Integrand size = 475, antiderivative size = 39 \[ \int \frac {e^{5 x} \left (-128-512 x-192 x^2\right )+e^{4 x} \left (-3072 x-5376 x^2-1536 x^3\right )+e^{2 x} \left (2304 x+6336 x^2-52224 x^3-34560 x^4\right )+e^{3 x} \left (192+896 x-20000 x^2-20608 x^3-3456 x^4\right )+e^x \left (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6\right )}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} \left (1024 x^2+1024 x^3+256 x^4\right )+e^{7 x} \left (24576 x^3+24576 x^4+6144 x^5\right )+e^{6 x} \left (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6\right )+e^{5 x} \left (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7\right )+e^{4 x} \left (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8\right )+e^{3 x} \left (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9\right )+e^{2 x} \left (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10}\right )+e^x \left (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11}\right )} \, dx=\frac {e^x}{4 x (2+x) \left (-x+\left (\frac {3}{4}+x-\left (e^x+3 x\right )^2\right )^2\right )} \] Output:
exp(x)/x/(2+x)/(4*(3/4+x-(3*x+exp(x))^2)^2-4*x)
Leaf count is larger than twice the leaf count of optimal. \(83\) vs. \(2(39)=78\).
Time = 6.84 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.13 \[ \int \frac {e^{5 x} \left (-128-512 x-192 x^2\right )+e^{4 x} \left (-3072 x-5376 x^2-1536 x^3\right )+e^{2 x} \left (2304 x+6336 x^2-52224 x^3-34560 x^4\right )+e^{3 x} \left (192+896 x-20000 x^2-20608 x^3-3456 x^4\right )+e^x \left (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6\right )}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} \left (1024 x^2+1024 x^3+256 x^4\right )+e^{7 x} \left (24576 x^3+24576 x^4+6144 x^5\right )+e^{6 x} \left (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6\right )+e^{5 x} \left (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7\right )+e^{4 x} \left (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8\right )+e^{3 x} \left (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9\right )+e^{2 x} \left (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10}\right )+e^x \left (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11}\right )} \, dx=\frac {4 e^x}{x (2+x) \left (9+16 e^{4 x}+8 x+192 e^{3 x} x-200 x^2-288 x^3+1296 x^4+48 e^x x \left (-3-4 x+36 x^2\right )+8 e^{2 x} \left (-3-4 x+108 x^2\right )\right )} \] Input:
Integrate[(E^(5*x)*(-128 - 512*x - 192*x^2) + E^(4*x)*(-3072*x - 5376*x^2 - 1536*x^3) + E^(2*x)*(2304*x + 6336*x^2 - 52224*x^3 - 34560*x^4) + E^(3*x )*(192 + 896*x - 20000*x^2 - 20608*x^3 - 3456*x^4) + E^x*(-72 - 128*x + 48 04*x^2 + 10848*x^3 - 49184*x^4 - 21888*x^5 + 5184*x^6))/(324*x^2 + 900*x^3 - 13487*x^4 - 47536*x^5 + 197808*x^6 + 770240*x^7 - 1139360*x^8 - 4591872 *x^9 + 3297024*x^10 + 5971968*x^11 + 1679616*x^12 + E^(8*x)*(1024*x^2 + 10 24*x^3 + 256*x^4) + E^(7*x)*(24576*x^3 + 24576*x^4 + 6144*x^5) + E^(6*x)*( -3072*x^2 - 7168*x^3 + 253184*x^4 + 257024*x^5 + 64512*x^6) + E^(5*x)*(-55 296*x^3 - 129024*x^4 + 1460736*x^5 + 1529856*x^6 + 387072*x^7) + E^(4*x)*( 3456*x^2 + 10624*x^3 - 400544*x^4 - 959744*x^5 + 5150976*x^6 + 5667840*x^7 + 1451520*x^8) + E^(3*x)*(41472*x^3 + 127488*x^4 - 1488768*x^5 - 3775488* x^6 + 11326464*x^7 + 13381632*x^8 + 3483648*x^9) + E^(2*x)*(-1728*x^2 - 55 68*x^3 + 177232*x^4 + 563520*x^5 - 2972352*x^6 - 8281600*x^7 + 15075072*x^ 8 + 19657728*x^9 + 5225472*x^10) + E^x*(-10368*x^3 - 33408*x^4 + 316896*x^ 5 + 1086336*x^6 - 2980224*x^7 - 9600000*x^8 + 10990080*x^9 + 16422912*x^10 + 4478976*x^11)),x]
Output:
(4*E^x)/(x*(2 + x)*(9 + 16*E^(4*x) + 8*x + 192*E^(3*x)*x - 200*x^2 - 288*x ^3 + 1296*x^4 + 48*E^x*x*(-3 - 4*x + 36*x^2) + 8*E^(2*x)*(-3 - 4*x + 108*x ^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.
