∫ −1215000+1761750x2−972000x4+256320x6−32256x8+1536x10+e4x(−120x4−96x5−18x6+24x7)+(−1296000+1814400x2−977400x4+254112x6−31872x8+1536x10) log(2)+(−518400+699840x2−367920x4+94356x6−11808x8+576x10) log2(2)+(−92160+119808x2−61440x4+15552x6−1944x8+96x10) log3(2)+(−6144+7680x2−3840x4+960x6−120x8+6x10) log4(2)+e3x(5760x3+4320x4−864x5−2232x6−192x7+288x8+(1536x3+1152x4−192x5−576x6−48x7+72x8) log(2))+e2x(−97200x2−64800x3+45900x4+50760x5−3168x6−13248x7−576x8+1152x9+(−51840x2−34560x3+23040x4+26496x5−1368x6−6768x7−288x8+576x9) log(2)+(−6912x2−4608x3+2880x4+3456x5−144x6−864x7−36x8+72x9) log2(2))+ex(648000x+324000x2−550800x3−340200x4+155520x5+133920x6−14592x7−23424x8+1536x10+(518400x+259200x2−423360x3−267840x4+114912x5+103752x6−10368x7−17856x8+1152x10) log(2)+(138240x+69120x2−108288x3−70272x4+28224x5+26784x6−2448x7−4536x8+288x10) log2(2)+(12288x+6144x2−9216x3−6144x4+2304x5+2304x6−192x7−384x8+24x10) log3(2))___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Optimal. Leaf size=27 \[ 6 x \left (-4-\frac {1+e^x x}{-4+x^2}-\log (2)\right )^4 \]

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Rubi [B] time = 6.02, antiderivative size = 1088, normalized size of antiderivative = 40.30, number of steps used = 39, number of rules used = 8, integrand size = 609, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6688, 12, 6742, 2288, 288, 321, 207, 199}

\begin {gather*} \begin {aligned} \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\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B] time = 4.68, size = 699, normalized size = 25.89 \begin {gather*} 6 \left (\frac {e^{4 x} x^5}{\left (-4+x^2\right )^4}+\frac {x^9 (4+\log (2))^4}{\left (-4+x^2\right )^4}-\frac {3 \left (2 x \left (-6720+6160 x^2-2044 x^4+279 x^6\right )+105 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2))^4}{64 \left (-4+x^2\right )^4}+\frac {4 e^{3 x} x^4 \left (-15-4 \log (2)+x^2 (4+\log (2))\right )}{\left (-4+x^2\right )^4}+\frac {x (15+\log (16))^4}{8 \left (-4+x^2\right )^4}+\frac {7 \left (-2 x \left (528-160 x^2+15 x^4\right )+15 \left (-4+x^2\right )^3 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (15+\log (16))^4}{49152 \left (-4+x^2\right )^3}+\frac {6 e^{2 x} x^3 \left (-15-4 \log (2)+x^2 (4+\log (2))\right ) \left (x^4 (4+\log (2))+4 (15+\log (16))-x^2 (31+\log (256))\right )}{\left (-4+x^2\right )^5}+\frac {4 e^x x^2 \left (15-x^2 (4+\log (2))+\log (16)\right )^2 \left (x^4 (4+\log (2))+4 (15+\log (16))-x^2 (31+\log (256))\right )}{\left (-4+x^2\right )^5}+\frac {x^3 (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{5 \left (-4+x^2\right )^4}+\frac {\left (-2 x \left (960+1168 x^2-220 x^4+15 x^6\right )+15 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2)) (15+\log (16))^2 (180+\log (16)+3 \log (256)+\log (4096))}{20480 \left (-4+x^2\right )^4}-\frac {4 x^5 (4+\log (2))^3 (15+\log (16)) (178+\log (16)+3 \log (4096))}{3 \left (-4+x^2\right )^4 (16+\log (16))}+\frac {5 \left (-384 x+352 x^3+88 x^5-6 x^7+3 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2))^3 (15+\log (16)) (178+\log (16)+3 \log (4096))}{768 \left (-4+x^2\right )^4 (16+\log (16))}+\frac {3 x^7 (4+\log (2))^3 (15+\log (16)) (84+\log (1048576))}{\left (-4+x^2\right )^4 (45+\log (4096))}+\frac {7 \left (-2 x \left (960-880 x^2+292 x^4+15 x^6\right )+15 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2))^3 (15+\log (16)) (84+\log (1048576))}{256 \left (-4+x^2\right )^4 (45+\log (4096))}-\frac {12 x (4+\log (2)) (15+\log (16))^3 (87+\log (1048576))}{7 \left (-4+x^2\right )^4 (48+\log (4096))}+\frac {\left (35712 x-16352 x^3+3080 x^5-210 x^7+105 \left (-4+x^2\right )^4 \tanh ^{-1}\left (\frac {x}{2}\right )\right ) (4+\log (2)) (15+\log (16))^3 (87+\log (1048576))}{28672 \left (-4+x^2\right )^4 (48+\log (4096))}\right ) \end {gather*}

