Integrand size = 609, antiderivative size = 27 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=6 x \left (-4-\frac {1+e^x x}{-4+x^2}-\log (2)\right )^4 \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(1088\) vs. \(2(27)=54\).
Time = 3.14 (sec) , antiderivative size = 1088, normalized size of antiderivative = 40.30, number of steps used = 39, number of rules used = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6820, 12, 6874, 2326, 294, 327, 213, 205} \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx =\text {Too large to display} \]
[In]
[Out]
Rule 12
Rule 205
Rule 213
Rule 294
Rule 327
Rule 2326
Rule 6820
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {6 \left (e^x x-15 \left (1+\frac {4 \log (2)}{15}\right )+x^2 (4+\log (2))\right )^3 \left (-e^x x \left (-20-16 x-3 x^2+4 x^3\right )-60 \left (1+\frac {4 \log (2)}{15}\right )-x^4 (4+\log (2))+x^2 (39+\log (256))\right )}{\left (4-x^2\right )^5} \, dx \\ & = 6 \int \frac {\left (e^x x-15 \left (1+\frac {4 \log (2)}{15}\right )+x^2 (4+\log (2))\right )^3 \left (-e^x x \left (-20-16 x-3 x^2+4 x^3\right )-60 \left (1+\frac {4 \log (2)}{15}\right )-x^4 (4+\log (2))+x^2 (39+\log (256))\right )}{\left (4-x^2\right )^5} \, dx \\ & = 6 \int \left (\frac {e^{4 x} x^4 \left (-20-16 x-3 x^2+4 x^3\right )}{\left (-4+x^2\right )^5}+\frac {e^{3 x} x^3 \left (144 x^2 \left (1+\frac {2 \log (2)}{9}\right )+32 x^4 \left (1+\frac {\log (2)}{4}\right )-48 x^5 \left (1+\frac {\log (2)}{4}\right )+372 x^3 \left (1+\frac {8 \log (2)}{31}\right )-960 \left (1+\frac {4 \log (2)}{15}\right )-720 x \left (1+\frac {4 \log (2)}{15}\right )\right )}{\left (4-x^2\right )^5}+\frac {x^{10} (4+\log (2))^4}{\left (-4+x^2\right )^5}+\frac {3 e^{2 x} x^2 \left (74 x^2 \left (1+\frac {8 \log (2)}{37}\right )+8 x^4 \left (1+\frac {\log (2)}{4}\right )-16 x^5 \left (1+\frac {\log (2)}{4}\right )+124 x^3 \left (1+\frac {8 \log (2)}{31}\right )-360 \left (1+\frac {4 \log (2)}{15}\right )-240 x \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (-15-4 \log (2)+x^2 (4+\log (2))\right )}{\left (4-x^2\right )^5}-\frac {4 (15+\log (16))^4}{\left (-4+x^2\right )^5}+\frac {4 e^x x \left (38 x^2 \left (1+\frac {4 \log (2)}{19}\right )-4 x^5 \left (1+\frac {\log (2)}{4}\right )+31 x^3 \left (1+\frac {8 \log (2)}{31}\right )-120 \left (1+\frac {4 \log (2)}{15}\right )-60 x \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (15-x^2 (4+\log (2))+\log (16)\right )^2}{\left (4-x^2\right )^5}-\frac {12 x^4 (4+\log (2))^2 (15+\log (16))^2 \left (1+\frac {\log (16)+3 (44+\log (256))}{12 (4+\log (2))}\right )}{\left (-4+x^2\right )^5}-\frac {3 x^8 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right )}{\left (-4+x^2\right )^5}+\frac {12 x^2 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right )}{\left (-4+x^2\right )^5}+\frac {4 x^6 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{\left (-4+x^2\right )^5}\right ) \, dx \\ & = 6 \int \frac {e^{4 x} x^4 \left (-20-16 x-3 x^2+4 x^3\right )}{\left (-4+x^2\right )^5} \, dx+6 \int \frac {e^{3 x} x^3 \left (144 x^2 \left (1+\frac {2 \log (2)}{9}\right )+32 x^4 \left (1+\frac {\log (2)}{4}\right )-48 x^5 \left (1+\frac {\log (2)}{4}\right )+372 x^3 \left (1+\frac {8 \log (2)}{31}\right )-960 \left (1+\frac {4 \log (2)}{15}\right )-720 x \left (1+\frac {4 \log (2)}{15}\right )\right )}{\left (4-x^2\right )^5} \, dx+18 \int \frac {e^{2 x} x^2 \left (74 x^2 \left (1+\frac {8 \log (2)}{37}\right )+8 x^4 \left (1+\frac {\log (2)}{4}\right )-16 x^5 \left (1+\frac {\log (2)}{4}\right )+124 x^3 \left (1+\frac {8 \log (2)}{31}\right )-360 \left (1+\frac {4 \log (2)}{15}\right )-240 x \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (-15-4 \log (2)+x^2 (4+\log (2))\right )}{\left (4-x^2\right )^5} \, dx+24 \int \frac {e^x x \left (38 x^2 \left (1+\frac {4 \log (2)}{19}\right )-4 x^5 \left (1+\frac {\log (2)}{4}\right )+31 x^3 \left (1+\frac {8 \log (2)}{31}\right )-120 \left (1+\frac {4 \log (2)}{15}\right )-60 x \left (1+\frac {4 \log (2)}{15}\right )\right ) \left (15-x^2 (4+\log (2))+\log (16)\right )^2}{\left (4-x^2\right )^5} \, dx+\left (6 (4+\log (2))^4\right ) \int \frac {x^{10}}{\left (-4+x^2\right )^5} \, dx-\left (24 (15+\log (16))^4\right ) \int \frac {1}{\left (-4+x^2\right )^5} \, dx-\left (6 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))\right ) \int \frac {x^4}{\left (-4+x^2\right )^5} \, dx-\left (18 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right )\right ) \int \frac {x^8}{\left (-4+x^2\right )^5} \, dx+\left (72 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right )\right ) \int \frac {x^2}{\left (-4+x^2\right )^5} \, dx+\left (24 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )\right ) \int \frac {x^6}{\left (-4+x^2\right )^5} \, dx \\ & = \frac {6 e^{4 x} x^4 \left (4 x-x^3\right )}{\left (4-x^2\right )^5}-\frac {3 x^9 (4+\log (2))^4}{4 \left (4-x^2\right )^4}+\frac {3 x (15+\log (16))^4}{4 \left (4-x^2\right )^4}-\frac {24 e^{3 x} x^3 \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}+\frac {36 e^{2 x} x^2 \left (15-x^2 (4+\log (2))+\log (16)\right ) \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}-\frac {24 e^x x \left (15-x^2 (4+\log (2))+\log (16)\right )^2 \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}+\frac {9 x^7 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096))}{4 \left (4-x^2\right )^4 (45+\log (4096))}-\frac {9 x (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096))}{\left (4-x^2\right )^4 (48+\log (4096))}+\frac {3 x^3 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{4 \left (4-x^2\right )^4}-\frac {3 x^5 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{\left (4-x^2\right )^4}+\frac {1}{4} \left (27 (4+\log (2))^4\right ) \int \frac {x^8}{\left (-4+x^2\right )^4} \, dx+\frac {1}{4} \left (21 (15+\log (16))^4\right ) \int \frac {1}{\left (-4+x^2\right )^4} \, dx-\frac {1}{4} \left (9 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))\right ) \int \frac {x^2}{\left (-4+x^2\right )^4} \, dx-\frac {1}{4} \left (63 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right )\right ) \int \frac {x^6}{\left (-4+x^2\right )^4} \, dx+\left (9 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right )\right ) \int \frac {1}{\left (-4+x^2\right )^4} \, dx+\left (15 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )\right ) \int \frac {x^4}{\left (-4+x^2\right )^4} \, dx \\ & = \frac {6 e^{4 x} x^4 \left (4 x-x^3\right )}{\left (4-x^2\right )^5}-\frac {3 x^9 (4+\log (2))^4}{4 \left (4-x^2\right )^4}+\frac {9 x^7 (4+\log (2))^4}{8 \left (4-x^2\right )^3}+\frac {3 x (15+\log (16))^4}{4 \left (4-x^2\right )^4}+\frac {7 x (15+\log (16))^4}{32 \left (4-x^2\right )^3}-\frac {24 e^{3 x} x^3 \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}+\frac {36 e^{2 x} x^2 \left (15-x^2 (4+\log (2))+\log (16)\right ) \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}-\frac {24 e^x x \left (15-x^2 (4+\log (2))+\log (16)\right )^2 \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}+\frac {9 x^7 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096))}{4 \left (4-x^2\right )^4 (45+\log (4096))}-\frac {21 x^5 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096))}{8 \left (4-x^2\right )^3 (45+\log (4096))}-\frac {9 x (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096))}{\left (4-x^2\right )^4 (48+\log (4096))}+\frac {3 x (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096))}{8 \left (4-x^2\right )^3 (48+\log (4096))}+\frac {3 x^3 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{4 \left (4-x^2\right )^4}-\frac {3 x (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{8 \left (4-x^2\right )^3}-\frac {3 