Integrand size = 609, antiderivative size = 27 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=6 x \left (-4-\frac {1+e^x x}{-4+x^2}-\log (2)\right )^4 \] Output:
6*(-4-ln(2)-(exp(x)*x+1)/(x^2-4))^4*x
Leaf count is larger than twice the leaf count of optimal. \(1529\) vs. \(2(27)=54\).
Time = 2.73 (sec) , antiderivative size = 1529, normalized size of antiderivative = 56.63 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx =\text {Too large to display} \] Input:
Integrate[(-1215000 + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 1536*x^10 + E^(4*x)*(-120*x^4 - 96*x^5 - 18*x^6 + 24*x^7) + (-1296000 + 18 14400*x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10)*Log[2] + (-51 8400 + 699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10)*Log[2]^ 2 + (-92160 + 119808*x^2 - 61440*x^4 + 15552*x^6 - 1944*x^8 + 96*x^10)*Log [2]^3 + (-6144 + 7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10)*Log[2]^ 4 + E^(3*x)*(5760*x^3 + 4320*x^4 - 864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8 + (1536*x^3 + 1152*x^4 - 192*x^5 - 576*x^6 - 48*x^7 + 72*x^8)*Log[2]) + E^ (2*x)*(-97200*x^2 - 64800*x^3 + 45900*x^4 + 50760*x^5 - 3168*x^6 - 13248*x ^7 - 576*x^8 + 1152*x^9 + (-51840*x^2 - 34560*x^3 + 23040*x^4 + 26496*x^5 - 1368*x^6 - 6768*x^7 - 288*x^8 + 576*x^9)*Log[2] + (-6912*x^2 - 4608*x^3 + 2880*x^4 + 3456*x^5 - 144*x^6 - 864*x^7 - 36*x^8 + 72*x^9)*Log[2]^2) + E ^x*(648000*x + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920* x^6 - 14592*x^7 - 23424*x^8 + 1536*x^10 + (518400*x + 259200*x^2 - 423360* x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 - 10368*x^7 - 17856*x^8 + 1152* x^10)*Log[2] + (138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7 - 4536*x^8 + 288*x^10)*Log[2]^2 + (12288*x + 6144*x ^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 384*x^8 + 24*x^ 10)*Log[2]^3))/(-1024 + 1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10),x]
Output:
6*((E^(4*x)*x^5)/(-4 + x^2)^4 + (2016*x*(4 + Log[2])^4)/(-4 + x^2)^4 - (13 44*x^3*(4 + Log[2])^4)/(-4 + x^2)^4 + (336*x^5*(4 + Log[2])^4)/(-4 + x^2)^ 4 - (36*x^7*(4 + Log[2])^4)/(-4 + x^2)^4 + (x^9*(4 + Log[2])^4)/(-4 + x^2) ^4 + (84*x*(4 + Log[2])^4)/(-4 + x^2)^3 - (105*x*(4 + Log[2])^4)/(4*(-4 + x^2)^2) + (315*x*(4 + Log[2])^4)/(32*(-4 + x^2)) - (315*ArcTanh[x/2]*(4 + Log[2])^4)/64 + (4*E^(3*x)*x^4*(-15 - 4*Log[2] + x^2*(4 + Log[2])))/(-4 + x^2)^4 + (x*(15 + Log[16])^4)/(8*(-4 + x^2)^4) - (7*x*(15 + Log[16])^4)/(1 92*(-4 + x^2)^3) + (35*x*(15 + Log[16])^4)/(3072*(-4 + x^2)^2) - (35*x*(15 + Log[16])^4)/(8192*(-4 + x^2)) + (35*ArcTanh[x/2]*(15 + Log[16])^4)/1638 4 + (6*E^(2*x)*x^3*(-15 - 4*Log[2] + x^2*(4 + Log[2]))*(x^4*(4 + Log[2]) + 4*(15 + Log[16]) - x^2*(31 + Log[256])))/(-4 + x^2)^5 + (4*E^x*x^2*(15 - x^2*(4 + Log[2]) + Log[16])^2*(x^4*(4 + Log[2]) + 4*(15 + Log[16]) - x^2*( 31 + Log[256])))/(-4 + x^2)^5 - (3*x*(4 + Log[2])*(2928*Log[2]^2 + 256*Log [2]^3 + 675*(60 + Log[256]) + 24*Log[2]*(Log[4]*(39 + Log[256]) + 15*(70 + Log[256]))))/(10*(-4 + x^2)^4) + (x^3*(4 + Log[2])*(2928*Log[2]^2 + 256*L og[2]^3 + 675*(60 + Log[256]) + 24*Log[2]*(Log[4]*(39 + Log[256]) + 15*(70 + Log[256]))))/(5*(-4 + x^2)^4) - (x*(4 + Log[2])*(2928*Log[2]^2 + 256*Lo g[2]^3 + 675*(60 + Log[256]) + 24*Log[2]*(Log[4]*(39 + Log[256]) + 15*(70 + Log[256]))))/(80*(-4 + x^2)^3) + (x*(4 + Log[2])*(2928*Log[2]^2 + 256*Lo g[2]^3 + 675*(60 + Log[256]) + 24*Log[2]*(Log[4]*(39 + Log[256]) + 15*(...
Leaf count is larger than twice the leaf count of optimal. \(1114\) vs. \(2(27)=54\).
Time = 7.84 (sec) , antiderivative size = 1114, normalized size of antiderivative = 41.26, number of steps used = 7, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {2070, 7239, 27, 25, 7292, 7293, 2009}
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.
