3.21 Integrals 2001 to 2100

\(\int \genfrac {}{}{}{}{25-100 e^{-1+4 x}+e^{e^{-1+4 x}} (-6+2 x+x^2)}{25+e^{e^{-1+4 x}} (-6+x^2)} \, dx\) [2001]
\(\int \genfrac {}{}{}{}{20 e^2 x^2-20 e^2 x^2 \log (x \log (4))+(3+3 x^2) \log ^2(x \log (4))}{3 x^2 \log ^2(x \log (4))} \, dx\) [2002]
\(\int (3072+1536 x+21504 \log (\log (4))) \, dx\) [2003]
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{x}{\log (x)}} \log (\genfrac {}{}{}{}{1}{2} (4-e^5+2 e^{\genfrac {}{}{}{}{x}{\log (x)}})) (-4+4 \log (x))}{2 e^{\genfrac {}{}{}{}{x}{\log (x)}} \log ^2(x)+(4-e^5) \log ^2(x)} \, dx\) [2004]
\(\int \genfrac {}{}{}{}{90-3 e^{\genfrac {}{}{}{}{1}{2} (-10-3 x)} x^2}{-90 x+2 e^{\genfrac {}{}{}{}{1}{2} (-10-3 x)} x^2} \, dx\) [2005]
\(\int \genfrac {}{}{}{}{-8+8 x}{e^{2 e^2} x+2 e^{e^2} x^2+x^3+(-2 e^{e^2} x-2 x^2) \log (x)+x \log ^2(x)} \, dx\) [2006]
\(\int \genfrac {}{}{}{}{-72 x+20 x^2-36 x^3+18 x \log (15 e^{\genfrac {}{}{}{}{1}{81} (25-90 x+81 x^2)})}{-576+432 \log (15 e^{\genfrac {}{}{}{}{1}{81} (25-90 x+81 x^2)})-108 \log ^2(15 e^{\genfrac {}{}{}{}{1}{81} (25-90 x+81 x^2)})+9 \log ^3(15 e^{\genfrac {}{}{}{}{1}{81} (25-90 x+81 x^2)})} \, dx\) [2007]
\(\int \genfrac {}{}{}{}{-16+8 x^2+e^{5/x} (-9+2 x^2)}{4 x^2+e^{5/x} x^2} \, dx\) [2008]
\(\int \genfrac {}{}{}{}{7+4 e^x+4 x}{36+4 e^x+7 x+2 x^2} \, dx\) [2009]
\(\int \genfrac {}{}{}{}{-6368+6352 x+e^{10+2 x} x+16 x^2+e^{5+x} (4-1596 x-4 x^2)+(16-16 x+4 e^{5+x} x) \log (x)}{8 x} \, dx\) [2010]
\(\int e^{-x} (e^{4 e^{-x} (4+e)} (16 e^x-256 x-64 e x)+e^x (4096+8192 x+4608 x^2+1024 x^3+80 x^4)+e^{3 e^{-x} (4+e)} (-3072 x-768 x^2+e^x (256+128 x)+e (-768 x-192 x^2))+e^{2 e^{-x} (4+e)} (-12288 x-6144 x^2-768 x^3+e^x (1536+1536 x+288 x^2)+e (-3072 x-1536 x^2-192 x^3))+e^{e^{-x} (4+e)} (-16384 x-12288 x^2-3072 x^3-256 x^4+e^x (4096+6144 x+2304 x^2+256 x^3)+e (-4096 x-3072 x^2-768 x^3-64 x^4))) \, dx\) [2011]
\(\int \genfrac {}{}{}{}{18 e^{3+2 x}+8 e^3 x^2+e^{3+x} (-16 x-10 x^2)}{e^{2 x}-2 e^x x+x^2} \, dx\) [2012]
\(\int (1+4 x+\sqrt {e} (-6 x-4 x^3)) \, dx\) [2013]
\(\int \genfrac {}{}{}{}{256+16 e-64 x+24 x^2-2 x^3}{(-4096+2944 x-704 x^2+52 x^3+x^4+e (-16+4 x)) \log ^2(\genfrac {}{}{}{}{1024+4 e-480 x+56 x^2+x^3}{64-32 x+4 x^2})} \, dx\) [2014]
\(\int \genfrac {}{}{}{}{-12+e^{\genfrac {}{}{}{}{1}{4} (40+\log (2 x))} x}{4 x^2} \, dx\) [2015]