| \(\displaystyle \int \frac {e^{5 x} \left (-192 x^2-512 x-128\right )+e^{4 x} \left (-1536 x^3-5376 x^2-3072 x\right )+e^{2 x} \left (-34560 x^4-52224 x^3+6336 x^2+2304 x\right )+e^{3 x} \left (-3456 x^4-20608 x^3-20000 x^2+896 x+192\right )+e^x \left (5184 x^6-21888 x^5-49184 x^4+10848 x^3+4804 x^2-128 x-72\right )}{1679616 x^{12}+5971968 x^{11}+3297024 x^{10}-4591872 x^9-1139360 x^8+770240 x^7+197808 x^6-47536 x^5-13487 x^4+900 x^3+324 x^2+e^{7 x} \left (6144 x^5+24576 x^4+24576 x^3\right )+e^{8 x} \left (256 x^4+1024 x^3+1024 x^2\right )+e^{5 x} \left (387072 x^7+1529856 x^6+1460736 x^5-129024 x^4-55296 x^3\right )+e^{6 x} \left (64512 x^6+257024 x^5+253184 x^4-7168 x^3-3072 x^2\right )+e^{3 x} \left (3483648 x^9+13381632 x^8+11326464 x^7-3775488 x^6-1488768 x^5+127488 x^4+41472 x^3\right )+e^{4 x} \left (1451520 x^8+5667840 x^7+5150976 x^6-959744 x^5-400544 x^4+10624 x^3+3456 x^2\right )+e^x \left (4478976 x^{11}+16422912 x^{10}+10990080 x^9-9600000 x^8-2980224 x^7+1086336 x^6+316896 x^5-33408 x^4-10368 x^3\right )+e^{2 x} \left (5225472 x^{10}+19657728 x^9+15075072 x^8-8281600 x^7-2972352 x^6+563520 x^5+177232 x^4-5568 x^3-1728 x^2\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 e^x \left (1296 x^6-5472 x^5-12296 x^4+2712 x^3+1201 x^2-192 e^{3 x} \left (2 x^2+7 x+4\right ) x-16 e^{4 x} \left (3 x^2+8 x+2\right )-48 e^x \left (180 x^3+272 x^2-33 x-12\right ) x-8 e^{2 x} \left (108 x^4+644 x^3+625 x^2-28 x-6\right )-32 x-18\right )}{x^2 (x+2)^2 \left (1296 x^4-288 x^3-200 x^2+48 e^x \left (36 x^2-4 x-3\right ) x+8 e^{2 x} \left (108 x^2-4 x-3\right )+192 e^{3 x} x+8 x+16 e^{4 x}+9\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {e^x \left (-1296 x^6+5472 x^5+12296 x^4-2712 x^3-1201 x^2+192 e^{3 x} \left (2 x^2+7 x+4\right ) x-48 e^x \left (-180 x^3-272 x^2+33 x+12\right ) x+32 x+16 e^{4 x} \left (3 x^2+8 x+2\right )-8 e^{2 x} \left (-108 x^4-644 x^3-625 x^2+28 x+6\right )+18\right )}{x^2 (x+2)^2 \left (1296 x^4-288 x^3-200 x^2+192 e^{3 x} x-48 e^x \left (-36 x^2+4 x+3\right ) x+8 x+16 e^{4 x}-8 e^{2 x} \left (-108 x^2+4 x+3\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {e^x \left (-1296 x^6+5472 x^5+12296 x^4-2712 x^3-1201 x^2+192 e^{3 x} \left (2 x^2+7 x+4\right ) x-48 e^x \left (-180 x^3-272 x^2+33 x+12\right ) x+32 x+16 e^{4 x} \left (3 x^2+8 x+2\right )-8 e^{2 x} \left (-108 x^4-644 x^3-625 x^2+28 x+6\right )+18\right )}{x^2 (x+2)^2 \left (1296 x^4-288 x^3-200 x^2+192 e^{3 x} x-48 e^x \left (-36 x^2+4 x+3\right ) x+8 x+16 e^{4 x}-8 e^{2 x} \left (-108 x^2+4 x+3\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {e^x \left (3 x^2+8 x+2\right )}{x^2 (x+2)^2 \left (1296 x^4+1728 e^x x^3-288 x^3-192 e^x x^2+864 e^{2 x} x^2-200 x^2-144 e^x x-32 e^{2 x} x+192 e^{3 x} x+8 x-24 e^{2 x}+16 e^{4 x}+9\right )}-\frac {4 e^x \left (1296 x^4+1296 e^x x^3-1584 x^3-1440 e^x x^2+432 e^{2 x} x^2+16 x^2-12 e^x x-448 e^{2 x} x+48 e^{3 x} x+108 x+36 e^x-4 e^{2 x}-48 e^{3 x}+7\right )}{x (x+2) \left (1296 x^4+1728 e^x x^3-288 x^3-192 e^x x^2+864 e^{2 x} x^2-200 x^2-144 e^x x-32 e^{2 x} x+192 e^{3 x} x+8 x-24 e^{2 x}+16 e^{4 x}+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -4 \int \left (\frac {e^x \left (3 x^2+8 x+2\right )}{x^2 (x+2)^2 \left (1296 x^4+1728 e^x x^3-288 x^3-192 e^x x^2+864 e^{2 x} x^2-200 x^2-144 e^x x-32 e^{2 x} x+192 e^{3 x} x+8 x-24 e^{2 x}+16 e^{4 x}+9\right )}-\frac {4 e^x \left (1296 x^4+1296 e^x x^3-1584 x^3-1440 e^x x^2+432 e^{2 x} x^2+16 x^2-12 e^x x-448 e^{2 x} x+48 e^{3 x} x+108 x+36 e^x-4 e^{2 x}-48 e^{3 x}+7\right )}{x (x+2) \left (1296 x^4+1728 e^x x^3-288 x^3-192 e^x x^2+864 e^{2 x} x^2-200 x^2-144 e^x x-32 e^{2 x} x+192 e^{3 x} x+8 x-24 e^{2 x}+16 e^{4 x}+9\right )^2}\right )dx\) |
