+240 x^{13}+64 x^{15}-64 x^{16}+e^{36/x} \left (20 x^9-20 x^{10}\right )+e^{40/x} \left (-2 x^{10}+2 x^{11}\right )+e^{28/x} \left (240 x^7-240 x^8-160 x^{10}+160 x^{11}\right )+e^{20/x} \left (504 x^5-504 x^6-1920 x^8+1020 x^9+480 x^{11}-480 x^{12}\right )+e^{32/x} \left (-90 x^8+90 x^9+20 x^{11}-20 x^{12}\right )+e^{24/x} \left (-420 x^6+420 x^7+720 x^9-550 x^{10}-80 x^{12}+80 x^{13}\right )+e^{12/x} \left (240 x^3-240 x^4-2720 x^6+520 x^7+3520 x^9-1360 x^{10}-640 x^{12}+640 x^{13}\right )+e^{4/x} \left (20 x-20 x^2-320 x^4-100 x^5+1120 x^7+880 x^8+250 x^9-1280 x^{10}+560 x^{11}+320 x^{13}-320 x^{14}\right )+e^{16/x} \left (-420 x^4+420 x^5+3000 x^7-1050 x^8-1840 x^{10}+1180 x^{11}+160 x^{13}-160 x^{14}\right )+e^{8/x} \left (-90 x^2+90 x^3+1360 x^5-10 x^6-3120 x^8-200 x^9-25 x^{10}+1600 x^{11}-1000 x^{12}-160 x^{14}+160 x^{15}\right )}{1-10 x^3+40 x^6-80 x^9-10 e^{36/x} x^9+e^{40/x} x^{10}+80 x^{12}-32 x^{15}+e^{28/x} \left (-120 x^7+80 x^{10}\right )+e^{20/x} \left (-252 x^5+560 x^8-240 x^{11}\right )+e^{32/x} \left (45 x^8-10 x^{11}\right )+e^{24/x} \left (210 x^6-280 x^9+40 x^{12}\right )+e^{12/x} \left (-120 x^3+560 x^6-800 x^9+320 x^{12}\right )+e^{4/x} \left (-10 x+80 x^4-240 x^7+320 x^{10}-160 x^{13}\right )+e^{16/x} \left (210 x^4-700 x^7+600 x^{10}-80 x^{13}\right )+e^{8/x} \left (45 x^2-280 x^5+600 x^8-480 x^{11}+80 x^{14}\right )} \, dx=\int \frac {{\mathrm {e}}^{16/x}\,\left (160\,x^{14}-160\,x^{13}-1180\,x^{11}+1840\,x^{10}+1050\,x^8-3000\,x^7-420\,x^5+420\,x^4\right )-2\,x-{\mathrm {e}}^{12/x}\,\left (640\,x^{13}-640\,x^{12}-1360\,x^{10}+3520\,x^9+520\,x^7-2720\,x^6-240\,x^4+240\,x^3\right )+{\mathrm {e}}^{32/x}\,\left (20\,x^{12}-20\,x^{11}-90\,x^9+90\,x^8\right )-{\mathrm {e}}^{28/x}\,\left (160\,x^{11}-160\,x^{10}-240\,x^8+240\,x^7\right )-{\mathrm {e}}^{4/x}\,\left (-320\,x^{14}+320\,x^{13}+560\,x^{11}-1280\,x^{10}+250\,x^9+880\,x^8+1120\,x^7-100\,x^5-320\,x^4-20\,x^2+20\,x\right )+{\mathrm {e}}^{24/x}\,\left (-80\,x^{13}+80\,x^{12}+550\,x^{10}-720\,x^9-420\,x^7+420\,x^6\right )-{\mathrm {e}}^{20/x}\,\left (-480\,x^{12}+480\,x^{11}+1020\,x^9-1920\,x^8-504\,x^6+504\,x^5\right )+{\mathrm {e}}^{8/x}\,\left (-160\,x^{15}+160\,x^{14}+1000\,x^{12}-1600\,x^{11}+25\,x^{10}+200\,x^9+3120\,x^8+10\,x^6-1360\,x^5-90\,x^3+90\,x^2\right )+{\mathrm {e}}^{40/x}\,\left (2\,x^{10}-2\,x^{11}\right )-{\mathrm {e}}^{36/x}\,\left (20\,x^9-20\,x^{10}\right )-20\,x^3-30\,x^4+80\,x^6+100\,x^7+225\,x^8-160\,x^9+40\,x^{10}+150\,x^{11}+160\,x^{12}-240\,x^{13}-64\,x^{15}+64\,x^{16}+2}{{\mathrm {e}}^{4/x}\,\left (160\,x^{13}-320\,x^{10}+240\,x^7-80\,x^4+10\,x\right )-{\mathrm {e}}^{16/x}\,\left (-80\,x^{13}+600\,x^{10}-700\,x^7+210\,x^4\right )+{\mathrm {e}}^{12/x}\,\left (-320\,x^{12}+800\,x^9-560\,x^6+120\,x^3\right )-{\mathrm {e}}^{8/x}\,\left (80\,x^{14}-480\,x^{11}+600\,x^8-280\,x^5+45\,x^2\right )-{\mathrm {e}}^{32/x}\,\left (45\,x^8-10\,x^{11}\right )+{\mathrm {e}}^{28/x}\,\left (120\,x^7-80\,x^{10}\right )+10\,x^9\,{\mathrm {e}}^{36/x}-x^{10}\,{\mathrm {e}}^{40/x}+10\,x^3-40\,x^6+80\,x^9-80\,x^{12}+32\,x^{15}-{\mathrm {e}}^{24/x}\,\left (40\,x^{12}-280\,x^9+210\,x^6\right )+{\mathrm {e}}^{20/x}\,\left (240\,x^{11}-560\,x^8+252\,x^5\right )-1} \,d x \]
