Integrand size = 282, antiderivative size = 25 \[ \int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx=\frac {(10+x)^2}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2} \] Output:
(x+10)^2/(exp(x^4*(x+16)^8)*x^2-16)^2
Time = 5.79 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx=\frac {(10+x)^2}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2} \] Input:
Integrate[(-320 - 32*x + E^(4294967296*x^4 + 2147483648*x^5 + 469762048*x^ 6 + 58720256*x^7 + 4587520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12) *(-400*x - 60*x^2 - 2*x^3 - 3435973836800*x^5 - 2834678415360*x^6 - 102757 0925568*x^7 - 216426086400*x^8 - 29418848256*x^9 - 2702966784*x^10 - 17031 1680*x^11 - 7277568*x^12 - 202080*x^13 - 3296*x^14 - 24*x^15))/(-4096 + 76 8*E^(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256*x^7 + 4587 520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12)*x^2 - 48*E^(8589934592 *x^4 + 4294967296*x^5 + 939524096*x^6 + 117440512*x^7 + 9175040*x^8 + 4587 52*x^9 + 14336*x^10 + 256*x^11 + 2*x^12)*x^4 + E^(12884901888*x^4 + 644245 0944*x^5 + 1409286144*x^6 + 176160768*x^7 + 13762560*x^8 + 688128*x^9 + 21 504*x^10 + 384*x^11 + 3*x^12)*x^6),x]
Output:
(10 + x)^2/(-16 + E^(x^4*(16 + x)^8)*x^2)^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.
| \(\displaystyle \int \frac {\left (-24 x^{15}-3296 x^{14}-202080 x^{13}-7277568 x^{12}-170311680 x^{11}-2702966784 x^{10}-29418848256 x^9-216426086400 x^8-1027570925568 x^7-2834678415360 x^6-3435973836800 x^5-2 x^3-60 x^2-400 x\right ) \exp \left (x^{12}+128 x^{11}+7168 x^{10}+229376 x^9+4587520 x^8+58720256 x^7+469762048 x^6+2147483648 x^5+4294967296 x^4\right )-32 x-320}{x^6 \exp \left (3 x^{12}+384 x^{11}+21504 x^{10}+688128 x^9+13762560 x^8+176160768 x^7+1409286144 x^6+6442450944 x^5+12884901888 x^4\right )-48 x^4 \exp \left (2 x^{12}+256 x^{11}+14336 x^{10}+458752 x^9+9175040 x^8+117440512 x^7+939524096 x^6+4294967296 x^5+8589934592 x^4\right )+768 x^2 \exp \left (x^{12}+128 x^{11}+7168 x^{10}+229376 x^9+4587520 x^8+58720256 x^7+469762048 x^6+2147483648 x^5+4294967296 x^4\right )-4096} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 (x+10) \left (e^{x^4 (x+16)^8} x \left (12 x^{13}+1528 x^{12}+85760 x^{11}+2781184 x^{10}+57344000 x^9+778043392 x^8+6928990208 x^7+38923141120 x^6+124554051584 x^5+171798691840 x^4+x+20\right )+16\right )}{\left (16-e^{x^4 (x+16)^8} x^2\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {(x+10) \left (e^{x^4 (x+16)^8} x \left (12 x^{13}+1528 x^{12}+85760 x^{11}+2781184 x^{10}+57344000 x^9+778043392 x^8+6928990208 x^7+38923141120 x^6+124554051584 x^5+171798691840 x^4+x+20\right )+16\right )}{\left (16-e^{x^4 (x+16)^8} x^2\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {32 \left (6 x^{12}+704 x^{11}+35840 x^{10}+1032192 x^9+18350080 x^8+205520896 x^7+1409286144 x^6+5368709120 x^5+8589934592 x^4+1\right ) (x+10)^2}{x \left (e^{x^4 (x+16)^8} x^2-16\right )^3}-\frac {12 x^{14}+1648 x^{13}+101040 x^{12}+3638784 x^{11}+85155840 x^{10}+1351483392 x^9+14709424128 x^8+108213043200 x^7+513785462784 x^6+1417339207680 x^5+1717986918400 x^4+x^2+30 x+200}{x \left (e^{x^4 (x+16)^8} x^2-16\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 2 \left (-640 \int \frac {1}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-3200 \int \frac {1}{x \left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-32 \int \frac {x}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-22677427322880 \int \frac {x^4}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-30 \int \frac {1}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-200 \int \frac {1}{x \left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-\int \frac {x}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-1417339207680 \int \frac {x^4}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-192 \int \frac {x^{13}}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-12 \int \frac {x^{13}}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-26368 \int \frac {x^{12}}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-1648 \int \frac {x^{12}}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-1616640 \int \frac {x^{11}}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-101040 \int \frac {x^{11}}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-58220544 \int \frac {x^{10}}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-3638784 \int \frac {x^{10}}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-1362493440 \int \frac {x^9}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-85155840 \int \frac {x^9}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-21623734272 \int \frac {x^8}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-1351483392 \int \frac {x^8}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-235350786048 \int \frac {x^7}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-14709424128 \int \frac {x^7}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-1731408691200 \int \frac {x^6}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-108213043200 \int \frac {x^6}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-8220567404544 \int \frac {x^5}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-513785462784 \int \frac {x^5}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx-27487790694400 \int \frac {x^3}{\left (e^{x^4 (x+16)^8} x^2-16\right )^3}dx-1717986918400 \int \frac {x^3}{\left (e^{x^4 (x+16)^8} x^2-16\right )^2}dx\right )\) |
Input:
Int[(-320 - 32*x + E^(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58 720256*x^7 + 4587520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12)*(-400 *x - 60*x^2 - 2*x^3 - 3435973836800*x^5 - 2834678415360*x^6 - 102757092556 8*x^7 - 216426086400*x^8 - 29418848256*x^9 - 2702966784*x^10 - 170311680*x ^11 - 7277568*x^12 - 202080*x^13 - 3296*x^14 - 24*x^15))/(-4096 + 768*E^(4 294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256*x^7 + 4587520*x^ 8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12)*x^2 - 48*E^(8589934592*x^4 + 4294967296*x^5 + 939524096*x^6 + 117440512*x^7 + 9175040*x^8 + 458752*x^9 + 14336*x^10 + 256*x^11 + 2*x^12)*x^4 + E^(12884901888*x^4 + 6442450944*x ^5 + 1409286144*x^6 + 176160768*x^7 + 13762560*x^8 + 688128*x^9 + 21504*x^ 10 + 384*x^11 + 3*x^12)*x^6),x]
Output:
$Aborted
Timed out.
\[\int \frac {\left (-24 x^{15}-3296 x^{14}-202080 x^{13}-7277568 x^{12}-170311680 x^{11}-2702966784 x^{10}-29418848256 x^{9}-216426086400 x^{8}-1027570925568 x^{7}-2834678415360 x^{6}-3435973836800 x^{5}-2 x^{3}-60 x^{2}-400 x \right ) {\mathrm e}^{x^{12}+128 x^{11}+7168 x^{10}+229376 x^{9}+4587520 x^{8}+58720256 x^{7}+469762048 x^{6}+2147483648 x^{5}+4294967296 x^{4}}-32 x -320}{x^{6} {\mathrm e}^{3 x^{12}+384 x^{11}+21504 x^{10}+688128 x^{9}+13762560 x^{8}+176160768 x^{7}+1409286144 x^{6}+6442450944 x^{5}+12884901888 x^{4}}-48 x^{4} {\mathrm e}^{2 x^{12}+256 x^{11}+14336 x^{10}+458752 x^{9}+9175040 x^{8}+117440512 x^{7}+939524096 x^{6}+4294967296 x^{5}+8589934592 x^{4}}+768 x^{2} {\mathrm e}^{x^{12}+128 x^{11}+7168 x^{10}+229376 x^{9}+4587520 x^{8}+58720256 x^{7}+469762048 x^{6}+2147483648 x^{5}+4294967296 x^{4}}-4096}d x\]
Input:
int(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-270296678 4*x^10-29418848256*x^9-216426086400*x^8-1027570925568*x^7-2834678415360*x^ 6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+229376 *x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4) -32*x-320)/(x^6*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+5872025 6*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12+128*x ^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648 *x^5+4294967296*x^4)^2+768*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587 520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-4096),x)
Output:
int(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-270296678 4*x^10-29418848256*x^9-216426086400*x^8-1027570925568*x^7-2834678415360*x^ 6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+229376 *x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4) -32*x-320)/(x^6*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+5872025 6*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12+128*x ^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648 *x^5+4294967296*x^4)^2+768*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587 520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-4096),x)
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (24) = 48\).