Input:
Int[(E^(5*x)*(-128 - 512*x - 192*x^2) + E^(4*x)*(-3072*x - 5376*x^2 - 1536 *x^3) + E^(2*x)*(2304*x + 6336*x^2 - 52224*x^3 - 34560*x^4) + E^(3*x)*(192 + 896*x - 20000*x^2 - 20608*x^3 - 3456*x^4) + E^x*(-72 - 128*x + 4804*x^2 + 10848*x^3 - 49184*x^4 - 21888*x^5 + 5184*x^6))/(324*x^2 + 900*x^3 - 134 87*x^4 - 47536*x^5 + 197808*x^6 + 770240*x^7 - 1139360*x^8 - 4591872*x^9 + 3297024*x^10 + 5971968*x^11 + 1679616*x^12 + E^(8*x)*(1024*x^2 + 1024*x^3 + 256*x^4) + E^(7*x)*(24576*x^3 + 24576*x^4 + 6144*x^5) + E^(6*x)*(-3072* x^2 - 7168*x^3 + 253184*x^4 + 257024*x^5 + 64512*x^6) + E^(5*x)*(-55296*x^ 3 - 129024*x^4 + 1460736*x^5 + 1529856*x^6 + 387072*x^7) + E^(4*x)*(3456*x ^2 + 10624*x^3 - 400544*x^4 - 959744*x^5 + 5150976*x^6 + 5667840*x^7 + 145 1520*x^8) + E^(3*x)*(41472*x^3 + 127488*x^4 - 1488768*x^5 - 3775488*x^6 + 11326464*x^7 + 13381632*x^8 + 3483648*x^9) + E^(2*x)*(-1728*x^2 - 5568*x^3 + 177232*x^4 + 563520*x^5 - 2972352*x^6 - 8281600*x^7 + 15075072*x^8 + 19 657728*x^9 + 5225472*x^10) + E^x*(-10368*x^3 - 33408*x^4 + 316896*x^5 + 10 86336*x^6 - 2980224*x^7 - 9600000*x^8 + 10990080*x^9 + 16422912*x^10 + 447 8976*x^11)),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(88\) vs. \(2(34)=68\).
Time = 1.26 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.28
| method | result | size |
| risch | \(\frac {4 \,{\mathrm e}^{x}}{x \left (2+x \right ) \left (1296 x^{4}+1728 \,{\mathrm e}^{x} x^{3}+864 \,{\mathrm e}^{2 x} x^{2}+192 x \,{\mathrm e}^{3 x}+16 \,{\mathrm e}^{4 x}-288 x^{3}-192 \,{\mathrm e}^{x} x^{2}-32 x \,{\mathrm e}^{2 x}-200 x^{2}-144 \,{\mathrm e}^{x} x -24 \,{\mathrm e}^{2 x}+8 x +9\right )}\) | \(89\) |
| parallelrisch | \(\frac {4 \,{\mathrm e}^{x}}{x \left (16 x \,{\mathrm e}^{4 x}+192 x^{2} {\mathrm e}^{3 x}+864 \,{\mathrm e}^{2 x} x^{3}+1728 \,{\mathrm e}^{x} x^{4}+1296 x^{5}+32 \,{\mathrm e}^{4 x}+384 x \,{\mathrm e}^{3 x}+1696 \,{\mathrm e}^{2 x} x^{2}+3264 \,{\mathrm e}^{x} x^{3}+2304 x^{4}-88 x \,{\mathrm e}^{2 x}-528 \,{\mathrm e}^{x} x^{2}-776 x^{3}-48 \,{\mathrm e}^{2 x}-288 \,{\mathrm e}^{x} x -392 x^{2}+25 x +18\right )}\) | \(121\) |
Input:
int(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x)^4+(- 3456*x^4-20608*x^3-20000*x^2+896*x+192)*exp(x)^3+(-34560*x^4-52224*x^3+633 6*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+4804*x^2-12 8*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+24576*x^4+ 24576*x^3)*exp(x)^7+(64512*x^6+257024*x^5+253184*x^4-7168*x^3-3072*x^2)*ex p(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)*exp(x)^5+ (1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3+3456* x^2)*exp(x)^4+(3483648*x^9+13381632*x^8+11326464*x^7-3775488*x^6-1488768*x ^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+15075072*x^8- 8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp(x)^2+ (4478976*x^11+16422912*x^10+10990080*x^9-9600000*x^8-2980224*x^7+1086336*x ^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+5971968*x^11+329702 4*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487*x^4+9 00*x^3+324*x^2),x,method=_RETURNVERBOSE)
Output:
4/x/(2+x)*exp(x)/(1296*x^4+1728*exp(x)*x^3+864*exp(x)^2*x^2+192*x*exp(x)^3 +16*exp(x)^4-288*x^3-192*exp(x)*x^2-32*x*exp(x)^2-200*x^2-144*exp(x)*x-24* exp(x)^2+8*x+9)
Leaf count of result is larger than twice the leaf count of optimal. 113 vs. \(2 (35) = 70\).