int((exp(16/x)*(420*x^4 - 420*x^5 - 3000*x^7 + 1050*x^8 + 1840*x^10 - 1180 *x^11 - 160*x^13 + 160*x^14) - 2*x - exp(12/x)*(240*x^3 - 240*x^4 - 2720*x ^6 + 520*x^7 + 3520*x^9 - 1360*x^10 - 640*x^12 + 640*x^13) + exp(32/x)*(90 *x^8 - 90*x^9 - 20*x^11 + 20*x^12) - exp(28/x)*(240*x^7 - 240*x^8 - 160*x^ 10 + 160*x^11) - exp(4/x)*(20*x - 20*x^2 - 320*x^4 - 100*x^5 + 1120*x^7 + 880*x^8 + 250*x^9 - 1280*x^10 + 560*x^11 + 320*x^13 - 320*x^14) + exp(24/x )*(420*x^6 - 420*x^7 - 720*x^9 + 550*x^10 + 80*x^12 - 80*x^13) - exp(20/x) *(504*x^5 - 504*x^6 - 1920*x^8 + 1020*x^9 + 480*x^11 - 480*x^12) + exp(8/x )*(90*x^2 - 90*x^3 - 1360*x^5 + 10*x^6 + 3120*x^8 + 200*x^9 + 25*x^10 - 16 00*x^11 + 1000*x^12 + 160*x^14 - 160*x^15) + exp(40/x)*(2*x^10 - 2*x^11) - exp(36/x)*(20*x^9 - 20*x^10) - 20*x^3 - 30*x^4 + 80*x^6 + 100*x^7 + 225*x ^8 - 160*x^9 + 40*x^10 + 150*x^11 + 160*x^12 - 240*x^13 - 64*x^15 + 64*x^1 6 + 2)/(exp(4/x)*(10*x - 80*x^4 + 240*x^7 - 320*x^10 + 160*x^13) - exp(16/ x)*(210*x^4 - 700*x^7 + 600*x^10 - 80*x^13) + exp(12/x)*(120*x^3 - 560*x^6 + 800*x^9 - 320*x^12) - exp(8/x)*(45*x^2 - 280*x^5 + 600*x^8 - 480*x^11 + 80*x^14) - exp(32/x)*(45*x^8 - 10*x^11) + exp(28/x)*(120*x^7 - 80*x^10) + 10*x^9*exp(36/x) - x^10*exp(40/x) + 10*x^3 - 40*x^6 + 80*x^9 - 80*x^12 + 32*x^15 - exp(24/x)*(210*x^6 - 280*x^9 + 40*x^12) + exp(20/x)*(252*x^5 - 5 60*x^8 + 240*x^11) - 1),x)
int((exp(16/x)*(420*x^4 - 420*x^5 - 3000*x^7 + 1050*x^8 + 1840*x^10 - 1180 *x^11 - 160*x^13 + 160*x^14) - 2*x - exp(12/x)*(240*x^3 - 240*x^4 - 2720*x ^6 + 520*x^7 + 3520*x^9 - 1360*x^10 - 640*x^12 + 640*x^13) + exp(32/x)*(90 *x^8 - 90*x^9 - 20*x^11 + 20*x^12) - exp(28/x)*(240*x^7 - 240*x^8 - 160*x^ 10 + 160*x^11) - exp(4/x)*(20*x - 20*x^2 - 320*x^4 - 100*x^5 + 1120*x^7 + 880*x^8 + 250*x^9 - 1280*x^10 + 560*x^11 + 320*x^13 - 320*x^14) + exp(24/x )*(420*x^6 - 420*x^7 - 720*x^9 + 550*x^10 + 80*x^12 - 80*x^13) - exp(20/x) *(504*x^5 - 504*x^6 - 1920*x^8 + 1020*x^9 + 480*x^11 - 480*x^12) + exp(8/x )*(90*x^2 - 90*x^3 - 1360*x^5 + 10*x^6 + 3120*x^8 + 200*x^9 + 25*x^10 - 16 00*x^11 + 1000*x^12 + 160*x^14 - 160*x^15) + exp(40/x)*(2*x^10 - 2*x^11) - exp(36/x)*(20*x^9 - 20*x^10) - 20*x^3 - 30*x^4 + 80*x^6 + 100*x^7 + 225*x ^8 - 160*x^9 + 40*x^10 + 150*x^11 + 160*x^12 - 240*x^13 - 64*x^15 + 64*x^1 6 + 2)/(exp(4/x)*(10*x - 80*x^4 + 240*x^7 - 320*x^10 + 160*x^13) - exp(16/ x)*(210*x^4 - 700*x^7 + 600*x^10 - 80*x^13) + exp(12/x)*(120*x^3 - 560*x^6 + 800*x^9 - 320*x^12) - exp(8/x)*(45*x^2 - 280*x^5 + 600*x^8 - 480*x^11 + 80*x^14) - exp(32/x)*(45*x^8 - 10*x^11) + exp(28/x)*(120*x^7 - 80*x^10) + 10*x^9*exp(36/x) - x^10*exp(40/x) + 10*x^3 - 40*x^6 + 80*x^9 - 80*x^12 + 32*x^15 - exp(24/x)*(210*x^6 - 280*x^9 + 40*x^12) + exp(20/x)*(252*x^5 - 5 60*x^8 + 240*x^11) - 1), x)