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fricas [B] time = 0.88, size = 362, normalized size = 13.41 \begin {gather*} \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 \relax (2)^{4} + 4 \, {\left (4 \, x^{9} - 63 \, x^{7} + 372 \, x^{5} - 976 \, x^{3} + 960 \, x\right )} \log \relax (2)^{3} - 54000 \, x^{3} + 6 \, {\left (16 \, x^{9} - 248 \, x^{7} + 1441 \, x^{5} - 3720 \, x^{3} + 3600 \, x\right )} \log \relax (2)^{2} + 4 \, {\left (4 \, x^{6} - 15 \, x^{4} + {\left (x^{6} - 4 \, x^{4}\right )} \log \relax (2)\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 \relax (2)^{2} + 2 \, {\left (4 \, x^{7} - 31 \, x^{5} + 60 \, x^{3}\right )} \log \relax (2)\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 \relax (2)^{3} + 3 \, {\left (4 \, x^{8} - 47 \, x^{6} + 184 \, x^{4} - 240 \, x^{2}\right )} \log \relax (2)^{2} - 3375 \, x^{2} + 3 \, {\left (16 \, x^{8} - 184 \, x^{6} + 705 \, x^{4} - 900 \, x^{2}\right )} \log \relax (2)\right )} e^{x} + 4 \, {\left (64 \, x^{9} - 976 \, x^{7} + 5580 \, x^{5} - 14175 \, x^{3} + 13500 \, x\right )} \log \relax (2) + 50625 \, x\right )}}{x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256} \end {gather*}

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giac [B] time = 0.63, size = 508, normalized size = 18.81 \begin {gather*} \frac {6 \, {\left (x^{9} \log \relax (2)^{4} + 16 \, x^{9} \log \relax (2)^{3} + 4 \, x^{8} e^{x} \log \relax (2)^{3} + 96 \, x^{9} \log \relax (2)^{2} + 48 \, x^{8} e^{x} \log \relax (2)^{2} - 16 \, x^{7} \log \relax (2)^{4} + 256 \, x^{9} \log \relax (2) + 192 \, x^{8} e^{x} \log \relax (2) + 6 \, x^{7} e^{\left (2 \, x\right )} \log \relax (2)^{2} - 252 \, x^{7} \log \relax (2)^{3} - 48 \, x^{6} e^{x} \log \relax (2)^{3} + 256 \, x^{9} + 256 \, x^{8} e^{x} + 48 \, x^{7} e^{\left (2 \, x\right )} \log \relax (2) - 1488 \, x^{7} \log \relax (2)^{2} - 564 \, x^{6} e^{x} \log \relax (2)^{2} + 96 \, x^{5} \log \relax (2)^{4} + 96 \, x^{7} e^{\left (2 \, x\right )} - 3904 \, x^{7} \log \relax (2) + 4 \, x^{6} e^{\left (3 \, x\right )} \log \relax (2) - 2208 \, x^{6} e^{x} \log \relax (2) - 48 \, x^{5} e^{\left (2 \, x\right )} \log \relax (2)^{2} + 1488 \, x^{5} \log \relax (2)^{3} + 192 \, x^{4} e^{x} \log \relax (2)^{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 \relax (2) + 8646 \, x^{5} \log \relax (2)^{2} + 2208 \, x^{4} e^{x} \log \relax (2)^{2} - 256 \, x^{3} \log \relax (2)^{4} + x^{5} e^{\left (4 \, x\right )} - 720 \, x^{5} e^{\left (2 \, x\right )} + 22320 \, x^{5} \log \relax (2) - 16 \, x^{4} e^{\left (3 \, x\right )} \log \relax (2) + 8460 \, x^{4} e^{x} \log \relax (2) + 96 \, x^{3} e^{\left (2 \, x\right )} \log \relax (2)^{2} - 3904 \, x^{3} \log \relax (2)^{3} - 256 \, x^{2} e^{x} \log \relax (2)^{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 \relax (2) - 22320 \, x^{3} \log \relax (2)^{2} - 2880 \, x^{2} e^{x} \log \relax (2)^{2} + 256 \, x \log \relax (2)^{4} + 1350 \, x^{3} e^{\left (2 \, x\right )} - 56700 \, x^{3} \log \relax (2) - 10800 \, x^{2} e^{x} \log \relax (2) + 3840 \, x \log \relax (2)^{3} - 54000 \, x^{3} - 13500 \, x^{2} e^{x} + 21600 \, x \log \relax (2)^{2} + 54000 \, x \log \relax (2) + 50625 \, x\right )}}{x^{8} - 16 \, x^{6} + 96 \, x^{4} - 256 \, x^{2} + 256} \end {gather*}