| \(\displaystyle \int \frac {1536 x^{10}-32256 x^8+256320 x^6-972000 x^4+1761750 x^2+e^{4 x} \left (24 x^7-18 x^6-96 x^5-120 x^4\right )+\left (6 x^{10}-120 x^8+960 x^6-3840 x^4+7680 x^2-6144\right ) \log ^4(2)+\left (96 x^{10}-1944 x^8+15552 x^6-61440 x^4+119808 x^2-92160\right ) \log ^3(2)+\left (576 x^{10}-11808 x^8+94356 x^6-367920 x^4+699840 x^2-518400\right ) \log ^2(2)+\left (1536 x^{10}-31872 x^8+254112 x^6-977400 x^4+1814400 x^2-1296000\right ) \log (2)+e^{3 x} \left (288 x^8-192 x^7-2232 x^6-864 x^5+4320 x^4+5760 x^3+\left (72 x^8-48 x^7-576 x^6-192 x^5+1152 x^4+1536 x^3\right ) \log (2)\right )+e^x \left (1536 x^{10}-23424 x^8-14592 x^7+133920 x^6+155520 x^5-340200 x^4-550800 x^3+324000 x^2+\left (24 x^{10}-384 x^8-192 x^7+2304 x^6+2304 x^5-6144 x^4-9216 x^3+6144 x^2+12288 x\right ) \log ^3(2)+\left (288 x^{10}-4536 x^8-2448 x^7+26784 x^6+28224 x^5-70272 x^4-108288 x^3+69120 x^2+138240 x\right ) \log ^2(2)+\left (1152 x^{10}-17856 x^8-10368 x^7+103752 x^6+114912 x^5-267840 x^4-423360 x^3+259200 x^2+518400 x\right ) \log (2)+648000 x\right )+e^{2 x} \left (1152 x^9-576 x^8-13248 x^7-3168 x^6+50760 x^5+45900 x^4-64800 x^3-97200 x^2+\left (72 x^9-36 x^8-864 x^7-144 x^6+3456 x^5+2880 x^4-4608 x^3-6912 x^2\right ) \log ^2(2)+\left (576 x^9-288 x^8-6768 x^7-1368 x^6+26496 x^5+23040 x^4-34560 x^3-51840 x^2\right ) \log (2)\right )-1215000}{x^{10}-20 x^8+160 x^6-640 x^4+1280 x^2-1024} \, dx\) |
| \(\Big \downarrow \) 2070 |
| \(\displaystyle \int \frac {1536 x^{10}-32256 x^8+256320 x^6-972000 x^4+1761750 x^2+e^{4 x} \left (24 x^7-18 x^6-96 x^5-120 x^4\right )+\left (6 x^{10}-120 x^8+960 x^6-3840 x^4+7680 x^2-6144\right ) \log ^4(2)+\left (96 x^{10}-1944 x^8+15552 x^6-61440 x^4+119808 x^2-92160\right ) \log ^3(2)+\left (576 x^{10}-11808 x^8+94356 x^6-367920 x^4+699840 x^2-518400\right ) \log ^2(2)+\left (1536 x^{10}-31872 x^8+254112 x^6-977400 x^4+1814400 x^2-1296000\right ) \log (2)+e^{3 x} \left (288 x^8-192 x^7-2232 x^6-864 x^5+4320 x^4+5760 x^3+\left (72 x^8-48 x^7-576 x^6-192 x^5+1152 x^4+1536 x^3\right ) \log (2)\right )+e^x \left (1536 x^{10}-23424 x^8-14592 x^7+133920 x^6+155520 x^5-340200 x^4-550800 x^3+324000 x^2+\left (24 x^{10}-384 x^8-192 x^7+2304 x^6+2304 x^5-6144 x^4-9216 x^3+6144 x^2+12288 x\right ) \log ^3(2)+\left (288 x^{10}-4536 x^8-2448 x^7+26784 x^6+28224 x^5-70272 x^4-108288 x^3+69120 x^2+138240 x\right ) \log ^2(2)+\left (1152 x^{10}-17856 x^8-10368 x^7+103752 x^6+114912 x^5-267840 x^4-423360 x^3+259200 x^2+518400 x\right ) \log (2)+648000 x\right )+e^{2 x} \left (1152 x^9-576 x^8-13248 x^7-3168 x^6+50760 x^5+45900 x^4-64800 x^3-97200 x^2+\left (72 x^9-36 x^8-864 x^7-144 x^6+3456 x^5+2880 x^4-4608 x^3-6912 x^2\right ) \log ^2(2)+\left (576 x^9-288 x^8-6768 x^7-1368 x^6+26496 x^5+23040 x^4-34560 x^3-51840 x^2\right ) \log (2)\right )-1215000}{\left (x^2-4\right )^5}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 \left (x^2 (4+\log (2))+e^x x-15 \left (1+\frac {4 \log (2)}{15}\right )\right )^3 \left (-\left (x^4 (4+\log (2))\right )+x^2 (39+\log (256))-e^x \left (4 x^3-3 x^2-16 x-20\right ) x-60 \left (1+\frac {4 \log (2)}{15}\right )\right )}{\left (4-x^2\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 6 \int -\frac {\left (-\left ((4+\log (2)) x^2\right )-e^x x+4 \log (2)+15\right )^3 \left (-\left ((4+\log (2)) x^4\right )+(39+\log (256)) x^2+e^x \left (-4 x^3+3 x^2+16 x+20\right ) x-4 (15+\log (16))\right )}{\left (4-x^2\right )^5}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -6 \int \frac {\left (-\left ((4+\log (2)) x^2\right )-e^x x+\log (16)+15\right )^3 \left (-\left ((4+\log (2)) x^4\right )+(39+\log (256)) x^2+e^x \left (-4 x^3+3 x^2+16 x+20\right ) x-4 (15+\log (16))\right )}{\left (4-x^2\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle -6 \int \frac {\left ((4+\log (2)) x^2+e^x x-15 \left (1+\frac {4 \log (2)}{15}\right )\right )^3 \left ((4+\log (2)) x^4-(39+\log (256)) x^2-e^x \left (-4 x^3+3 x^2+16 x+20\right ) x+4 (15+\log (16))\right )}{\left (4-x^2\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6 \int \left (-\frac {(4+\log (2))^4 x^{10}}{\left (x^2-4\right )^5}+\frac {3 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right ) x^8}{\left (x^2-4\right )^5}-\frac {4 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right ) x^6}{\left (x^2-4\right )^5}-\frac {e^{4 x} \left (4 x^3-3 x^2-16 x-20\right ) x^4}{\left (x^2-4\right )^5}+\frac {12 (4+\log (2))^2 (15+\log (16))^2 \left (1+\frac {\log (16)+3 (44+\log (256))}{12 (4+\log (2))}\right ) x^4}{\left (x^2-4\right )^5}+\frac {e^{3 x} \left (48 \left (1+\frac {\log (2)}{4}\right ) x^5-32 \left (1+\frac {\log (2)}{4}\right ) x^4-372 \left (1+\frac {8 \log (2)}{31}\right ) x^3-144 \left (1+\frac {2 \log (2)}{9}\right ) x^2+720 \left (1+\frac {4 \log (2)}{15}\right ) x+960 \left (1+\frac {4 \log (2)}{15}\right )\right ) x^3}{\left (4-x^2\right )^5}+\frac {3 e^{2 x} \left (-16 \left (1+\frac {\log (2)}{4}\right ) x^5+8 \left (1+\frac {\log (2)}{4}\right ) x^4+124 \left (1+\frac {8 \log (2)}{31}\right ) x^3+74 \left (1+\frac {8 \log (2)}{37}\right ) x^2-240 \left (1+\frac {4 \log (2)}{15}\right ) x-360 \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (-\left ((4+\log (2)) x^2\right )+4 \log (2)+15\right ) x^2}{\left (4-x^2\right )^5}-\frac {12 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right ) x^2}{\left (x^2-4\right )^5}+\frac {4 e^x \left (4 \left (1+\frac {\log (2)}{4}\right ) x^5-31 \left (1+\frac {8 \log (2)}{31}\right ) x^3-38 \left (1+\frac {4 \log (2)}{19}\right ) x^2+60 \left (1+\frac {4 \log (2)}{15}\right ) x+120 \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (-\left ((4+\log (2)) x^2\right )+\log (16)+15\right )^2 x}{\left (4-x^2\right )^5}+\frac {4 (15+\log (16))^4}{\left (x^2-4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -6 \left (\frac {(4+\log (2))^4 x^9}{8 \left (4-x^2\right )^4}-\frac {3 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096)) x^7}{8 \left (4-x^2\right )^4 (45+\log (4096))}-\frac {3 (4+\log (2))^4 x^7}{16 \left (4-x^2\right )^3}+\frac {(4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right ) x^5}{2 \left (4-x^2\right )^4}+\frac {7 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096)) x^5}{16 \left (4-x^2\right )^3 (45+\log (4096))}+\frac {21 (4+\log (2))^4 x^5}{64 \left (4-x^2\right )^2}-\frac {e^{4 x} \left (4 x-x^3\right ) x^4}{\left (4-x^2\right )^5}+\frac {4 e^{3 x} \left ((4+\log (2)) x^5-(31+\log (256)) x^3+4 (15+\log (16)) x\right ) x^3}{\left (4-x^2\right )^5}-\frac {5 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right ) x^3}{12 \left (4-x^2\right )^3}-\frac {(4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096)) x^3}{8 \left (4-x^2\right )^4}-\frac {35 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096)) x^3}{64 \left (4-x^2\right )^2 (45+\log (4096))}-\frac {105 (4+\log (2))^4 x^3}{128 \left (4-x^2\right )}-\frac {6 e^{2 x} \left (-\left ((4+\log (2)) x^2\right )+\log (16)+15\right ) \left ((4+\log (2)) x^5-(31+\log (256)) x^3+4 (15+\log (16)) x\right ) x^2}{\left (4-x^2\right )^5}+\frac {4 e^x \left (-\left ((4+\log (2)) x^2\right )+\log (16)+15\right )^2 \left ((4+\log (2)) x^5-(31+\log (256)) x^3+4 (15+\log (16)) x\right ) x}{\left (4-x^2\right )^5}-\frac {5 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right ) x}{128 \left (4-x^2\right )}+\frac {5 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right ) x}{16 \left (4-x^2\right )^2}-\frac {3 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096)) x}{2048 \left (4-x^2\right )}-\frac {(4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096)) x}{256 \left (4-x^2\right )^2}+\frac {(4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096)) x}{16 \left (4-x^2\right )^3}-\frac {15 (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096)) x}{2048 \left (4-x^2\right ) (48+\log (4096))}-\frac {5 (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096)) x}{256 \left (4-x^2\right )^2 (48+\log (4096))}-\frac {(4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096)) x}{16 \left (4-x^2\right )^3 (48+\log (4096))}+\frac {3 (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096)) x}{2 \left (4-x^2\right )^4 (48+\log (4096))}+\frac {105 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096)) x}{128 \left (4-x^2\right ) (45+\log (4096))}-\frac {35 (15+\log (16))^4 x}{8192 \left (4-x^2\right )}-\frac {35 (15+\log (16))^4 x}{3072 \left (4-x^2\right )^2}-\frac {7 (15+\log (16))^4 x}{192 \left (4-x^2\right )^3}-\frac {(15+\log (16))^4 x}{8 \left (4-x^2\right )^4}-\frac {315}{128} (4+\log (2))^4 x-\frac {5}{256} \text {arctanh}\left (\frac {x}{2}\right ) (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )-\frac {3 \text {arctanh}\left (\frac {x}{2}\right ) (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{4096}-\frac {15 \text {arctanh}\left (\frac {x}{2}\right ) (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096))}{4096 (48+\log (4096))}-\frac {105 \text {arctanh}\left (\frac {x}{2}\right ) (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096))}{256 (45+\log (4096))}-\frac {35 \text {arctanh}\left (\frac {x}{2}\right ) (15+\log (16))^4}{16384}+\frac {315}{64} \text {arctanh}\left (\frac {x}{2}\right ) (4+\log (2))^4\right )\) |
Input:
Int[(-1215000 + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 1536*x ^10 + E^(4*x)*(-120*x^4 - 96*x^5 - 18*x^6 + 24*x^7) + (-1296000 + 1814400* x^2 - 977400*x^4 + 254112*x^6 - 31872*x^8 + 1536*x^10)*Log[2] + (-518400 + 699840*x^2 - 367920*x^4 + 94356*x^6 - 11808*x^8 + 576*x^10)*Log[2]^2 + (- 92160 + 119808*x^2 - 61440*x^4 + 15552*x^6 - 1944*x^8 + 96*x^10)*Log[2]^3 + (-6144 + 7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10)*Log[2]^4 + E^ (3*x)*(5760*x^3 + 4320*x^4 - 864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8 + (153 6*x^3 + 1152*x^4 - 192*x^5 - 576*x^6 - 48*x^7 + 72*x^8)*Log[2]) + E^(2*x)* (-97200*x^2 - 64800*x^3 + 45900*x^4 + 50760*x^5 - 3168*x^6 - 13248*x^7 - 5 76*x^8 + 1152*x^9 + (-51840*x^2 - 34560*x^3 + 23040*x^4 + 26496*x^5 - 1368 *x^6 - 6768*x^7 - 288*x^8 + 576*x^9)*Log[2] + (-6912*x^2 - 4608*x^3 + 2880 *x^4 + 3456*x^5 - 144*x^6 - 864*x^7 - 36*x^8 + 72*x^9)*Log[2]^2) + E^x*(64 8000*x + 324000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^7 - 23424*x^8 + 1536*x^10 + (518400*x + 259200*x^2 - 423360*x^3 - 267840*x^4 + 114912*x^5 + 103752*x^6 - 10368*x^7 - 17856*x^8 + 1152*x^10)* Log[2] + (138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 2678 4*x^6 - 2448*x^7 - 4536*x^8 + 288*x^10)*Log[2]^2 + (12288*x + 6144*x^2 - 9 216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 384*x^8 + 24*x^10)*Lo g[2]^3))/(-1024 + 1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10),x]
Output:
-6*(-((E^(4*x)*x^4*(4*x - x^3))/(4 - x^2)^5) - (315*x*(4 + Log[2])^4)/128 + (x^9*(4 + Log[2])^4)/(8*(4 - x^2)^4) - (3*x^7*(4 + Log[2])^4)/(16*(4 - x ^2)^3) + (21*x^5*(4 + Log[2])^4)/(64*(4 - x^2)^2) - (105*x^3*(4 + Log[2])^ 4)/(128*(4 - x^2)) + (315*ArcTanh[x/2]*(4 + Log[2])^4)/64 - (x*(15 + Log[1 6])^4)/(8*(4 - x^2)^4) - (7*x*(15 + Log[16])^4)/(192*(4 - x^2)^3) - (35*x* (15 + Log[16])^4)/(3072*(4 - x^2)^2) - (35*x*(15 + Log[16])^4)/(8192*(4 - x^2)) - (35*ArcTanh[x/2]*(15 + Log[16])^4)/16384 + (4*E^(3*x)*x^3*(x^5*(4 + Log[2]) + 4*x*(15 + Log[16]) - x^3*(31 + Log[256])))/(4 - x^2)^5 - (6*E^ (2*x)*x^2*(15 - x^2*(4 + Log[2]) + Log[16])*(x^5*(4 + Log[2]) + 4*x*(15 + Log[16]) - x^3*(31 + Log[256])))/(4 - x^2)^5 + (4*E^x*x*(15 - x^2*(4 + Log [2]) + Log[16])^2*(x^5*(4 + Log[2]) + 4*x*(15 + Log[16]) - x^3*(31 + Log[2 56])))/(4 - x^2)^5 - (3*x^7*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[256] + Log[4096]))/(8*(4 - x^2)^4*(45 + Log[4096])) + (7*x^5*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[256] + Log[4096]))/(16*(4 - x^2)^3*(45 + Log[4096])) - (35*x^3*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[256] + Log[4096]))/(64*( 4 - x^2)^2*(45 + Log[4096])) + (105*x*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[256] + Log[4096]))/(128*(4 - x^2)*(45 + Log[4096])) - (105*ArcTanh[x/2 ]*(4 + Log[2])^3*(15 + Log[16])*(84 + Log[256] + Log[4096]))/(256*(45 + Lo g[4096])) + (3*x*(4 + Log[2])*(15 + Log[16])^3*(87 + Log[256] + Log[4096]) )/(2*(4 - x^2)^4*(48 + Log[4096])) - (x*(4 + Log[2])*(15 + Log[16])^3*(...
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x^2, 0], Expon[Px , x^2]], b = Rt[Coeff[Px, x^2, Expon[Px, x^2]], Expon[Px, x^2]]}, Int[u*(a + b*x^2)^(Expon[Px, x^2]*p), x] /; EqQ[Px, (a + b*x^2)^Expon[Px, x^2]]] /; IntegerQ[p] && PolyQ[Px, x^2] && GtQ[Expon[Px, x^2], 1] && NeQ[Coeff[Px, x^ 2, 0], 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(379\) vs. \(2(26)=52\).