\(\int 1125 e^{-2+225 x^5} x^4 \, dx\) [2016]
\(\int \genfrac {}{}{}{}{18-9 \log (x^2)+(-x+e^{e^2} x-9 \log (x^2)) \log (\genfrac {}{}{}{}{x-e^{e^2} x+9 \log (x^2)}{x})}{x^3-e^{e^2} x^3+9 x^2 \log (x^2)} \, dx\) [2017]
\(\int \genfrac {}{}{}{}{e^{e^{\genfrac {}{}{}{}{4+\log (4)}{x}}+\genfrac {}{}{}{}{4+\log (4)}{x}} (4+\log (4))}{4 x^2} \, dx\) [2018]
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{-2-x}{(-x+2 x^3) \log (x)}} (-2-x+4 x^2+2 x^3+(-2+12 x^2+4 x^3) \log (x))}{(x^2-4 x^4+4 x^6) \log ^2(x)} \, dx\) [2019]
\(\int e^{-e-x} (e^{7+x}+e^{e^{-x} x} (e^{2+x}+e^e (1-x)+e^2 (x-x^2))) \, dx\) [2020]
\(\int \genfrac {}{}{}{}{60+60 x+e^x (-16+24 x-9 x^2)+e^{x+e^x x} (16-8 x-15 x^2+9 x^3+e^x (16+8 x-23 x^2-6 x^3+9 x^4))+e^x (-16+8 x+15 x^2-9 x^3) \log (1+x)}{16-8 x-15 x^2+9 x^3} \, dx\) [2021]
\(\int \genfrac {}{}{}{}{16+4 e^{2 x}+(-36-72 x-24 x^2) \log (3)+e^x (-16+(18+18 x-6 x^2-4 x^3) \log (3)-4 \log (4))+(8+(-9-18 x-6 x^2) \log (3)) \log (4)+\log ^2(4)}{16+4 e^{2 x}+e^x (-16-4 \log (4))+8 \log (4)+\log ^2(4)} \, dx\) [2022]
\(\int \genfrac {}{}{}{}{150-x+e^{4-3 x^2+x^4} (-150+x+900 x^2-600 x^4)+(-50+e^{4-3 x^2+x^4} (50-300 x^2+200 x^4)) \log (-x+e^{4-3 x^2+x^4} x)}{-x+e^{4-3 x^2+x^4} x} \, dx\) [2023]
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{6 x+e^4 (6 x-24 x^2-x^4)+(x+e^4 (x-4 x^2)) \log (5)}{6+\log (5)}} (6+e^4 (6-48 x-4 x^3)+(1+e^4 (1-8 x)) \log (5))}{6+\log (5)} \, dx\) [2024]
\(\int \genfrac {}{}{}{}{-16 x+x^3+(16+x) \log (\genfrac {}{}{}{}{4}{\log (2)})}{x^3} \, dx\) [2025]
\(\int (2+e^{e^{e^{4+x}}+x} (1+e^{4+e^{4+x}+x})-\log (4)) \, dx\) [2026]
\(\int \genfrac {}{}{}{}{-900+9 x+1209 x \log (x)-400 x^2 \log ^2(x)}{450 x-600 x^2 \log (x)+200 x^3 \log ^2(x)} \, dx\) [2027]
\(\int -\genfrac {}{}{}{}{2 \log (x)}{e^8 x} \, dx\) [2028]
\(\int \genfrac {}{}{}{}{15 e^{5+\genfrac {}{}{}{}{x}{3}}+e^5 (6+2 x)}{(-6 x+e^{x/3} (-15 x+3 x^2)) \log (\genfrac {}{}{}{}{e^{-x/3} (2+e^{x/3} (5-x))}{x})} \, dx\) [2029]
\(\int \genfrac {}{}{}{}{-\log (4)+(x \log (4)+e^{e^8+2 e^4 x+x^2} (2 e^4 x+2 x^2) \log (4)) \log (x)}{(16 x+e^{2 e^8+4 e^4 x+2 x^2} x-8 x^2+x^3+e^{e^8+2 e^4 x+x^2} (-8 x+2 x^2)) \log (x)+(8 x-2 e^{e^8+2 e^4 x+x^2} x-2 x^2) \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))} \, dx\) [2030]
\(\int \genfrac {}{}{}{}{-4 e^{4/x}-x^2-50 e^{2 e^x+x} x^2}{5 x^2} \, dx\) [2031]