x^5 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{\left (4-x^2\right )^4}+\frac {5 x^3 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{2 \left (4-x^2\right )^3}+\frac {1}{8} \left (63 (4+\log (2))^4\right ) \int \frac {x^6}{\left (-4+x^2\right )^3} \, dx-\frac {1}{32} \left (35 (15+\log (16))^4\right ) \int \frac {1}{\left (-4+x^2\right )^3} \, dx-\frac {1}{8} \left (3 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))\right ) \int \frac {1}{\left (-4+x^2\right )^3} \, dx-\frac {1}{8} \left (105 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right )\right ) \int \frac {x^4}{\left (-4+x^2\right )^3} \, dx-\frac {1}{8} \left (15 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right )\right ) \int \frac {1}{\left (-4+x^2\right )^3} \, dx+\frac {1}{2} \left (15 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )\right ) \int \frac {x^2}{\left (-4+x^2\right )^3} \, dx \\ & = \frac {6 e^{4 x} x^4 \left (4 x-x^3\right )}{\left (4-x^2\right )^5}-\frac {3 x^9 (4+\log (2))^4}{4 \left (4-x^2\right )^4}+\frac {9 x^7 (4+\log (2))^4}{8 \left (4-x^2\right )^3}-\frac {63 x^5 (4+\log (2))^4}{32 \left (4-x^2\right )^2}+\frac {3 x (15+\log (16))^4}{4 \left (4-x^2\right )^4}+\frac {7 x (15+\log (16))^4}{32 \left (4-x^2\right )^3}+\frac {35 x (15+\log (16))^4}{512 \left (4-x^2\right )^2}-\frac {24 e^{3 x} x^3 \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}+\frac {36 e^{2 x} x^2 \left (15-x^2 (4+\log (2))+\log (16)\right ) \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}-\frac {24 e^x x \left (15-x^2 (4+\log (2))+\log (16)\right )^2 \left (x^5 (4+\log (2))+4 x (15+\log (16))-x^3 (31+\log (256))\right )}{\left (4-x^2\right )^5}+\frac {9 x^7 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096))}{4 \left (4-x^2\right )^4 (45+\log (4096))}-\frac {21 x^5 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096))}{8 \left (4-x^2\right )^3 (45+\log (4096))}+\frac {105 x^3 (4+\log (2))^3 (15+\log (16)) (84+\log (256)+\log (4096))}{32 \left (4-x^2\right )^2 (45+\log (4096))}-\frac {9 x (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096))}{\left (4-x^2\right )^4 (48+\log (4096))}+\frac {3 x (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096))}{8 \left (4-x^2\right )^3 (48+\log (4096))}+\frac {15 x (4+\log (2)) (15+\log (16))^3 (87+\log (256)+\log (4096))}{128 \left (4-x^2\right )^2 (48+\log (4096))}+\frac {3 x^3 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{4 \left (4-x^2\right )^4}-\frac {3 x (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{8 \left (4-x^2\right )^3}+\frac {3 x (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{128 \left (4-x^2\right )^2}-\frac {3 x^5 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{\left (4-x^2\right )^4}+\frac {5 x^3 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{2 \left (4-x^2\right )^3}-\frac {15 x (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )}{8 \left (4-x^2\right )^2}+\frac {1}{32} \left (315 (4+\log (2))^4\right ) \int \frac {x^4}{\left (-4+x^2\right )^2} \, dx+\frac {1}{512} \left (105 (15+\log (16))^4\right ) \int \frac {1}{\left (-4+x^2\right )^2} \, dx+\frac {1}{128} \left (9 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))\right ) \int \frac {1}{\left (-4+x^2\right )^2} \, dx-\frac {1}{32} \left (315 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {39+\log (256)}{45+\log (4096)}\right )\right ) \int \frac {x^2}{\left (-4+x^2\right )^2} \, dx+\frac {1}{128} \left (45 (4+\log (2)) (15+\log (16))^3 \left (1+\frac {39+\log (256)}{48+\log (4096)}\right )\right ) \int \frac {1}{\left (-4+x^2\right )^2} \, dx+\frac {1}{8} \left (15 (4+\log (2))^3 (15+\log (16)) \left (1+\frac {3 (54+\log (4096))}{16+\log (16)}\right )\right ) \int \frac {1}{\left (-4+x^2\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(1529\) vs. \(2(27)=54\).