Time = 173.26 (sec) , antiderivative size = 380, normalized size of antiderivative = 14.07
| method | result | size |
| risch | \(6 x \ln \left (2\right )^{4}+96 x \ln \left (2\right )^{3}+576 x \ln \left (2\right )^{2}+1536 x \ln \left (2\right )+1536 x +\frac {\left (24 \ln \left (2\right )^{3}+288 \ln \left (2\right )^{2}+1152 \ln \left (2\right )+1536\right ) x^{7}+\left (-288 \ln \left (2\right )^{3}-3420 \ln \left (2\right )^{2}-13536 \ln \left (2\right )-17856\right ) x^{5}+\left (1152 \ln \left (2\right )^{3}+13536 \ln \left (2\right )^{2}+53016 \ln \left (2\right )+69216\right ) x^{3}+\left (-1536 \ln \left (2\right )^{3}-17856 \ln \left (2\right )^{2}-69216 \ln \left (2\right )-89466\right ) x}{x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256}+\frac {6 x^{5} {\mathrm e}^{4 x}}{\left (x^{2}-4\right )^{4}}+\frac {24 x^{4} \left (x^{2} \ln \left (2\right )+4 x^{2}-4 \ln \left (2\right )-15\right ) {\mathrm e}^{3 x}}{\left (x^{2}-4\right )^{4}}+\frac {36 x^{3} \left (x^{4} \ln \left (2\right )^{2}+8 x^{4} \ln \left (2\right )-8 x^{2} \ln \left (2\right )^{2}+16 x^{4}-62 x^{2} \ln \left (2\right )+16 \ln \left (2\right )^{2}-120 x^{2}+120 \ln \left (2\right )+225\right ) {\mathrm e}^{2 x}}{\left (x^{2}-4\right )^{4}}+\frac {24 x^{2} \left (\ln \left (2\right )^{3} x^{6}+12 \ln \left (2\right )^{2} x^{6}-12 \ln \left (2\right )^{3} x^{4}+48 x^{6} \ln \left (2\right )-141 x^{4} \ln \left (2\right )^{2}+64 x^{6}+48 \ln \left (2\right )^{3} x^{2}-552 x^{4} \ln \left (2\right )+552 x^{2} \ln \left (2\right )^{2}-720 x^{4}-64 \ln \left (2\right )^{3}+2115 x^{2} \ln \left (2\right )-720 \ln \left (2\right )^{2}+2700 x^{2}-2700 \ln \left (2\right )-3375\right ) {\mathrm e}^{x}}{\left (x^{2}-4\right )^{4}}\) | \(380\) |
| parallelrisch | \(\frac {303750 x +51876 x^{5} \ln \left (2\right )^{2}+23040 x \ln \left (2\right )^{3}-3384 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{6}+1152 \ln \left (2\right )^{3} {\mathrm e}^{x} x^{4}+13248 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{4}+50760 \ln \left (2\right ) {\mathrm e}^{x} x^{4}-17280 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}+1536 x \ln \left (2\right )^{4}-96 x^{7} \ln \left (2\right )^{4}-1512 x^{7} \ln \left (2\right )^{3}-8928 x^{7} \ln \left (2\right )^{2}-23424 x^{7} \ln \left (2\right )-4320 x^{5} {\mathrm e}^{2 x}-133920 x^{3} \ln \left (2\right )^{2}-17280 x^{6} {\mathrm e}^{x}+129600 x \ln \left (2\right )^{2}+133920 x^{5} \ln \left (2\right )+64800 \,{\mathrm e}^{x} x^{4}+324000 x \ln \left (2\right )-340200 x^{3} \ln \left (2\right )-81000 \,{\mathrm e}^{x} x^{2}+576 \ln \left (2\right )^{2} x^{9}-360 \,{\mathrm e}^{3 x} x^{4}+8100 \,{\mathrm e}^{2 x} x^{3}-23040 x^{7}+1536 x^{9}-324000 x^{3}+129600 x^{5}-64800 x^{2} \ln \left (2\right ) {\mathrm e}^{x}-288 \ln \left (2\right )^{3} {\mathrm e}^{x} x^{6}+576 \,{\mathrm e}^{2 x} x^{7}+6 \,{\mathrm e}^{4 x} x^{5}+96 \,{\mathrm e}^{3 x} x^{6}+1536 \ln \left (2\right ) x^{9}+1536 \,{\mathrm e}^{x} x^{8}+8928 \ln \left (2\right )^{3} x^{5}+24 \ln \left (2\right )^{3} {\mathrm e}^{x} x^{8}+288 \ln \left (2\right )^{2} {\mathrm e}^{x} x^{8}+1152 \ln \left (2\right ) {\mathrm e}^{x} x^{8}-13248 \ln \left (2\right ) {\mathrm e}^{x} x^{6}-1536 \ln \left (2\right )^{3} {\mathrm e}^{x} x^{2}+576 \ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{3}+4320 \ln \left (2\right ) {\mathrm e}^{2 x} x^{3}+24 \ln \left (2\right ) {\mathrm e}^{3 x} x^{6}+288 \ln \left (2\right ) {\mathrm e}^{2 x} x^{7}-96 \ln \left (2\right ) {\mathrm e}^{3 x} x^{4}-2232 \ln \left (2\right ) {\mathrm e}^{2 x} x^{5}+96 \ln \left (2\right )^{3} x^{9}+576 \ln \left (2\right )^{4} x^{5}-1536 \ln \left (2\right )^{4} x^{3}+6 \ln \left (2\right )^{4} x^{9}-23424 \ln \left (2\right )^{3} x^{3}-288 \,{\mathrm e}^{2 x} \ln \left (2\right )^{2} x^{5}+36 \ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{7}}{x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256}\) | \(510\) |
| parts | \(\text {Expression too large to display}\) | \(859\) |
| default | \(\text {Expression too large to display}\) | \(7367\) |
Input:
int(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x ^5+1152*x^4+1536*x^3)*ln(2)+288*x^8-192*x^7-2232*x^6-864*x^5+4320*x^4+5760 *x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-4608*x^3- 6912*x^2)*ln(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4-3 4560*x^3-51840*x^2)*ln(2)+1152*x^9-576*x^8-13248*x^7-3168*x^6+50760*x^5+45 900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x^7+2304*x^6+2 304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*ln(2)^3+(288*x^10-4536*x^8-244 8*x^7+26784*x^6+28224*x^5-70272*x^4-108288*x^3+69120*x^2+138240*x)*ln(2)^2 +(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267840*x^4-423360*x^ 3+259200*x^2+518400*x)*ln(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^6+1555 20*x^5-340200*x^4-550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^10-120*x^8+9 60*x^6-3840*x^4+7680*x^2-6144)*ln(2)^4+(96*x^10-1944*x^8+15552*x^6-61440*x ^4+119808*x^2-92160)*ln(2)^3+(576*x^10-11808*x^8+94356*x^6-367920*x^4+6998 40*x^2-518400)*ln(2)^2+(1536*x^10-31872*x^8+254112*x^6-977400*x^4+1814400* x^2-1296000)*ln(2)+1536*x^10-32256*x^8+256320*x^6-972000*x^4+1761750*x^2-1 215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x,method=_RETURNVERBOS E)
Output:
6*x*ln(2)^4+96*x*ln(2)^3+576*x*ln(2)^2+1536*x*ln(2)+1536*x+((24*ln(2)^3+28 8*ln(2)^2+1152*ln(2)+1536)*x^7+(-288*ln(2)^3-3420*ln(2)^2-13536*ln(2)-1785 6)*x^5+(1152*ln(2)^3+13536*ln(2)^2+53016*ln(2)+69216)*x^3+(-1536*ln(2)^3-1 7856*ln(2)^2-69216*ln(2)-89466)*x)/(x^8-16*x^6+96*x^4-256*x^2+256)+6*x^5/( x^2-4)^4*exp(x)^4+24*x^4*(x^2*ln(2)+4*x^2-4*ln(2)-15)/(x^2-4)^4*exp(x)^3+3 6*x^3*(x^4*ln(2)^2+8*x^4*ln(2)-8*x^2*ln(2)^2+16*x^4-62*x^2*ln(2)+16*ln(2)^ 2-120*x^2+120*ln(2)+225)/(x^2-4)^4*exp(x)^2+24*x^2*(ln(2)^3*x^6+12*ln(2)^2 *x^6-12*ln(2)^3*x^4+48*x^6*ln(2)-141*x^4*ln(2)^2+64*x^6+48*ln(2)^3*x^2-552 *x^4*ln(2)+552*x^2*ln(2)^2-720*x^4-64*ln(2)^3+2115*x^2*ln(2)-720*ln(2)^2+2 700*x^2-2700*ln(2)-3375)/(x^2-4)^4*exp(x)
Leaf count of result is larger than twice the leaf count of optimal. 362 vs. \(2 (23) = 46\).