Time = 0.09 (sec) , antiderivative size = 114, normalized size of antiderivative = 4.56 \[ \int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx=\frac {x^{2} + 20 \, x + 100}{x^{4} e^{\left (2 \, x^{12} + 256 \, x^{11} + 14336 \, x^{10} + 458752 \, x^{9} + 9175040 \, x^{8} + 117440512 \, x^{7} + 939524096 \, x^{6} + 4294967296 \, x^{5} + 8589934592 \, x^{4}\right )} - 32 \, x^{2} e^{\left (x^{12} + 128 \, x^{11} + 7168 \, x^{10} + 229376 \, x^{9} + 4587520 \, x^{8} + 58720256 \, x^{7} + 469762048 \, x^{6} + 2147483648 \, x^{5} + 4294967296 \, x^{4}\right )} + 256} \] Input:
integrate(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-270 2966784*x^10-29418848256*x^9-216426086400*x^8-1027570925568*x^7-2834678415 360*x^6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+ 229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+429496729 6*x^4)-32*x-320)/(x^6*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+5 8720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12 +128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147 483648*x^5+4294967296*x^4)^2+768*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^ 9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-40 96),x, algorithm="fricas")
Output:
(x^2 + 20*x + 100)/(x^4*e^(2*x^12 + 256*x^11 + 14336*x^10 + 458752*x^9 + 9 175040*x^8 + 117440512*x^7 + 939524096*x^6 + 4294967296*x^5 + 8589934592*x ^4) - 32*x^2*e^(x^12 + 128*x^11 + 7168*x^10 + 229376*x^9 + 4587520*x^8 + 5 8720256*x^7 + 469762048*x^6 + 2147483648*x^5 + 4294967296*x^4) + 256)
Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (20) = 40\).
Time = 0.19 (sec) , antiderivative size = 110, normalized size of antiderivative = 4.40 \[ \int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx=\frac {x^{2} + 20 x + 100}{x^{4} e^{2 x^{12} + 256 x^{11} + 14336 x^{10} + 458752 x^{9} + 9175040 x^{8} + 117440512 x^{7} + 939524096 x^{6} + 4294967296 x^{5} + 8589934592 x^{4}} - 32 x^{2} e^{x^{12} + 128 x^{11} + 7168 x^{10} + 229376 x^{9} + 4587520 x^{8} + 58720256 x^{7} + 469762048 x^{6} + 2147483648 x^{5} + 4294967296 x^{4}} + 256} \] Input:
integrate(((-24*x**15-3296*x**14-202080*x**13-7277568*x**12-170311680*x**1 1-2702966784*x**10-29418848256*x**9-216426086400*x**8-1027570925568*x**7-2 834678415360*x**6-3435973836800*x**5-2*x**3-60*x**2-400*x)*exp(x**12+128*x **11+7168*x**10+229376*x**9+4587520*x**8+58720256*x**7+469762048*x**6+2147 483648*x**5+4294967296*x**4)-32*x-320)/(x**6*exp(x**12+128*x**11+7168*x**1 0+229376*x**9+4587520*x**8+58720256*x**7+469762048*x**6+2147483648*x**5+42 94967296*x**4)**3-48*x**4*exp(x**12+128*x**11+7168*x**10+229376*x**9+45875 20*x**8+58720256*x**7+469762048*x**6+2147483648*x**5+4294967296*x**4)**2+7 68*x**2*exp(x**12+128*x**11+7168*x**10+229376*x**9+4587520*x**8+58720256*x **7+469762048*x**6+2147483648*x**5+4294967296*x**4)-4096),x)
Output:
(x**2 + 20*x + 100)/(x**4*exp(2*x**12 + 256*x**11 + 14336*x**10 + 458752*x **9 + 9175040*x**8 + 117440512*x**7 + 939524096*x**6 + 4294967296*x**5 + 8 589934592*x**4) - 32*x**2*exp(x**12 + 128*x**11 + 7168*x**10 + 229376*x**9 + 4587520*x**8 + 58720256*x**7 + 469762048*x**6 + 2147483648*x**5 + 42949 67296*x**4) + 256)
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (24) = 48\).