\(\int \genfrac {}{}{}{}{1+4 x-16 x^2-16 x^3+(-8 x-12 x^2) \log (x)+(-x+4 x^2+4 x^3+(2 x+3 x^2) \log (x)) \log (2 x)+(-4+\log (2 x)) \log (-4+\log (2 x))}{-4+\log (2 x)} \, dx\) [2032]
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{15 x}{12+58 x+3 x^2+3 x^3}} (180-45 x^2-90 x^3)}{144+1392 x+3436 x^2+420 x^3+357 x^4+18 x^5+9 x^6} \, dx\) [2033]
\(\int \genfrac {}{}{}{}{e^5 (-x-3 x^3)+3 e^5 x^2 \log (5)+(e^5 (-5+x-45 x^2+9 x^3)+e^5 (30 x-6 x^2) \log (5)) \log (5-x)}{(-15+3 x) \log ^2(5-x)} \, dx\) [2034]
\(\int \genfrac {}{}{}{}{1+e^{4+x}}{e^4} \, dx\) [2035]
\(\int \genfrac {}{}{}{}{-250 e^{3 x} x-150 e^{2 x} x^2-2 x^4+e^x (-30 x^3+e^{\genfrac {}{}{}{}{1+4 e^2}{e^2}} (250 x-250 x^2) \log (2))}{125 e^{\genfrac {}{}{}{}{1+4 e^2}{e^2}+3 x}+75 e^{\genfrac {}{}{}{}{1+4 e^2}{e^2}+2 x} x+15 e^{\genfrac {}{}{}{}{1+4 e^2}{e^2}+x} x^2+e^{\genfrac {}{}{}{}{1+4 e^2}{e^2}} x^3} \, dx\) [2036]
\(\int \genfrac {}{}{}{}{-1-e^{4+x}}{e^{4+x}+x-e^4 (i \pi +\log (16))} \, dx\) [2037]
\(\int \genfrac {}{}{}{}{e^{-6-2 x} (-4-8 x+e^{3+x} (64+64 x-4 x^2)+e^{6+2 x} (-256-16 e^{25}+x^2))}{16 x^2} \, dx\) [2038]
\(\int \genfrac {}{}{}{}{e^{-\genfrac {}{}{}{}{5}{-2-x+16 x^2+8 x^3+x^4}} (4-x+97 x^2+56 x^3+256 x^4+254 x^5+96 x^6+16 x^7+x^8)}{(4+4 x-63 x^2-64 x^3+236 x^4+254 x^5+96 x^6+16 x^7+x^8) \log (2)} \, dx\) [2039]
\(\int \genfrac {}{}{}{}{-400+100 x-200 x^2-121 x^3-37 x^4-48 x^5+3 x^6-6 x^7}{-400 x-200 x^3+48 x^4-25 x^5+24 x^6+3 x^8} \, dx\) [2040]
\(\int \genfrac {}{}{}{}{-60 x+15 x^2+e^{-e^4+x} (30 x^2+15 x^3-15 x^4)+e^x (-3+x+e^{-e^4+x} (2+x-x^2))}{e^x (-2+x)-30 x^2+15 x^3} \, dx\) [2041]
\(\int \genfrac {}{}{}{}{4+27 x^4-x^8+(108 x^4-8 x^8) \log (x)}{(-4 x-27 x^5+x^9) \log (x)} \, dx\) [2042]
\(\int \genfrac {}{}{}{}{-28512 x^2+4032 x^3-224 x^4+(-297432 x+77112 x^2-5256 x^3+104 x^4) \log (3-x)+(-708588+314928 x-29160 x^2+1008 x^3-12 x^4) \log ^2(3-x)}{59049 x^4-26244 x^5+2430 x^6-84 x^7+x^8} \, dx\) [2043]
\(\int \genfrac {}{}{}{}{4 x^2+e^{2 e^x-2 x-2 e^5 x} (-2 x-2 e^5 x+2 e^x x)}{x} \, dx\) [2044]
\(\int \genfrac {}{}{}{}{20-4 x+225 x^2-90 x^3+9 x^4+20 \log (2 x)}{75-30 x+3 x^2} \, dx\) [2045]
\(\int \genfrac {}{}{}{}{1+e^x (1+x)+\log (i \pi +\log (-2+e^8))}{x+e^x x+x \log (i \pi +\log (-2+e^8))} \, dx\) [2046]