Time = 0.09 (sec) , antiderivative size = 362, normalized size of antiderivative = 13.41 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=\frac {6 \, {\left (256 \, x^{9} - 3840 \, x^{7} + x^{5} e^{\left (4 \, x\right )} + 21600 \, x^{5} + {\left (x^{9} - 16 \, x^{7} + 96 \, x^{5} - 256 \, x^{3} + 256 \, x\right )} \log \left (2\right )^{4} + 4 \, {\left (4 \, x^{9} - 63 \, x^{7} + 372 \, x^{5} - 976 \, x^{3} + 960 \, x\right )} \log \left (2\right )^{3} - 54000 \, x^{3} + 6 \, {\left (16 \, x^{9} - 248 \, x^{7} + 1441 \, x^{5} - 3720 \, x^{3} + 3600 \, x\right )} \log \left (2\right )^{2} + 4 \, {\left (4 \, x^{6} - 15 \, x^{4} + {\left (x^{6} - 4 \, x^{4}\right )} \log \left (2\right )\right )} e^{\left (3 \, x\right )} + 6 \, {\left (16 \, x^{7} - 120 \, x^{5} + 225 \, x^{3} + {\left (x^{7} - 8 \, x^{5} + 16 \, x^{3}\right )} \log \left (2\right )^{2} + 2 \, {\left (4 \, x^{7} - 31 \, x^{5} + 60 \, x^{3}\right )} \log \left (2\right )\right )} e^{\left (2 \, x\right )} + 4 \, {\left (64 \, x^{8} - 720 \, x^{6} + 2700 \, x^{4} + {\left (x^{8} - 12 \, x^{6} + 48 \, x^{4} - 64 \, x^{2}\right )} \log \left (2\right )^{3} + 3 \, {\left (4 \, x^{8} - 47 \, x^{6} + 184 \, x^{4} - 240 \, x^{2}\right )} \log \left (2\right )^{2} - 3375 \, x^{2} + 3 \, {\left (16 \, x^{8} - 184 \, x^{6} + 705 \, x^{4} - 900 \, x^{2}\right )} \log \left (2\right )\right )} e^{x} + 4 \, {\left (64 \, x^{9} - 976 \, x^{7} + 5580 \, x^{5} - 14175 \, x^{3} + 13500 \, x\right )} \log \left (2\right ) + 50625 \, x\right )}}{x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256} \] Input:
integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6 -192*x^5+1152*x^4+1536*x^3)*log(2)+288*x^8-192*x^7-2232*x^6-864*x^5+4320*x ^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-46 08*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+230 40*x^4-34560*x^3-51840*x^2)*log(2)+1152*x^9-576*x^8-13248*x^7-3168*x^6+507 60*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x^7+2 304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-45 36*x^8-2448*x^7+26784*x^6+28224*x^5-70272*x^4-108288*x^3+69120*x^2+138240* x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267840*x^ 4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133 920*x^6+155520*x^5-340200*x^4-550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^ 10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*x^8+1555 2*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-3 67920*x^4+699840*x^2-518400)*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-9774 00*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^6-972000*x ^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, alg orithm="fricas")
Output:
6*(256*x^9 - 3840*x^7 + x^5*e^(4*x) + 21600*x^5 + (x^9 - 16*x^7 + 96*x^5 - 256*x^3 + 256*x)*log(2)^4 + 4*(4*x^9 - 63*x^7 + 372*x^5 - 976*x^3 + 960*x )*log(2)^3 - 54000*x^3 + 6*(16*x^9 - 248*x^7 + 1441*x^5 - 3720*x^3 + 3600* x)*log(2)^2 + 4*(4*x^6 - 15*x^4 + (x^6 - 4*x^4)*log(2))*e^(3*x) + 6*(16*x^ 7 - 120*x^5 + 225*x^3 + (x^7 - 8*x^5 + 16*x^3)*log(2)^2 + 2*(4*x^7 - 31*x^ 5 + 60*x^3)*log(2))*e^(2*x) + 4*(64*x^8 - 720*x^6 + 2700*x^4 + (x^8 - 12*x ^6 + 48*x^4 - 64*x^2)*log(2)^3 + 3*(4*x^8 - 47*x^6 + 184*x^4 - 240*x^2)*lo g(2)^2 - 3375*x^2 + 3*(16*x^8 - 184*x^6 + 705*x^4 - 900*x^2)*log(2))*e^x + 4*(64*x^9 - 976*x^7 + 5580*x^5 - 14175*x^3 + 13500*x)*log(2) + 50625*x)/( x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)
Leaf count of result is larger than twice the leaf count of optimal. 1402 vs. \(2 (22) = 44\).
Time = 2.76 (sec) , antiderivative size = 1402, normalized size of antiderivative = 51.93 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=\text {Too large to display} \] Input:
integrate(((24*x**7-18*x**6-96*x**5-120*x**4)*exp(x)**4+((72*x**8-48*x**7- 576*x**6-192*x**5+1152*x**4+1536*x**3)*ln(2)+288*x**8-192*x**7-2232*x**6-8 64*x**5+4320*x**4+5760*x**3)*exp(x)**3+((72*x**9-36*x**8-864*x**7-144*x**6 +3456*x**5+2880*x**4-4608*x**3-6912*x**2)*ln(2)**2+(576*x**9-288*x**8-6768 *x**7-1368*x**6+26496*x**5+23040*x**4-34560*x**3-51840*x**2)*ln(2)+1152*x* *9-576*x**8-13248*x**7-3168*x**6+50760*x**5+45900*x**4-64800*x**3-97200*x* *2)*exp(x)**2+((24*x**10-384*x**8-192*x**7+2304*x**6+2304*x**5-6144*x**4-9 216*x**3+6144*x**2+12288*x)*ln(2)**3+(288*x**10-4536*x**8-2448*x**7+26784* x**6+28224*x**5-70272*x**4-108288*x**3+69120*x**2+138240*x)*ln(2)**2+(1152 *x**10-17856*x**8-10368*x**7+103752*x**6+114912*x**5-267840*x**4-423360*x* *3+259200*x**2+518400*x)*ln(2)+1536*x**10-23424*x**8-14592*x**7+133920*x** 6+155520*x**5-340200*x**4-550800*x**3+324000*x**2+648000*x)*exp(x)+(6*x**1 0-120*x**8+960*x**6-3840*x**4+7680*x**2-6144)*ln(2)**4+(96*x**10-1944*x**8 +15552*x**6-61440*x**4+119808*x**2-92160)*ln(2)**3+(576*x**10-11808*x**8+9 4356*x**6-367920*x**4+699840*x**2-518400)*ln(2)**2+(1536*x**10-31872*x**8+ 254112*x**6-977400*x**4+1814400*x**2-1296000)*ln(2)+1536*x**10-32256*x**8+ 256320*x**6-972000*x**4+1761750*x**2-1215000)/(x**10-20*x**8+160*x**6-640* x**4+1280*x**2-1024),x)
Output:
x*(6*log(2)**4 + 96*log(2)**3 + 576*log(2)**2 + 1536*log(2) + 1536) + (x** 7*(24*log(2)**3 + 288*log(2)**2 + 1152*log(2) + 1536) + x**5*(-17856 - 135 36*log(2) - 3420*log(2)**2 - 288*log(2)**3) + x**3*(1152*log(2)**3 + 13536 *log(2)**2 + 53016*log(2) + 69216) + x*(-89466 - 69216*log(2) - 17856*log( 2)**2 - 1536*log(2)**3))/(x**8 - 16*x**6 + 96*x**4 - 256*x**2 + 256) + ((6 *x**29 - 288*x**27 + 6336*x**25 - 84480*x**23 + 760320*x**21 - 4866048*x** 19 + 22708224*x**17 - 77856768*x**15 + 194641920*x**13 - 346030080*x**11 + 415236096*x**9 - 301989888*x**7 + 100663296*x**5)*exp(4*x) + (24*x**30*lo g(2) + 96*x**30 - 4968*x**28 - 1248*x**28*log(2) + 29952*x**26*log(2) + 11 8656*x**26 - 1731840*x**24 - 439296*x**24*log(2) + 4392960*x**22*log(2) + 17233920*x**22 - 123475968*x**20 - 31629312*x**20*log(2) + 168689664*x**18 *log(2) + 655294464*x**18 - 2608201728*x**16 - 674758656*x**16*log(2) + 20 24275968*x**14*log(2) + 7785676800*x**14 - 17214996480*x**12 - 4498391040* x**12*log(2) + 7197425664*x**10*log(2) + 27405582336*x**10 - 29746003968*x **8 - 7851737088*x**8*log(2) + 5234491392*x**6*log(2) + 19730006016*x**6 - 6039797760*x**4 - 1610612736*x**4*log(2))*exp(3*x) + (36*x**31*log(2)**2 + 288*x**31*log(2) + 576*x**31 - 31968*x**29 - 16056*x**29*log(2) - 2016*x **29*log(2)**2 + 52416*x**27*log(2)**2 + 415584*x**27*log(2) + 823716*x**2 7 - 13060800*x**25 - 6619392*x**25*log(2) - 838656*x**25*log(2)**2 + 92252 16*x**23*log(2)**2 + 72483840*x**23*log(2) + 142369920*x**23 - 11286190...