Time = 0.19 (sec) , antiderivative size = 114, normalized size of antiderivative = 4.56 \[ \int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx=\frac {x^{2} + 20 \, x + 100}{x^{4} e^{\left (2 \, x^{12} + 256 \, x^{11} + 14336 \, x^{10} + 458752 \, x^{9} + 9175040 \, x^{8} + 117440512 \, x^{7} + 939524096 \, x^{6} + 4294967296 \, x^{5} + 8589934592 \, x^{4}\right )} - 32 \, x^{2} e^{\left (x^{12} + 128 \, x^{11} + 7168 \, x^{10} + 229376 \, x^{9} + 4587520 \, x^{8} + 58720256 \, x^{7} + 469762048 \, x^{6} + 2147483648 \, x^{5} + 4294967296 \, x^{4}\right )} + 256} \] Input:
integrate(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-270 2966784*x^10-29418848256*x^9-216426086400*x^8-1027570925568*x^7-2834678415 360*x^6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+ 229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+429496729 6*x^4)-32*x-320)/(x^6*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+5 8720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12 +128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147 483648*x^5+4294967296*x^4)^2+768*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^ 9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-40 96),x, algorithm="maxima")
Output:
(x^2 + 20*x + 100)/(x^4*e^(2*x^12 + 256*x^11 + 14336*x^10 + 458752*x^9 + 9 175040*x^8 + 117440512*x^7 + 939524096*x^6 + 4294967296*x^5 + 8589934592*x ^4) - 32*x^2*e^(x^12 + 128*x^11 + 7168*x^10 + 229376*x^9 + 4587520*x^8 + 5 8720256*x^7 + 469762048*x^6 + 2147483648*x^5 + 4294967296*x^4) + 256)
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (24) = 48\).
Time = 0.90 (sec) , antiderivative size = 114, normalized size of antiderivative = 4.56 \[ \int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx=\frac {x^{2} + 20 \, x + 100}{x^{4} e^{\left (2 \, x^{12} + 256 \, x^{11} + 14336 \, x^{10} + 458752 \, x^{9} + 9175040 \, x^{8} + 117440512 \, x^{7} + 939524096 \, x^{6} + 4294967296 \, x^{5} + 8589934592 \, x^{4}\right )} - 32 \, x^{2} e^{\left (x^{12} + 128 \, x^{11} + 7168 \, x^{10} + 229376 \, x^{9} + 4587520 \, x^{8} + 58720256 \, x^{7} + 469762048 \, x^{6} + 2147483648 \, x^{5} + 4294967296 \, x^{4}\right )} + 256} \] Input:
integrate(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-270 2966784*x^10-29418848256*x^9-216426086400*x^8-1027570925568*x^7-2834678415 360*x^6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+ 229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+429496729 6*x^4)-32*x-320)/(x^6*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+5 8720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12 +128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147 483648*x^5+4294967296*x^4)^2+768*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^ 9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-40 96),x, algorithm="giac")
Output:
(x^2 + 20*x + 100)/(x^4*e^(2*x^12 + 256*x^11 + 14336*x^10 + 458752*x^9 + 9 175040*x^8 + 117440512*x^7 + 939524096*x^6 + 4294967296*x^5 + 8589934592*x ^4) - 32*x^2*e^(x^12 + 128*x^11 + 7168*x^10 + 229376*x^9 + 4587520*x^8 + 5 8720256*x^7 + 469762048*x^6 + 2147483648*x^5 + 4294967296*x^4) + 256)
Time = 2.91 (sec) , antiderivative size = 114, normalized size of antiderivative = 4.56 \[ \int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx=\frac {x^2+20\,x+100}{x^4\,{\mathrm {e}}^{2\,x^{12}+256\,x^{11}+14336\,x^{10}+458752\,x^9+9175040\,x^8+117440512\,x^7+939524096\,x^6+4294967296\,x^5+8589934592\,x^4}-32\,x^2\,{\mathrm {e}}^{x^{12}+128\,x^{11}+7168\,x^{10}+229376\,x^9+4587520\,x^8+58720256\,x^7+469762048\,x^6+2147483648\,x^5+4294967296\,x^4}+256} \] Input:
int((32*x + exp(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256 *x^7 + 4587520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12)*(400*x + 60 *x^2 + 2*x^3 + 3435973836800*x^5 + 2834678415360*x^6 + 1027570925568*x^7 + 216426086400*x^8 + 29418848256*x^9 + 2702966784*x^10 + 170311680*x^11 + 7 277568*x^12 + 202080*x^13 + 3296*x^14 + 24*x^15) + 320)/(48*x^4*exp(858993 4592*x^4 + 4294967296*x^5 + 939524096*x^6 + 117440512*x^7 + 9175040*x^8 + 458752*x^9 + 14336*x^10 + 256*x^11 + 2*x^12) - 768*x^2*exp(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256*x^7 + 4587520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12) - x^6*exp(12884901888*x^4 + 6442450944*x^5 + 1409286144*x^6 + 176160768*x^7 + 13762560*x^8 + 688128*x^9 + 21504*x^10 + 384*x^11 + 3*x^12) + 4096),x)
Output:
(20*x + x^2 + 100)/(x^4*exp(8589934592*x^4 + 4294967296*x^5 + 939524096*x^ 6 + 117440512*x^7 + 9175040*x^8 + 458752*x^9 + 14336*x^10 + 256*x^11 + 2*x ^12) - 32*x^2*exp(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 587202 56*x^7 + 4587520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12) + 256)
\[ \int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx=\int \frac {\left (-24 x^{15}-3296 x^{14}-202080 x^{13}-7277568 x^{12}-170311680 x^{11}-2702966784 x^{10}-29418848256 x^{9}-216426086400 x^{8}-1027570925568 x^{7}-2834678415360 x^{6}-3435973836800 x^{5}-2 x^{3}-60 x^{2}-400 x \right ) {\mathrm e}^{x^{12}+128 x^{11}+7168 x^{10}+229376 x^{9}+4587520 x^{8}+58720256 x^{7}+469762048 x^{6}+2147483648 x^{5}+4294967296 x^{4}}-32 x -320}{x^{6} \left ({\mathrm e}^{x^{12}+128 x^{11}+7168 x^{10}+229376 x^{9}+4587520 x^{8}+58720256 x^{7}+469762048 x^{6}+2147483648 x^{5}+4294967296 x^{4}}\right )^{3}-48 x^{4} \left ({\mathrm e}^{x^{12}+128 x^{11}+7168 x^{10}+229376 x^{9}+4587520 x^{8}+58720256 x^{7}+469762048 x^{6}+2147483648 x^{5}+4294967296 x^{4}}\right )^{2}+768 x^{2} {\mathrm e}^{x^{12}+128 x^{11}+7168 x^{10}+229376 x^{9}+4587520 x^{8}+58720256 x^{7}+469762048 x^{6}+2147483648 x^{5}+4294967296 x^{4}}-4096}d x \] Input:
int(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-270296678 4*x^10-29418848256*x^9-216426086400*x^8-1027570925568*x^7-2834678415360*x^ 6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+229376 *x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4) -32*x-320)/(x^6*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+5872025 6*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12+128*x ^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648 *x^5+4294967296*x^4)^2+768*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587 520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-4096),x)
Output:
int(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-270296678 4*x^10-29418848256*x^9-216426086400*x^8-1027570925568*x^7-2834678415360*x^ 6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+229376 *x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4) -32*x-320)/(x^6*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+5872025 6*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12+128*x ^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648 *x^5+4294967296*x^4)^2+768*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587 520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-4096),x)