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method	result	size

risch	\(6 x \ln \relax (2)^{4}+96 x \ln \relax (2)^{3}+576 x \ln \relax (2)^{2}+1536 x \ln \relax (2)+1536 x +\frac {\left (24 \ln \relax (2)^{3}+288 \ln \relax (2)^{2}+1152 \ln \relax (2)+1536\right ) x^{7}+\left (-288 \ln \relax (2)^{3}-3420 \ln \relax (2)^{2}-13536 \ln \relax (2)-17856\right ) x^{5}+\left (1152 \ln \relax (2)^{3}+13536 \ln \relax (2)^{2}+53016 \ln \relax (2)+69216\right ) x^{3}+\left (-1536 \ln \relax (2)^{3}-17856 \ln \relax (2)^{2}-69216 \ln \relax (2)-89466\right ) x}{x^{8}-16 x^{6}+96 x^{4}-256 x^{2}+256}+\frac {6 x^{5} {\mathrm e}^{4 x}}{\left (x^{2}-4\right )^{4}}+\frac {24 x^{4} \left (x^{2} \ln \relax (2)+4 x^{2}-4 \ln \relax (2)-15\right ) {\mathrm e}^{3 x}}{\left (x^{2}-4\right )^{4}}+\frac {36 x^{3} \left (x^{4} \ln \relax (2)^{2}+8 x^{4} \ln \relax (2)-8 x^{2} \ln \relax (2)^{2}+16 x^{4}-62 x^{2} \ln \relax (2)+16 \ln \relax (2)^{2}-120 x^{2}+120 \ln \relax (2)+225\right ) {\mathrm e}^{2 x}}{\left (x^{2}-4\right )^{4}}+\frac {24 x^{2} \left (x^{6} \ln \relax (2)^{3}+12 x^{6} \ln \relax (2)^{2}-12 x^{4} \ln \relax (2)^{3}+48 x^{6} \ln \relax (2)-141 x^{4} \ln \relax (2)^{2}+64 x^{6}+48 x^{2} \ln \relax (2)^{3}-552 x^{4} \ln \relax (2)+552 x^{2} \ln \relax (2)^{2}-720 x^{4}-64 \ln \relax (2)^{3}+2115 x^{2} \ln \relax (2)-720 \ln \relax (2)^{2}+2700 x^{2}-2700 \ln \relax (2)-3375\right ) {\mathrm e}^{x}}{\left (x^{2}-4\right )^{4}}\)	\(380\)
default	\(1536 x -\frac {9 \ln \relax (2)^{2}}{2 \left (2+x \right )^{2}}+1536 \,{\mathrm e}^{x}+24 \ln \relax (2)^{3} {\mathrm e}^{x}+288 \ln \relax (2)^{2} {\mathrm e}^{x}+96 x \ln \relax (2)^{3}+\frac {3}{64 \left (x -2\right )^{4}}+1152 \,{\mathrm e}^{x} \ln \relax (2)+\frac {768}{2+x}+6 x \ln \relax (2)^{4}+576 x \ln \relax (2)^{2}+1536 x \ln \relax (2)+\frac {768}{x -2}+\frac {3 \,{\mathrm e}^{x}}{8 \left (2+x \right )^{4}}+\frac {18717 \,{\mathrm e}^{x}}{64 \left (2+x \right )^{2}}-\frac {18 \,{\mathrm e}^{x}}{\left (2+x \right )^{3}}-\frac {214755 \,{\mathrm e}^{x}}{128 \left (2+x \right )}+\frac {18 \,{\mathrm e}^{x}}{\left (x -2\right )^{3}}+\frac {214755 \,{\mathrm e}^{x}}{128 \left (x -2\right )}+\frac {18717 \,{\mathrm e}^{x}}{64 \left (x -2\right )^{2}}+\frac {3 \,{\mathrm e}^{x}}{8 \left (x -2\right )^{4}}+\frac {12 \ln \relax (2)^{3}}{x -2}+\frac {12 \ln \relax (2)^{3}}{2+x}+\frac {144 \ln \relax (2)^{2}}{2+x}+\frac {9 \ln \relax (2)^{2}}{2 \left (x -2\right )^{2}}+\frac {144 \ln \relax (2)^{2}}{x -2}+\frac {3 \ln \relax (2)}{4 \left (x -2\right )^{3}}+\frac {573 \ln \relax (2)}{16 \left (x -2\right )^{2}}+\frac {576 \ln \relax (2)}{x -2}+\frac {3 \ln \relax (2)}{4 \left (2+x \right )^{3}}-\frac {573 \ln \relax (2)}{16 \left (2+x \right )^{2}}+\frac {576 \ln \relax (2)}{2+x}-\frac {36483}{512 \left (2+x \right )^{2}}+\frac {36483}{512 \left (x -2\right )^{2}}-\frac {3}{64 \left (2+x \right )^{4}}-\frac {24 \ln \relax (2)^{3} {\mathrm e}^{x}}{2+x}+\frac {24 \ln \relax (2)^{3} {\mathrm e}^{x}}{x -2}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{x}}{\left (2+x \right )^{2}}-\frac {297 \ln \relax (2)^{2} {\mathrm e}^{x}}{2+x}+\frac {297 \ln \relax (2)^{2} {\mathrm e}^{x}}{x -2}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{x}}{\left (x -2\right )^{2}}+\frac {381}{128 \left (x -2\right )^{3}}+\frac {381}{128 \left (2+x \right )^{3}}+\frac {9 \ln \relax (2) {\mathrm e}^{2 x}}{\left (x -2\right )^{3}}-\frac {603 \ln \relax (2) {\mathrm e}^{2 x}}{4 \left (2+x \right )^{2}}+\frac {9 \ln \relax (2) {\mathrm e}^{2 x}}{\left (2+x \right )^{3}}+\frac {144 \ln \relax (2) {\mathrm e}^{2 x}}{x -2}+\frac {603 \ln \relax (2) {\mathrm e}^{2 x}}{4 \left (x -2\right )^{2}}+\frac {144 \ln \relax (2) {\mathrm e}^{2 x}}{2+x}+\frac {6 \ln \relax (2) {\mathrm e}^{3 x}}{\left (x -2\right )^{3}}+\frac {15 \ln \relax (2) {\mathrm e}^{3 x}}{2 \left (2+x \right )^{2}}-\frac {6 \ln \relax (2) {\mathrm e}^{3 x}}{\left (2+x \right )^{3}}+\frac {9 \ln \relax (2) {\mathrm e}^{3 x}}{4 \left (x -2\right )}+\frac {15 \ln \relax (2) {\mathrm e}^{3 x}}{2 \left (x -2\right )^{2}}-\frac {9 \ln \relax (2) {\mathrm e}^{3 x}}{4 \left (2+x \right )}-\frac {18 \ln \relax (2)^{2} {\mathrm e}^{2 x}}{\left (2+x \right )^{2}}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{2 x}}{x -2}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{2 x}}{\left (x -2\right )^{2}}+\frac {18 \ln \relax (2)^{2} {\mathrm e}^{2 x}}{2+x}-\frac {9 \,{\mathrm e}^{2 x}}{8 \left (2+x \right )^{4}}+\frac {585 \,{\mathrm e}^{2 x}}{16 \left (x -2\right )^{3}}-\frac {20151 \,{\mathrm e}^{2 x}}{64 \left (2+x \right )^{2}}+\frac {585 \,{\mathrm e}^{2 x}}{16 \left (2+x \right )^{3}}+\frac {288 \,{\mathrm e}^{2 x}}{x -2}+\frac {20151 \,{\mathrm e}^{2 x}}{64 \left (x -2\right )^{2}}+\frac {288 \,{\mathrm e}^{2 x}}{2+x}+\frac {9 \,{\mathrm e}^{2 x}}{8 \left (x -2\right )^{4}}-\frac {15 \,{\mathrm e}^{4 x}}{32 \left (2+x \right )^{2}}+\frac {9 \,{\mathrm e}^{4 x}}{8 \left (2+x \right )^{3}}+\frac {9 \,{\mathrm e}^{4 x}}{8 \left (x -2\right )^{3}}+\frac {15 \,{\mathrm e}^{4 x}}{32 \left (x -2\right )^{2}}-\frac {3 \,{\mathrm e}^{4 x}}{4 \left (2+x \right )^{4}}+\frac {3 \,{\mathrm e}^{4 x}}{4 \left (x -2\right )^{4}}+\frac {3 \,{\mathrm e}^{3 x}}{2 \left (2+x \right )^{4}}+\frac {51 \,{\mathrm e}^{3 x}}{2 \left (x -2\right )^{3}}+\frac {483 \,{\mathrm e}^{3 x}}{16 \left (2+x \right )^{2}}-\frac {51 \,{\mathrm e}^{3 x}}{2 \left (2+x \right )^{3}}+\frac {285 \,{\mathrm e}^{3 x}}{32 \left (x -2\right )}+\frac {483 \,{\mathrm e}^{3 x}}{16 \left (x -2\right )^{2}}-\frac {285 \,{\mathrm e}^{3 x}}{32 \left (2+x \right )}+\frac {3 \,{\mathrm e}^{3 x}}{2 \left (x -2\right )^{4}}+\frac {1161 \ln \relax (2) {\mathrm e}^{x}}{8 \left (2+x \right )^{2}}-\frac {9 \ln \relax (2) {\mathrm e}^{x}}{2 \left (2+x \right )^{3}}-\frac {19575 \ln \relax (2) {\mathrm e}^{x}}{16 \left (2+x \right )}+\frac {9 \ln \relax (2) {\mathrm e}^{x}}{2 \left (x -2\right )^{3}}+\frac {19575 \ln \relax (2) {\mathrm e}^{x}}{16 \left (x -2\right )}+\frac {1161 \ln \relax (2) {\mathrm e}^{x}}{8 \left (x -2\right )^{2}}\)	\(907\)

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maxima [B] time = 0.84, size = 1957, normalized size = 72.48 result too large to display

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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^x\,\left (648000\,x+{\ln \relax (2)}^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 \relax (2)}^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 \relax (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 )+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 \relax (2)\,\left (1536\,x^{10}-31872\,x^8+254112\,x^6-977400\,x^4+1814400\,x^2-1296000\right )+{\ln \relax (2)}^4\,\left (6\,x^{10}-120\,x^8+960\,x^6-3840\,x^4+7680\,x^2-6144\right )+{\ln \relax (2)}^3\,\left (96\,x^{10}-1944\,x^8+15552\,x^6-61440\,x^4+119808\,x^2-92160\right )+{\ln \relax (2)}^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 \relax (2)\,\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 \relax (2)}^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 \relax (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 )\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 \end {gather*}

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sympy [B] time = 5.21, size = 1402, normalized size = 51.93 result too large to display

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