Time = 0.10 (sec) , antiderivative size = 113, normalized size of antiderivative = 2.90 \[ \int \frac {e^{5 x} \left (-128-512 x-192 x^2\right )+e^{4 x} \left (-3072 x-5376 x^2-1536 x^3\right )+e^{2 x} \left (2304 x+6336 x^2-52224 x^3-34560 x^4\right )+e^{3 x} \left (192+896 x-20000 x^2-20608 x^3-3456 x^4\right )+e^x \left (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6\right )}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} \left (1024 x^2+1024 x^3+256 x^4\right )+e^{7 x} \left (24576 x^3+24576 x^4+6144 x^5\right )+e^{6 x} \left (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6\right )+e^{5 x} \left (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7\right )+e^{4 x} \left (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8\right )+e^{3 x} \left (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9\right )+e^{2 x} \left (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10}\right )+e^x \left (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11}\right )} \, dx=\frac {4 \, e^{x}}{1296 \, x^{6} + 2304 \, x^{5} - 776 \, x^{4} - 392 \, x^{3} + 25 \, x^{2} + 16 \, {\left (x^{2} + 2 \, x\right )} e^{\left (4 \, x\right )} + 192 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (3 \, x\right )} + 8 \, {\left (108 \, x^{4} + 212 \, x^{3} - 11 \, x^{2} - 6 \, x\right )} e^{\left (2 \, x\right )} + 48 \, {\left (36 \, x^{5} + 68 \, x^{4} - 11 \, x^{3} - 6 \, x^{2}\right )} e^{x} + 18 \, x} \] Input:
integrate(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x )^4+(-3456*x^4-20608*x^3-20000*x^2+896*x+192)*exp(x)^3+(-34560*x^4-52224*x ^3+6336*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+4804* x^2-128*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+2457 6*x^4+24576*x^3)*exp(x)^7+(64512*x^6+257024*x^5+253184*x^4-7168*x^3-3072*x ^2)*exp(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)*exp (x)^5+(1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3 +3456*x^2)*exp(x)^4+(3483648*x^9+13381632*x^8+11326464*x^7-3775488*x^6-148 8768*x^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+1507507 2*x^8-8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp (x)^2+(4478976*x^11+16422912*x^10+10990080*x^9-9600000*x^8-2980224*x^7+108 6336*x^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+5971968*x^11+ 3297024*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487 *x^4+900*x^3+324*x^2),x, algorithm="fricas")
Output:
4*e^x/(1296*x^6 + 2304*x^5 - 776*x^4 - 392*x^3 + 25*x^2 + 16*(x^2 + 2*x)*e ^(4*x) + 192*(x^3 + 2*x^2)*e^(3*x) + 8*(108*x^4 + 212*x^3 - 11*x^2 - 6*x)* e^(2*x) + 48*(36*x^5 + 68*x^4 - 11*x^3 - 6*x^2)*e^x + 18*x)
Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (27) = 54\).
Time = 0.43 (sec) , antiderivative size = 110, normalized size of antiderivative = 2.82 \[ \int \frac {e^{5 x} \left (-128-512 x-192 x^2\right )+e^{4 x} \left (-3072 x-5376 x^2-1536 x^3\right )+e^{2 x} \left (2304 x+6336 x^2-52224 x^3-34560 x^4\right )+e^{3 x} \left (192+896 x-20000 x^2-20608 x^3-3456 x^4\right )+e^x \left (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6\right )}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} \left (1024 x^2+1024 x^3+256 x^4\right )+e^{7 x} \left (24576 x^3+24576 x^4+6144 x^5\right )+e^{6 x} \left (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6\right )+e^{5 x} \left (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7\right )+e^{4 x} \left (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8\right )+e^{3 x} \left (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9\right )+e^{2 x} \left (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10}\right )+e^x \left (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11}\right )} \, dx=\frac {e^{x}}{324 x^{6} + 576 x^{5} - 194 x^{4} - 98 x^{3} + \frac {25 x^{2}}{4} + \frac {9 x}{2} + \left (4 x^{2} + 8 x\right ) e^{4 x} + \left (48 x^{3} + 96 x^{2}\right ) e^{3 x} + \left (216 x^{4} + 424 x^{3} - 22 x^{2} - 12 x\right ) e^{2 x} + \left (432 x^{5} + 816 x^{4} - 132 x^{3} - 72 x^{2}\right ) e^{x}} \] Input:
integrate(((-192*x**2-512*x-128)*exp(x)**5+(-1536*x**3-5376*x**2-3072*x)*e xp(x)**4+(-3456*x**4-20608*x**3-20000*x**2+896*x+192)*exp(x)**3+(-34560*x* *4-52224*x**3+6336*x**2+2304*x)*exp(x)**2+(5184*x**6-21888*x**5-49184*x**4 +10848*x**3+4804*x**2-128*x-72)*exp(x))/((256*x**4+1024*x**3+1024*x**2)*ex p(x)**8+(6144*x**5+24576*x**4+24576*x**3)*exp(x)**7+(64512*x**6+257024*x** 5+253184*x**4-7168*x**3-3072*x**2)*exp(x)**6+(387072*x**7+1529856*x**6+146 0736*x**5-129024*x**4-55296*x**3)*exp(x)**5+(1451520*x**8+5667840*x**7+515 0976*x**6-959744*x**5-400544*x**4+10624*x**3+3456*x**2)*exp(x)**4+(3483648 *x**9+13381632*x**8+11326464*x**7-3775488*x**6-1488768*x**5+127488*x**4+41 472*x**3)*exp(x)**3+(5225472*x**10+19657728*x**9+15075072*x**8-8281600*x** 7-2972352*x**6+563520*x**5+177232*x**4-5568*x**3-1728*x**2)*exp(x)**2+(447 8976*x**11+16422912*x**10+10990080*x**9-9600000*x**8-2980224*x**7+1086336* x**6+316896*x**5-33408*x**4-10368*x**3)*exp(x)+1679616*x**12+5971968*x**11 +3297024*x**10-4591872*x**9-1139360*x**8+770240*x**7+197808*x**6-47536*x** 5-13487*x**4+900*x**3+324*x**2),x)
Output:
exp(x)/(324*x**6 + 576*x**5 - 194*x**4 - 98*x**3 + 25*x**2/4 + 9*x/2 + (4* x**2 + 8*x)*exp(4*x) + (48*x**3 + 96*x**2)*exp(3*x) + (216*x**4 + 424*x**3 - 22*x**2 - 12*x)*exp(2*x) + (432*x**5 + 816*x**4 - 132*x**3 - 72*x**2)*e xp(x))
Leaf count of result is larger than twice the leaf count of optimal. 113 vs. \(2 (35) = 70\).
Time = 0.28 (sec) , antiderivative size = 113, normalized size of antiderivative = 2.90 \[ \int \frac {e^{5 x} \left (-128-512 x-192 x^2\right )+e^{4 x} \left (-3072 x-5376 x^2-1536 x^3\right )+e^{2 x} \left (2304 x+6336 x^2-52224 x^3-34560 x^4\right )+e^{3 x} \left (192+896 x-20000 x^2-20608 x^3-3456 x^4\right )+e^x \left (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6\right )}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} \left (1024 x^2+1024 x^3+256 x^4\right )+e^{7 x} \left (24576 x^3+24576 x^4+6144 x^5\right )+e^{6 x} \left (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6\right )+e^{5 x} \left (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7\right )+e^{4 x} \left (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8\right )+e^{3 x} \left (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9\right )+e^{2 x} \left (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10}\right )+e^x \left (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11}\right )} \, dx=\frac {4 \, e^{x}}{1296 \, x^{6} + 2304 \, x^{5} - 776 \, x^{4} - 392 \, x^{3} + 25 \, x^{2} + 16 \, {\left (x^{2} + 2 \, x\right )} e^{\left (4 \, x\right )} + 192 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (3 \, x\right )} + 8 \, {\left (108 \, x^{4} + 212 \, x^{3} - 11 \, x^{2} - 6 \, x\right )} e^{\left (2 \, x\right )} + 48 \, {\left (36 \, x^{5} + 68 \, x^{4} - 11 \, x^{3} - 6 \, x^{2}\right )} e^{x} + 18 \, x} \] Input:
integrate(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x )^4+(-3456*x^4-20608*x^3-20000*x^2+896*x+192)*exp(x)^3+(-34560*x^4-52224*x ^3+6336*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+4804* x^2-128*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+2457 6*x^4+24576*x^3)*exp(x)^7+(64512*x^6+257024*x^5+253184*x^4-7168*x^3-3072*x ^2)*exp(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)*exp (x)^5+(1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3 +3456*x^2)*exp(x)^4+(3483648*x^9+13381632*x^8+11326464*x^7-3775488*x^6-148 8768*x^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+1507507 2*x^8-8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp (x)^2+(4478976*x^11+16422912*x^10+10990080*x^9-9600000*x^8-2980224*x^7+108 6336*x^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+5971968*x^11+ 3297024*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487 *x^4+900*x^3+324*x^2),x, algorithm="maxima")
Output:
4*e^x/(1296*x^6 + 2304*x^5 - 776*x^4 - 392*x^3 + 25*x^2 + 16*(x^2 + 2*x)*e ^(4*x) + 192*(x^3 + 2*x^2)*e^(3*x) + 8*(108*x^4 + 212*x^3 - 11*x^2 - 6*x)* e^(2*x) + 48*(36*x^5 + 68*x^4 - 11*x^3 - 6*x^2)*e^x + 18*x)
Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (35) = 70\).