Leaf count of result is larger than twice the leaf count of optimal. 1957 vs. \(2 (23) = 46\).
Time = 0.25 (sec) , antiderivative size = 1957, normalized size of antiderivative = 72.48 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=\text {Too large to display} \] Input:
integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6 -192*x^5+1152*x^4+1536*x^3)*log(2)+288*x^8-192*x^7-2232*x^6-864*x^5+4320*x ^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-46 08*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+230 40*x^4-34560*x^3-51840*x^2)*log(2)+1152*x^9-576*x^8-13248*x^7-3168*x^6+507 60*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x^7+2 304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-45 36*x^8-2448*x^7+26784*x^6+28224*x^5-70272*x^4-108288*x^3+69120*x^2+138240* x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267840*x^ 4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133 920*x^6+155520*x^5-340200*x^4-550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^ 10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*x^8+1555 2*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-3 67920*x^4+699840*x^2-518400)*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-9774 00*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^6-972000*x ^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, alg orithm="maxima")
Output:
3/64*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 315*log(x + 2) + 315*log(x - 2))*log(2)^4 + 5/6 4*(4*(279*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 256 *x^2 + 256) + 105*log(x + 2) - 105*log(x - 2))*log(2)^4 - 1/64*(4*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 105*log(x + 2) + 105*log(x - 2))*log(2)^4 - 5/32*(4*(15*x^7 + 292*x^5 - 880*x^3 + 960*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^4 - 5/64*(4*(15*x^7 - 220*x^5 + 1168*x^3 + 960*x)/( x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*lo g(2)^4 - 15/32*(4*(3*x^7 - 44*x^5 - 176*x^3 + 192*x)/(x^8 - 16*x^6 + 96*x^ 4 - 256*x^2 + 256) - 3*log(x + 2) + 3*log(x - 2))*log(2)^4 + 3/4*(128*x - 4*(325*x^7 - 3060*x^5 + 10288*x^3 - 11968*x)/(x^8 - 16*x^6 + 96*x^4 - 256* x^2 + 256) - 315*log(x + 2) + 315*log(x - 2))*log(2)^3 + 81/64*(4*(279*x^7 - 2044*x^5 + 6160*x^3 - 6720*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) + 105*log(x + 2) - 105*log(x - 2))*log(2)^3 - 15/64*(4*(105*x^7 - 1540*x^5 + 8176*x^3 - 17856*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 105*log(x + 2) + 105*log(x - 2))*log(2)^3 - 81/32*(4*(15*x^7 + 292*x^5 - 880*x^3 + 9 60*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^3 - 39/32*(4*(15*x^7 - 220*x^5 + 1168*x^3 + 960*x)/(x^8 - 16*x ^6 + 96*x^4 - 256*x^2 + 256) - 15*log(x + 2) + 15*log(x - 2))*log(2)^3 ...
Leaf count of result is larger than twice the leaf count of optimal. 508 vs. \(2 (23) = 46\).
Time = 0.16 (sec) , antiderivative size = 508, normalized size of antiderivative = 18.81 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx =\text {Too large to display} \] Input:
integrate(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6 -192*x^5+1152*x^4+1536*x^3)*log(2)+288*x^8-192*x^7-2232*x^6-864*x^5+4320*x ^4+5760*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-46 08*x^3-6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+230 40*x^4-34560*x^3-51840*x^2)*log(2)+1152*x^9-576*x^8-13248*x^7-3168*x^6+507 60*x^5+45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x^7+2 304*x^6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-45 36*x^8-2448*x^7+26784*x^6+28224*x^5-70272*x^4-108288*x^3+69120*x^2+138240* x)*log(2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267840*x^ 4-423360*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133 920*x^6+155520*x^5-340200*x^4-550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^ 10-120*x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*x^8+1555 2*x^6-61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-3 67920*x^4+699840*x^2-518400)*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-9774 00*x^4+1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^6-972000*x ^4+1761750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x, alg orithm="giac")
Output:
6*(x^9*log(2)^4 + 16*x^9*log(2)^3 + 4*x^8*e^x*log(2)^3 + 96*x^9*log(2)^2 + 48*x^8*e^x*log(2)^2 - 16*x^7*log(2)^4 + 256*x^9*log(2) + 192*x^8*e^x*log( 2) + 6*x^7*e^(2*x)*log(2)^2 - 252*x^7*log(2)^3 - 48*x^6*e^x*log(2)^3 + 256 *x^9 + 256*x^8*e^x + 48*x^7*e^(2*x)*log(2) - 1488*x^7*log(2)^2 - 564*x^6*e ^x*log(2)^2 + 96*x^5*log(2)^4 + 96*x^7*e^(2*x) - 3904*x^7*log(2) + 4*x^6*e ^(3*x)*log(2) - 2208*x^6*e^x*log(2) - 48*x^5*e^(2*x)*log(2)^2 + 1488*x^5*l og(2)^3 + 192*x^4*e^x*log(2)^3 - 3840*x^7 + 16*x^6*e^(3*x) - 2880*x^6*e^x - 372*x^5*e^(2*x)*log(2) + 8646*x^5*log(2)^2 + 2208*x^4*e^x*log(2)^2 - 256 *x^3*log(2)^4 + x^5*e^(4*x) - 720*x^5*e^(2*x) + 22320*x^5*log(2) - 16*x^4* e^(3*x)*log(2) + 8460*x^4*e^x*log(2) + 96*x^3*e^(2*x)*log(2)^2 - 3904*x^3* log(2)^3 - 256*x^2*e^x*log(2)^3 + 21600*x^5 - 60*x^4*e^(3*x) + 10800*x^4*e ^x + 720*x^3*e^(2*x)*log(2) - 22320*x^3*log(2)^2 - 2880*x^2*e^x*log(2)^2 + 256*x*log(2)^4 + 1350*x^3*e^(2*x) - 56700*x^3*log(2) - 10800*x^2*e^x*log( 2) + 3840*x*log(2)^3 - 54000*x^3 - 13500*x^2*e^x + 21600*x*log(2)^2 + 5400 0*x*log(2) + 50625*x)/(x^8 - 16*x^6 + 96*x^4 - 256*x^2 + 256)