Time = 4.35 (sec) , antiderivative size = 1529, normalized size of antiderivative = 56.63 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx =\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(379\) vs. \(2(26)=52\).
Time = 0.47 (sec) , antiderivative size = 380, normalized size of antiderivative = 14.07
method | result | size |
risch | \(6 x \ln \left (2\right )^{4}+96 x \ln \left (2\right )^{3}+576 x \ln \left (2\right )^{2}+1536 x \ln \left (2\right )+1536 x +\frac {\left (24 \ln \left (2\right )^{3}+288 \ln \left (2\right )^{2}+1152 \ln \left (2\right )+1536\right ) x^{7}+\left (-288 \ln \left (2\right )^{3}-3420 \ln \left (2\right )^{2}-13536 \ln \left (2\right )-17856\right ) x^{5}+\left (1152 \ln \left (2\right )^{3}+13536 \ln \left (2\right )^{2}+53016 \ln \left (2\right )+69216\right ) x^{3}+\left (-1536 \ln \left (2\right )^{3}-17856 \ln \left (2\right )^{2}-69216 \ln \left (2\right )-89466\right ) x}{x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256}+\frac {6 x^{5} {\mathrm e}^{4 x}}{\left (x^{2}-4\right )^{4}}+\frac {24 x^{4} \left (x^{2} \ln \left (2\right )+4 x^{2}-4 \ln \left (2\right )-15\right ) {\mathrm e}^{3 x}}{\left (x^{2}-4\right )^{4}}+\frac {36 x^{3} \left (x^{4} \ln \left (2\right )^{2}+8 x^{4} \ln \left (2\right )-8 x^{2} \ln \left (2\right )^{2}+16 x^{4}-62 x^{2} \ln \left (2\right )+16 \ln \left (2\right )^{2}-120 x^{2}+120 \ln \left (2\right )+225\right ) {\mathrm e}^{2 x}}{\left (x^{2}-4\right )^{4}}+\frac {24 x^{2} \left (x^{6} \ln \left (2\right )^{3}+12 x^{6} \ln \left (2\right )^{2}-12 x^{4} \ln \left (2\right )^{3}+48 x^{6} \ln \left (2\right )-141 x^{4} \ln \left (2\right )^{2}+64 x^{6}+48 x^{2} \ln \left (2\right )^{3}-552 x^{4} \ln \left (2\right )+552 x^{2} \ln \left (2\right )^{2}-720 x^{4}-64 \ln \left (2\right )^{3}+2115 x^{2} \ln \left (2\right )-720 \ln \left (2\right )^{2}+2700 x^{2}-2700 \ln \left (2\right )-3375\right ) {\mathrm e}^{x}}{\left (x^{2}-4\right )^{4}}\) | \(380\) |
parallelrisch | \(\frac {303750 x +23040 x \ln \left (2\right )^{3}+576 x^{5} \ln \left (2\right )^{4}-1536 x^{3} \ln \left (2\right )^{4}+1536 x^{8} {\mathrm e}^{x}+8100 \,{\mathrm e}^{2 x} x^{3}+51876 x^{5} \ln \left (2\right )^{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}+8928 x^{5} \ln \left (2\right )^{3}+6 x^{9} \ln \left (2\right )^{4}-64800 x^{2} \ln \left (2\right ) {\mathrm e}^{x}+1536 x^{9}-23040 x^{7}-324000 x^{3}+129600 x^{5}-23424 x^{3} \ln \left (2\right )^{3}+576 \ln \left (2\right )^{2} x^{9}+24 \,{\mathrm e}^{x} \ln \left (2\right )^{3} x^{8}+288 \,{\mathrm e}^{x} \ln \left (2\right )^{2} x^{8}+50760 \,{\mathrm e}^{x} \ln \left (2\right ) x^{4}+1152 \,{\mathrm e}^{x} \ln \left (2\right ) x^{8}-13248 \,{\mathrm e}^{x} \ln \left (2\right ) x^{6}-17280 \,{\mathrm e}^{x} \ln \left (2\right )^{2} x^{2}-288 \,{\mathrm e}^{x} \ln \left (2\right )^{3} x^{6}-3384 \,{\mathrm e}^{x} \ln \left (2\right )^{2} x^{6}+1152 \,{\mathrm e}^{x} \ln \left (2\right )^{3} x^{4}+13248 \,{\mathrm e}^{x} \ln \left (2\right )^{2} x^{4}-1536 \,{\mathrm e}^{x} \ln \left (2\right )^{3} x^{2}-360 \,{\mathrm e}^{3 x} x^{4}+6 x^{5} {\mathrm e}^{4 x}+1536 \ln \left (2\right ) x^{9}+4320 \ln \left (2\right ) {\mathrm e}^{2 x} x^{3}+576 \,{\mathrm e}^{2 x} x^{7}+96 x^{6} {\mathrm e}^{3 x}+36 \,{\mathrm e}^{2 x} \ln \left (2\right )^{2} x^{7}+24 \,{\mathrm e}^{3 x} \ln \left (2\right ) x^{6}+288 \,{\mathrm e}^{2 x} \ln \left (2\right ) x^{7}-288 \,{\mathrm e}^{2 x} \ln \left (2\right )^{2} x^{5}-96 \,{\mathrm e}^{3 x} \ln \left (2\right ) x^{4}-2232 \,{\mathrm e}^{2 x} \ln \left (2\right ) x^{5}+576 \,{\mathrm e}^{2 x} \ln \left (2\right )^{2} x^{3}+96 \ln \left (2\right )^{3} x^{9}}{x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256}\) | \(510\) |
parts | \(\text {Expression too large to display}\) | \(859\) |
default | \(\text {Expression too large to display}\) | \(7367\) |
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Leaf count of result is larger than twice the leaf count of optimal. 362 vs. \(2 (23) = 46\).
Time = 0.28 (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} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1402 vs. \(2 (22) = 44\).
Time = 2.96 (sec) , antiderivative size = 1402, normalized size of antiderivative = 51.93 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1957 vs. \(2 (23) = 46\).
Time = 0.41 (sec) , antiderivative size = 1957, normalized size of antiderivative = 72.48 \[ \int \frac {-1215000+1761750 x^2-972000 x^4+256320 x^6-32256 x^8+1536 x^{10}+e^{4 x} \left (-120 x^4-96 x^5-18 x^6+24 x^7\right )+\left (-1296000+1814400 x^2-977400 x^4+254112 x^6-31872 x^8+1536 x^{10}\right ) \log (2)+\left (-518400+699840 x^2-367920 x^4+94356 x^6-11808 x^8+576 x^{10}\right ) \log ^2(2)+\left (-92160+119808 x^2-61440 x^4+15552 x^6-1944 x^8+96 x^{10}\right ) \log ^3(2)+\left (-6144+7680 x^2-3840 x^4+960 x^6-120 x^8+6 x^{10}\right ) \log ^4(2)+e^{3 x} \left (5760 x^3+4320 x^4-864 x^5-2232 x^6-192 x^7+288 x^8+\left (1536 x^3+1152 x^4-192 x^5-576 x^6-48 x^7+72 x^8\right ) \log (2)\right )+e^{2 x} \left (-97200 x^2-64800 x^3+45900 x^4+50760 x^5-3168 x^6-13248 x^7-576 x^8+1152 x^9+\left (-51840 x^2-34560 x^3+23040 x^4+26496 x^5-1368 x^6-6768 x^7-288 x^8+576 x^9\right ) \log (2)+\left (-6912 x^2-4608 x^3+2880 x^4+3456 x^5-144 x^6-864 x^7-36 x^8+72 x^9\right ) \log ^2(2)\right )+e^x \left (648000 x+324000 x^2-550800 x^3-340200 x^4+155520 x^5+133920 x^6-14592 x^7-23424 x^8+1536 x^{10}+\left (518400 x+259200 x^2-423360 x^3-267840 x^4+114912 x^5+103752 x^6-10368 x^7-17856 x^8+1152 x^{10}\right ) \log (2)+\left (138240 x+69120 x^2-108288 x^3-70272 x^4+28224 x^5+26784 x^6-2448 x^7-4536 x^8+288 x^{10}\right ) \log ^2(2)+\left (12288 x+6144 x^2-9216 x^3-6144 x^4+2304 x^5+2304 x^6-192 x^7-384 x^8+24 x^{10}\right ) \log ^3(2)\right )}{-1024+1280 x^2-640 x^4+160 x^6-20 x^8+x^{10}} \, dx=\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. 508 vs. \(2 (23) = 46\).