Time = 3.24 (sec) , antiderivative size = 131, normalized size of antiderivative = 3.36 \[ \int \frac {e^{5 x} \left (-128-512 x-192 x^2\right )+e^{4 x} \left (-3072 x-5376 x^2-1536 x^3\right )+e^{2 x} \left (2304 x+6336 x^2-52224 x^3-34560 x^4\right )+e^{3 x} \left (192+896 x-20000 x^2-20608 x^3-3456 x^4\right )+e^x \left (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6\right )}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} \left (1024 x^2+1024 x^3+256 x^4\right )+e^{7 x} \left (24576 x^3+24576 x^4+6144 x^5\right )+e^{6 x} \left (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6\right )+e^{5 x} \left (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7\right )+e^{4 x} \left (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8\right )+e^{3 x} \left (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9\right )+e^{2 x} \left (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10}\right )+e^x \left (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11}\right )} \, dx=\frac {8 \, e^{x}}{1296 \, x^{6} + 1728 \, x^{5} e^{x} + 2304 \, x^{5} + 864 \, x^{4} e^{\left (2 \, x\right )} + 3264 \, x^{4} e^{x} - 776 \, x^{4} + 192 \, x^{3} e^{\left (3 \, x\right )} + 1696 \, x^{3} e^{\left (2 \, x\right )} - 528 \, x^{3} e^{x} - 392 \, x^{3} + 16 \, x^{2} e^{\left (4 \, x\right )} + 384 \, x^{2} e^{\left (3 \, x\right )} - 88 \, x^{2} e^{\left (2 \, x\right )} - 288 \, x^{2} e^{x} + 25 \, x^{2} + 32 \, x e^{\left (4 \, x\right )} - 48 \, x e^{\left (2 \, x\right )} + 18 \, x} \] Input:
integrate(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x )^4+(-3456*x^4-20608*x^3-20000*x^2+896*x+192)*exp(x)^3+(-34560*x^4-52224*x ^3+6336*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+4804* x^2-128*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+2457 6*x^4+24576*x^3)*exp(x)^7+(64512*x^6+257024*x^5+253184*x^4-7168*x^3-3072*x ^2)*exp(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)*exp (x)^5+(1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3 +3456*x^2)*exp(x)^4+(3483648*x^9+13381632*x^8+11326464*x^7-3775488*x^6-148 8768*x^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+1507507 2*x^8-8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp (x)^2+(4478976*x^11+16422912*x^10+10990080*x^9-9600000*x^8-2980224*x^7+108 6336*x^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+5971968*x^11+ 3297024*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487 *x^4+900*x^3+324*x^2),x, algorithm="giac")
Output:
8*e^x/(1296*x^6 + 1728*x^5*e^x + 2304*x^5 + 864*x^4*e^(2*x) + 3264*x^4*e^x - 776*x^4 + 192*x^3*e^(3*x) + 1696*x^3*e^(2*x) - 528*x^3*e^x - 392*x^3 + 16*x^2*e^(4*x) + 384*x^2*e^(3*x) - 88*x^2*e^(2*x) - 288*x^2*e^x + 25*x^2 + 32*x*e^(4*x) - 48*x*e^(2*x) + 18*x)
Timed out. \[ \int \frac {e^{5 x} \left (-128-512 x-192 x^2\right )+e^{4 x} \left (-3072 x-5376 x^2-1536 x^3\right )+e^{2 x} \left (2304 x+6336 x^2-52224 x^3-34560 x^4\right )+e^{3 x} \left (192+896 x-20000 x^2-20608 x^3-3456 x^4\right )+e^x \left (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6\right )}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} \left (1024 x^2+1024 x^3+256 x^4\right )+e^{7 x} \left (24576 x^3+24576 x^4+6144 x^5\right )+e^{6 x} \left (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6\right )+e^{5 x} \left (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7\right )+e^{4 x} \left (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8\right )+e^{3 x} \left (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9\right )+e^{2 x} \left (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10}\right )+e^x \left (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11}\right )} \, dx=\int -\frac {{\mathrm {e}}^{5\,x}\,\left (192\,x^2+512\,x+128\right )+{\mathrm {e}}^{4\,x}\,\left (1536\,x^3+5376\,x^2+3072\,x\right )+{\mathrm {e}}^{3\,x}\,\left (3456\,x^4+20608\,x^3+20000\,x^2-896\,x-192\right )-{\mathrm {e}}^{2\,x}\,\left (-34560\,x^4-52224\,x^3+6336\,x^2+2304\,x\right )+{\mathrm {e}}^x\,\left (-5184\,x^6+21888\,x^5+49184\,x^4-10848\,x^3-4804\,x^2+128\,x+72\right )}{{\mathrm {e}}^{6\,x}\,\left (64512\,x^6+257024\,x^5+253184\,x^4-7168\,x^3-3072\,x^2\right )+{\mathrm {e}}^{5\,x}\,\left (387072\,x^7+1529856\,x^6+1460736\,x^5-129024\,x^4-55296\,x^3\right )+{\mathrm {e}}^{4\,x}\,\left (1451520\,x^8+5667840\,x^7+5150976\,x^6-959744\,x^5-400544\,x^4+10624\,x^3+3456\,x^2\right )+{\mathrm {e}}^{3\,x}\,\left (3483648\,x^9+13381632\,x^8+11326464\,x^7-3775488\,x^6-1488768\,x^5+127488\,x^4+41472\,x^3\right )+{\mathrm {e}}^x\,\left (4478976\,x^{11}+16422912\,x^{10}+10990080\,x^9-9600000\,x^8-2980224\,x^7+1086336\,x^6+316896\,x^5-33408\,x^4-10368\,x^3\right )+{\mathrm {e}}^{8\,x}\,\left (256\,x^4+1024\,x^3+1024\,x^2\right )+{\mathrm {e}}^{7\,x}\,\left (6144\,x^5+24576\,x^4+24576\,x^3\right )+324\,x^2+900\,x^3-13487\,x^4-47536\,x^5+197808\,x^6+770240\,x^7-1139360\,x^8-4591872\,x^9+3297024\,x^{10}+5971968\,x^{11}+1679616\,x^{12}+{\mathrm {e}}^{2\,x}\,\left (5225472\,x^{10}+19657728\,x^9+15075072\,x^8-8281600\,x^7-2972352\,x^6+563520\,x^5+177232\,x^4-5568\,x^3-1728\,x^2\right )} \,d x \] Input:
int(-(exp(5*x)*(512*x + 192*x^2 + 128) + exp(4*x)*(3072*x + 5376*x^2 + 153 6*x^3) + exp(3*x)*(20000*x^2 - 896*x + 20608*x^3 + 3456*x^4 - 192) - exp(2 *x)*(2304*x + 6336*x^2 - 52224*x^3 - 34560*x^4) + exp(x)*(128*x - 4804*x^2 - 10848*x^3 + 49184*x^4 + 21888*x^5 - 5184*x^6 + 72))/(exp(6*x)*(253184*x ^4 - 7168*x^3 - 3072*x^2 + 257024*x^5 + 64512*x^6) + exp(5*x)*(1460736*x^5 - 129024*x^4 - 55296*x^3 + 1529856*x^6 + 387072*x^7) + exp(4*x)*(3456*x^2 + 10624*x^3 - 400544*x^4 - 959744*x^5 + 5150976*x^6 + 5667840*x^7 + 14515 20*x^8) + exp(3*x)*(41472*x^3 + 127488*x^4 - 1488768*x^5 - 3775488*x^6 + 1 1326464*x^7 + 13381632*x^8 + 3483648*x^9) + exp(x)*(316896*x^5 - 33408*x^4 - 10368*x^3 + 1086336*x^6 - 2980224*x^7 - 9600000*x^8 + 10990080*x^9 + 16 422912*x^10 + 4478976*x^11) + exp(8*x)*(1024*x^2 + 1024*x^3 + 256*x^4) + e xp(7*x)*(24576*x^3 + 24576*x^4 + 6144*x^5) + 324*x^2 + 900*x^3 - 13487*x^4 - 47536*x^5 + 197808*x^6 + 770240*x^7 - 1139360*x^8 - 4591872*x^9 + 32970 24*x^10 + 5971968*x^11 + 1679616*x^12 + exp(2*x)*(177232*x^4 - 5568*x^3 - 1728*x^2 + 563520*x^5 - 2972352*x^6 - 8281600*x^7 + 15075072*x^8 + 1965772 8*x^9 + 5225472*x^10)),x)
Output:
int(-(exp(5*x)*(512*x + 192*x^2 + 128) + exp(4*x)*(3072*x + 5376*x^2 + 153 6*x^3) + exp(3*x)*(20000*x^2 - 896*x + 20608*x^3 + 3456*x^4 - 192) - exp(2 *x)*(2304*x + 6336*x^2 - 52224*x^3 - 34560*x^4) + exp(x)*(128*x - 4804*x^2 - 10848*x^3 + 49184*x^4 + 21888*x^5 - 5184*x^6 + 72))/(exp(6*x)*(253184*x ^4 - 7168*x^3 - 3072*x^2 + 257024*x^5 + 64512*x^6) + exp(5*x)*(1460736*x^5 - 129024*x^4 - 55296*x^3 + 1529856*x^6 + 387072*x^7) + exp(4*x)*(3456*x^2 + 10624*x^3 - 400544*x^4 - 959744*x^5 + 5150976*x^6 + 5667840*x^7 + 14515 20*x^8) + exp(3*x)*(41472*x^3 + 127488*x^4 - 1488768*x^5 - 3775488*x^6 + 1 1326464*x^7 + 13381632*x^8 + 3483648*x^9) + exp(x)*(316896*x^5 - 33408*x^4 - 10368*x^3 + 1086336*x^6 - 2980224*x^7 - 9600000*x^8 + 10990080*x^9 + 16 422912*x^10 + 4478976*x^11) + exp(8*x)*(1024*x^2 + 1024*x^3 + 256*x^4) + e xp(7*x)*(24576*x^3 + 24576*x^4 + 6144*x^5) + 324*x^2 + 900*x^3 - 13487*x^4 - 47536*x^5 + 197808*x^6 + 770240*x^7 - 1139360*x^8 - 4591872*x^9 + 32970 24*x^10 + 5971968*x^11 + 1679616*x^12 + exp(2*x)*(177232*x^4 - 5568*x^3 - 1728*x^2 + 563520*x^5 - 2972352*x^6 - 8281600*x^7 + 15075072*x^8 + 1965772 8*x^9 + 5225472*x^10)), x)
Time = 0.23 (sec) , antiderivative size = 133, normalized size of antiderivative = 3.41 \[ \int \frac {e^{5 x} \left (-128-512 x-192 x^2\right )+e^{4 x} \left (-3072 x-5376 x^2-1536 x^3\right )+e^{2 x} \left (2304 x+6336 x^2-52224 x^3-34560 x^4\right )+e^{3 x} \left (192+896 x-20000 x^2-20608 x^3-3456 x^4\right )+e^x \left (-72-128 x+4804 x^2+10848 x^3-49184 x^4-21888 x^5+5184 x^6\right )}{324 x^2+900 x^3-13487 x^4-47536 x^5+197808 x^6+770240 x^7-1139360 x^8-4591872 x^9+3297024 x^{10}+5971968 x^{11}+1679616 x^{12}+e^{8 x} \left (1024 x^2+1024 x^3+256 x^4\right )+e^{7 x} \left (24576 x^3+24576 x^4+6144 x^5\right )+e^{6 x} \left (-3072 x^2-7168 x^3+253184 x^4+257024 x^5+64512 x^6\right )+e^{5 x} \left (-55296 x^3-129024 x^4+1460736 x^5+1529856 x^6+387072 x^7\right )+e^{4 x} \left (3456 x^2+10624 x^3-400544 x^4-959744 x^5+5150976 x^6+5667840 x^7+1451520 x^8\right )+e^{3 x} \left (41472 x^3+127488 x^4-1488768 x^5-3775488 x^6+11326464 x^7+13381632 x^8+3483648 x^9\right )+e^{2 x} \left (-1728 x^2-5568 x^3+177232 x^4+563520 x^5-2972352 x^6-8281600 x^7+15075072 x^8+19657728 x^9+5225472 x^{10}\right )+e^x \left (-10368 x^3-33408 x^4+316896 x^5+1086336 x^6-2980224 x^7-9600000 x^8+10990080 x^9+16422912 x^{10}+4478976 x^{11}\right )} \, dx=\frac {4 e^{x}}{x \left (16 e^{4 x} x +32 e^{4 x}+192 e^{3 x} x^{2}+384 e^{3 x} x +864 e^{2 x} x^{3}+1696 e^{2 x} x^{2}-88 e^{2 x} x -48 e^{2 x}+1728 e^{x} x^{4}+3264 e^{x} x^{3}-528 e^{x} x^{2}-288 e^{x} x +1296 x^{5}+2304 x^{4}-776 x^{3}-392 x^{2}+25 x +18\right )} \] Input:
int(((-192*x^2-512*x-128)*exp(x)^5+(-1536*x^3-5376*x^2-3072*x)*exp(x)^4+(- 3456*x^4-20608*x^3-20000*x^2+896*x+192)*exp(x)^3+(-34560*x^4-52224*x^3+633 6*x^2+2304*x)*exp(x)^2+(5184*x^6-21888*x^5-49184*x^4+10848*x^3+4804*x^2-12 8*x-72)*exp(x))/((256*x^4+1024*x^3+1024*x^2)*exp(x)^8+(6144*x^5+24576*x^4+ 24576*x^3)*exp(x)^7+(64512*x^6+257024*x^5+253184*x^4-7168*x^3-3072*x^2)*ex p(x)^6+(387072*x^7+1529856*x^6+1460736*x^5-129024*x^4-55296*x^3)*exp(x)^5+ (1451520*x^8+5667840*x^7+5150976*x^6-959744*x^5-400544*x^4+10624*x^3+3456* x^2)*exp(x)^4+(3483648*x^9+13381632*x^8+11326464*x^7-3775488*x^6-1488768*x ^5+127488*x^4+41472*x^3)*exp(x)^3+(5225472*x^10+19657728*x^9+15075072*x^8- 8281600*x^7-2972352*x^6+563520*x^5+177232*x^4-5568*x^3-1728*x^2)*exp(x)^2+ (4478976*x^11+16422912*x^10+10990080*x^9-9600000*x^8-2980224*x^7+1086336*x ^6+316896*x^5-33408*x^4-10368*x^3)*exp(x)+1679616*x^12+5971968*x^11+329702 4*x^10-4591872*x^9-1139360*x^8+770240*x^7+197808*x^6-47536*x^5-13487*x^4+9 00*x^3+324*x^2),x)
Output:
(4*e**x)/(x*(16*e**(4*x)*x + 32*e**(4*x) + 192*e**(3*x)*x**2 + 384*e**(3*x )*x + 864*e**(2*x)*x**3 + 1696*e**(2*x)*x**2 - 88*e**(2*x)*x - 48*e**(2*x) + 1728*e**x*x**4 + 3264*e**x*x**3 - 528*e**x*x**2 - 288*e**x*x + 1296*x** 5 + 2304*x**4 - 776*x**3 - 392*x**2 + 25*x + 18))