Timed out. \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=\int \frac {{\mathrm {e}}^x\,\left (648000\,x+{\ln \left (2\right )}^3\,\left (24\,x^{10}-384\,x^8-192\,x^7+2304\,x^6+2304\,x^5-6144\,x^4-9216\,x^3+6144\,x^2+12288\,x\right )+{\ln \left (2\right )}^2\,\left (288\,x^{10}-4536\,x^8-2448\,x^7+26784\,x^6+28224\,x^5-70272\,x^4-108288\,x^3+69120\,x^2+138240\,x\right )+\ln \left (2\right )\,\left (1152\,x^{10}-17856\,x^8-10368\,x^7+103752\,x^6+114912\,x^5-267840\,x^4-423360\,x^3+259200\,x^2+518400\,x\right )+324000\,x^2-550800\,x^3-340200\,x^4+155520\,x^5+133920\,x^6-14592\,x^7-23424\,x^8+1536\,x^{10}\right )+\ln \left (2\right )\,\left (1536\,x^{10}-31872\,x^8+254112\,x^6-977400\,x^4+1814400\,x^2-1296000\right )+{\ln \left (2\right )}^4\,\left (6\,x^{10}-120\,x^8+960\,x^6-3840\,x^4+7680\,x^2-6144\right )+{\ln \left (2\right )}^3\,\left (96\,x^{10}-1944\,x^8+15552\,x^6-61440\,x^4+119808\,x^2-92160\right )+{\ln \left (2\right )}^2\,\left (576\,x^{10}-11808\,x^8+94356\,x^6-367920\,x^4+699840\,x^2-518400\right )+{\mathrm {e}}^{3\,x}\,\left (\ln \left (2\right )\,\left (72\,x^8-48\,x^7-576\,x^6-192\,x^5+1152\,x^4+1536\,x^3\right )+5760\,x^3+4320\,x^4-864\,x^5-2232\,x^6-192\,x^7+288\,x^8\right )-{\mathrm {e}}^{2\,x}\,\left ({\ln \left (2\right )}^2\,\left (-72\,x^9+36\,x^8+864\,x^7+144\,x^6-3456\,x^5-2880\,x^4+4608\,x^3+6912\,x^2\right )+97200\,x^2+64800\,x^3-45900\,x^4-50760\,x^5+3168\,x^6+13248\,x^7+576\,x^8-1152\,x^9+\ln \left (2\right )\,\left (-576\,x^9+288\,x^8+6768\,x^7+1368\,x^6-26496\,x^5-23040\,x^4+34560\,x^3+51840\,x^2\right )\right )-{\mathrm {e}}^{4\,x}\,\left (-24\,x^7+18\,x^6+96\,x^5+120\,x^4\right )+1761750\,x^2-972000\,x^4+256320\,x^6-32256\,x^8+1536\,x^{10}-1215000}{x^{10}-20\,x^8+160\,x^6-640\,x^4+1280\,x^2-1024} \,d x \] Input:
int((exp(x)*(648000*x + log(2)^3*(12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 384*x^8 + 24*x^10) + log(2)^2*(138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7 - 4536*x^8 + 288*x^10) + log(2)*(518400*x + 259200*x^2 - 423360*x^3 - 26784 0*x^4 + 114912*x^5 + 103752*x^6 - 10368*x^7 - 17856*x^8 + 1152*x^10) + 324 000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^7 - 23424*x^8 + 1536*x^10) + log(2)*(1814400*x^2 - 977400*x^4 + 254112*x^6 - 3 1872*x^8 + 1536*x^10 - 1296000) + log(2)^4*(7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10 - 6144) + log(2)^3*(119808*x^2 - 61440*x^4 + 15552*x^6 - 1944*x^8 + 96*x^10 - 92160) + log(2)^2*(699840*x^2 - 367920*x^4 + 94356* x^6 - 11808*x^8 + 576*x^10 - 518400) + exp(3*x)*(log(2)*(1536*x^3 + 1152*x ^4 - 192*x^5 - 576*x^6 - 48*x^7 + 72*x^8) + 5760*x^3 + 4320*x^4 - 864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8) - exp(2*x)*(log(2)^2*(6912*x^2 + 4608*x^3 - 2880*x^4 - 3456*x^5 + 144*x^6 + 864*x^7 + 36*x^8 - 72*x^9) + 97200*x^2 + 64800*x^3 - 45900*x^4 - 50760*x^5 + 3168*x^6 + 13248*x^7 + 576*x^8 - 1152 *x^9 + log(2)*(51840*x^2 + 34560*x^3 - 23040*x^4 - 26496*x^5 + 1368*x^6 + 6768*x^7 + 288*x^8 - 576*x^9)) - exp(4*x)*(120*x^4 + 96*x^5 + 18*x^6 - 24* x^7) + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 1536*x^10 - 121 5000)/(1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10 - 1024),x)
Output:
int((exp(x)*(648000*x + log(2)^3*(12288*x + 6144*x^2 - 9216*x^3 - 6144*x^4 + 2304*x^5 + 2304*x^6 - 192*x^7 - 384*x^8 + 24*x^10) + log(2)^2*(138240*x + 69120*x^2 - 108288*x^3 - 70272*x^4 + 28224*x^5 + 26784*x^6 - 2448*x^7 - 4536*x^8 + 288*x^10) + log(2)*(518400*x + 259200*x^2 - 423360*x^3 - 26784 0*x^4 + 114912*x^5 + 103752*x^6 - 10368*x^7 - 17856*x^8 + 1152*x^10) + 324 000*x^2 - 550800*x^3 - 340200*x^4 + 155520*x^5 + 133920*x^6 - 14592*x^7 - 23424*x^8 + 1536*x^10) + log(2)*(1814400*x^2 - 977400*x^4 + 254112*x^6 - 3 1872*x^8 + 1536*x^10 - 1296000) + log(2)^4*(7680*x^2 - 3840*x^4 + 960*x^6 - 120*x^8 + 6*x^10 - 6144) + log(2)^3*(119808*x^2 - 61440*x^4 + 15552*x^6 - 1944*x^8 + 96*x^10 - 92160) + log(2)^2*(699840*x^2 - 367920*x^4 + 94356* x^6 - 11808*x^8 + 576*x^10 - 518400) + exp(3*x)*(log(2)*(1536*x^3 + 1152*x ^4 - 192*x^5 - 576*x^6 - 48*x^7 + 72*x^8) + 5760*x^3 + 4320*x^4 - 864*x^5 - 2232*x^6 - 192*x^7 + 288*x^8) - exp(2*x)*(log(2)^2*(6912*x^2 + 4608*x^3 - 2880*x^4 - 3456*x^5 + 144*x^6 + 864*x^7 + 36*x^8 - 72*x^9) + 97200*x^2 + 64800*x^3 - 45900*x^4 - 50760*x^5 + 3168*x^6 + 13248*x^7 + 576*x^8 - 1152 *x^9 + log(2)*(51840*x^2 + 34560*x^3 - 23040*x^4 - 26496*x^5 + 1368*x^6 + 6768*x^7 + 288*x^8 - 576*x^9)) - exp(4*x)*(120*x^4 + 96*x^5 + 18*x^6 - 24* x^7) + 1761750*x^2 - 972000*x^4 + 256320*x^6 - 32256*x^8 + 1536*x^10 - 121 5000)/(1280*x^2 - 640*x^4 + 160*x^6 - 20*x^8 + x^10 - 1024), x)