Time = 0.29 (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=\frac {6 \, {\left (x^{9} \log \left (2\right )^{4} + 16 \, x^{9} \log \left (2\right )^{3} + 4 \, x^{8} e^{x} \log \left (2\right )^{3} + 96 \, x^{9} \log \left (2\right )^{2} + 48 \, x^{8} e^{x} \log \left (2\right )^{2} - 16 \, x^{7} \log \left (2\right )^{4} + 256 \, x^{9} \log \left (2\right ) + 192 \, x^{8} e^{x} \log \left (2\right ) + 6 \, x^{7} e^{\left (2 \, x\right )} \log \left (2\right )^{2} - 252 \, x^{7} \log \left (2\right )^{3} - 48 \, x^{6} e^{x} \log \left (2\right )^{3} + 256 \, x^{9} + 256 \, x^{8} e^{x} + 48 \, x^{7} e^{\left (2 \, x\right )} \log \left (2\right ) - 1488 \, x^{7} \log \left (2\right )^{2} - 564 \, x^{6} e^{x} \log \left (2\right )^{2} + 96 \, x^{5} \log \left (2\right )^{4} + 96 \, x^{7} e^{\left (2 \, x\right )} - 3904 \, x^{7} \log \left (2\right ) + 4 \, x^{6} e^{\left (3 \, x\right )} \log \left (2\right ) - 2208 \, x^{6} e^{x} \log \left (2\right ) - 48 \, x^{5} e^{\left (2 \, x\right )} \log \left (2\right )^{2} + 1488 \, x^{5} \log \left (2\right )^{3} + 192 \, x^{4} e^{x} \log \left (2\right )^{3} - 3840 \, x^{7} + 16 \, x^{6} e^{\left (3 \, x\right )} - 2880 \, x^{6} e^{x} - 372 \, x^{5} e^{\left (2 \, x\right )} \log \left (2\right ) + 8646 \, x^{5} \log \left (2\right )^{2} + 2208 \, x^{4} e^{x} \log \left (2\right )^{2} - 256 \, x^{3} \log \left (2\right )^{4} + x^{5} e^{\left (4 \, x\right )} - 720 \, x^{5} e^{\left (2 \, x\right )} + 22320 \, x^{5} \log \left (2\right ) - 16 \, x^{4} e^{\left (3 \, x\right )} \log \left (2\right ) + 8460 \, x^{4} e^{x} \log \left (2\right ) + 96 \, x^{3} e^{\left (2 \, x\right )} \log \left (2\right )^{2} - 3904 \, x^{3} \log \left (2\right )^{3} - 256 \, x^{2} e^{x} \log \left (2\right )^{3} + 21600 \, x^{5} - 60 \, x^{4} e^{\left (3 \, x\right )} + 10800 \, x^{4} e^{x} + 720 \, x^{3} e^{\left (2 \, x\right )} \log \left (2\right ) - 22320 \, x^{3} \log \left (2\right )^{2} - 2880 \, x^{2} e^{x} \log \left (2\right )^{2} + 256 \, x \log \left (2\right )^{4} + 1350 \, x^{3} e^{\left (2 \, x\right )} - 56700 \, x^{3} \log \left (2\right ) - 10800 \, x^{2} e^{x} \log \left (2\right ) + 3840 \, x \log \left (2\right )^{3} - 54000 \, x^{3} - 13500 \, x^{2} e^{x} + 21600 \, x \log \left (2\right )^{2} + 54000 \, x \log \left (2\right ) + 50625 \, x\right )}}{x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256} \]
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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 \]
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