Time = 0.22 (sec) , antiderivative size = 525, normalized size of antiderivative = 19.44 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=\frac {6 x \left (50625+e^{4 x} x^{4}+16 e^{3 x} x^{5}+256 e^{x} x^{7}+256 \,\mathrm {log}\left (2\right ) x^{8}-3904 \,\mathrm {log}\left (2\right ) x^{6}+4 e^{3 x} \mathrm {log}\left (2\right ) x^{5}-16 e^{3 x} \mathrm {log}\left (2\right ) x^{3}+6 e^{2 x} \mathrm {log}\left (2\right )^{2} x^{6}-48 e^{2 x} \mathrm {log}\left (2\right )^{2} x^{4}+96 e^{2 x} \mathrm {log}\left (2\right )^{2} x^{2}+48 e^{2 x} \mathrm {log}\left (2\right ) x^{6}-372 e^{2 x} \mathrm {log}\left (2\right ) x^{4}+720 e^{2 x} \mathrm {log}\left (2\right ) x^{2}+4 e^{x} \mathrm {log}\left (2\right )^{3} x^{7}-48 e^{x} \mathrm {log}\left (2\right )^{3} x^{5}+192 e^{x} \mathrm {log}\left (2\right )^{3} x^{3}-256 e^{x} \mathrm {log}\left (2\right )^{3} x +48 e^{x} \mathrm {log}\left (2\right )^{2} x^{7}-564 e^{x} \mathrm {log}\left (2\right )^{2} x^{5}+2208 e^{x} \mathrm {log}\left (2\right )^{2} x^{3}-2880 e^{x} \mathrm {log}\left (2\right )^{2} x +192 e^{x} \mathrm {log}\left (2\right ) x^{7}-2208 e^{x} \mathrm {log}\left (2\right ) x^{5}+8460 e^{x} \mathrm {log}\left (2\right ) x^{3}+3840 \mathrm {log}\left (2\right )^{3}+1350 e^{2 x} x^{2}+10800 e^{x} x^{3}-56700 \,\mathrm {log}\left (2\right ) x^{2}-2880 e^{x} x^{5}+256 \mathrm {log}\left (2\right )^{4}-54000 x^{2}+96 e^{2 x} x^{6}+21600 \mathrm {log}\left (2\right )^{2}-10800 e^{x} \mathrm {log}\left (2\right ) x +96 \mathrm {log}\left (2\right )^{2} x^{8}-720 e^{2 x} x^{4}+8646 \mathrm {log}\left (2\right )^{2} x^{4}+22320 \,\mathrm {log}\left (2\right ) x^{4}+256 x^{8}-3840 x^{6}-60 e^{3 x} x^{3}-22320 \mathrm {log}\left (2\right )^{2} x^{2}+54000 \,\mathrm {log}\left (2\right )-1488 \mathrm {log}\left (2\right )^{2} x^{6}+21600 x^{4}-13500 e^{x} x +\mathrm {log}\left (2\right )^{4} x^{8}-16 \mathrm {log}\left (2\right )^{4} x^{6}+96 \mathrm {log}\left (2\right )^{4} x^{4}-256 \mathrm {log}\left (2\right )^{4} x^{2}+16 \mathrm {log}\left (2\right )^{3} x^{8}-252 \mathrm {log}\left (2\right )^{3} x^{6}+1488 \mathrm {log}\left (2\right )^{3} x^{4}-3904 \mathrm {log}\left (2\right )^{3} x^{2}\right )}{x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256} \] Input:
int(((24*x^7-18*x^6-96*x^5-120*x^4)*exp(x)^4+((72*x^8-48*x^7-576*x^6-192*x ^5+1152*x^4+1536*x^3)*log(2)+288*x^8-192*x^7-2232*x^6-864*x^5+4320*x^4+576 0*x^3)*exp(x)^3+((72*x^9-36*x^8-864*x^7-144*x^6+3456*x^5+2880*x^4-4608*x^3 -6912*x^2)*log(2)^2+(576*x^9-288*x^8-6768*x^7-1368*x^6+26496*x^5+23040*x^4 -34560*x^3-51840*x^2)*log(2)+1152*x^9-576*x^8-13248*x^7-3168*x^6+50760*x^5 +45900*x^4-64800*x^3-97200*x^2)*exp(x)^2+((24*x^10-384*x^8-192*x^7+2304*x^ 6+2304*x^5-6144*x^4-9216*x^3+6144*x^2+12288*x)*log(2)^3+(288*x^10-4536*x^8 -2448*x^7+26784*x^6+28224*x^5-70272*x^4-108288*x^3+69120*x^2+138240*x)*log (2)^2+(1152*x^10-17856*x^8-10368*x^7+103752*x^6+114912*x^5-267840*x^4-4233 60*x^3+259200*x^2+518400*x)*log(2)+1536*x^10-23424*x^8-14592*x^7+133920*x^ 6+155520*x^5-340200*x^4-550800*x^3+324000*x^2+648000*x)*exp(x)+(6*x^10-120 *x^8+960*x^6-3840*x^4+7680*x^2-6144)*log(2)^4+(96*x^10-1944*x^8+15552*x^6- 61440*x^4+119808*x^2-92160)*log(2)^3+(576*x^10-11808*x^8+94356*x^6-367920* x^4+699840*x^2-518400)*log(2)^2+(1536*x^10-31872*x^8+254112*x^6-977400*x^4 +1814400*x^2-1296000)*log(2)+1536*x^10-32256*x^8+256320*x^6-972000*x^4+176 1750*x^2-1215000)/(x^10-20*x^8+160*x^6-640*x^4+1280*x^2-1024),x)
Output:
(6*x*(e**(4*x)*x**4 + 4*e**(3*x)*log(2)*x**5 - 16*e**(3*x)*log(2)*x**3 + 1 6*e**(3*x)*x**5 - 60*e**(3*x)*x**3 + 6*e**(2*x)*log(2)**2*x**6 - 48*e**(2* x)*log(2)**2*x**4 + 96*e**(2*x)*log(2)**2*x**2 + 48*e**(2*x)*log(2)*x**6 - 372*e**(2*x)*log(2)*x**4 + 720*e**(2*x)*log(2)*x**2 + 96*e**(2*x)*x**6 - 720*e**(2*x)*x**4 + 1350*e**(2*x)*x**2 + 4*e**x*log(2)**3*x**7 - 48*e**x*l og(2)**3*x**5 + 192*e**x*log(2)**3*x**3 - 256*e**x*log(2)**3*x + 48*e**x*l og(2)**2*x**7 - 564*e**x*log(2)**2*x**5 + 2208*e**x*log(2)**2*x**3 - 2880* e**x*log(2)**2*x + 192*e**x*log(2)*x**7 - 2208*e**x*log(2)*x**5 + 8460*e** x*log(2)*x**3 - 10800*e**x*log(2)*x + 256*e**x*x**7 - 2880*e**x*x**5 + 108 00*e**x*x**3 - 13500*e**x*x + log(2)**4*x**8 - 16*log(2)**4*x**6 + 96*log( 2)**4*x**4 - 256*log(2)**4*x**2 + 256*log(2)**4 + 16*log(2)**3*x**8 - 252* log(2)**3*x**6 + 1488*log(2)**3*x**4 - 3904*log(2)**3*x**2 + 3840*log(2)** 3 + 96*log(2)**2*x**8 - 1488*log(2)**2*x**6 + 8646*log(2)**2*x**4 - 22320* log(2)**2*x**2 + 21600*log(2)**2 + 256*log(2)*x**8 - 3904*log(2)*x**6 + 22 320*log(2)*x**4 - 56700*log(2)*x**2 + 54000*log(2) + 256*x**8 - 3840*x**6 + 21600*x**4 - 54000*x**2 + 50625))/(x**8 - 16*x**6 + 96*x**4 - 256*x**2 + 256)