\(\int \genfrac {}{}{}{}{-8 x \log (9-x) \log (x)+(-36+4 x+(36-4 x) \log ^2(9-x)+(-36+4 x+(36-4 x) \log ^2(9-x)) \log (x)) \log (-1+\log ^2(9-x))}{9-x+(-9+x) \log ^2(9-x)} \, dx\) [2047]
\(\int \genfrac {}{}{}{}{e^{-x} (48-48 x+(-48+48 x-48 x^2) \log (x)+(-32 x+32 x^2-16 x^3+e^2 (-16+16 x-16 x^2)) \log ^2(x))}{(15-30 x+15 x^2) \log ^2(x)} \, dx\) [2048]
\(\int \genfrac {}{}{}{}{1}{8} (1728 x^5-96 x^3 \log (\log (9))+x \log ^2(\log (9))) \, dx\) [2049]
\(\int \genfrac {}{}{}{}{e^2 (2+e)}{-e^2+6 e^{2 x+e x}} \, dx\) [2050]
\(\int \genfrac {}{}{}{}{125 x-425 x^2+315 x^3+81 x^4+e^x (-25 x+90 x^2-81 x^3)+e^{3-e^x} (25-90 x+e^x (-5+48 x-54 x^2)+e^{2 x} (-5 x+9 x^2))+e^x (-25 x^2+90 x^3-81 x^4) \log (x)}{25 x^2-90 x^3+81 x^4} \, dx\) [2051]
\(\int \genfrac {}{}{}{}{(-384 x-768 x^2-384 x^3) \log (x)+(-384 x-1664 x^2-2304 x^3-1536 x^4-512 x^5) \log ^2(x)+(512 x^2+1536 x^3+1536 x^4+512 x^5) \log (x) \log (2 x+e^5 x)}{-27+(108 x+108 x^2) \log (2 x+e^5 x)+(-144 x^2-288 x^3-144 x^4) \log ^2(2 x+e^5 x)+(64 x^3+192 x^4+192 x^5+64 x^6) \log ^3(2 x+e^5 x)} \, dx\) [2052]
\(\int \genfrac {}{}{}{}{-x+x^3+(1-x^2+5 x^3-x^4) \log (x)+(1-x^2) \log ^2(x)}{(-x^2+x^4) \log (x)} \, dx\) [2053]
\(\int \genfrac {}{}{}{}{-3 e^2 \log (5)+e^{e^x+\genfrac {}{}{}{}{1}{3} e^{e^x} (-3-x)} (e^2 \log (5)+e^{2+x} (3+x) \log (5))}{75+3 e^{\genfrac {}{}{}{}{2}{3} e^{e^x} (-3-x)}+30 x+3 x^2+e^{\genfrac {}{}{}{}{1}{3} e^{e^x} (-3-x)} (30+6 x)} \, dx\) [2054]
\(\int \genfrac {}{}{}{}{\log ^{\genfrac {}{}{}{}{2 x}{e^4 (-8 x-2 x^2)+(5+2 x) \log (\log (6))}}(6) (4 e^4 x^2 \log (\log (6))+10 \log ^2(\log (6)))}{e^8 (64 x^2+32 x^3+4 x^4)+e^4 (-80 x-52 x^2-8 x^3) \log (\log (6))+(25+20 x+4 x^2) \log ^2(\log (6))} \, dx\) [2055]
\(\int \genfrac {}{}{}{}{2-3 x}{x} \, dx\) [2056]
\(\int \genfrac {}{}{}{}{x+(4+5 x+x^2) \log (\genfrac {}{}{}{}{1}{8} (-4-x))}{(4 x+x^2) \log (\genfrac {}{}{}{}{1}{8} (-4-x))} \, dx\) [2057]
\(\int \genfrac {}{}{}{}{-16588800 x-30965760 x^3-24883200 x^5-10936320 x^7-2744320 x^9-368640 x^{11}-20480 x^{13}+e^4 (3110400 x+10414080 x^3+12960000 x^5+8542720 x^7+3310080 x^9+760320 x^{11}+96000 x^{13}+5120 x^{15})}{19683+126846 x^2+331533 x^4+457552 x^6+369117 x^8+184710 x^{10}+58563 x^{12}+11532 x^{14}+1296 x^{16}+64 x^{18}} \, dx\) [2058]
\(\int \genfrac {}{}{}{}{4+e^5 (-9-8 x)+4 x+e^{5+x} (2+2 x-2 x^2)+e^5 (1+x) \log (2)+(-e^5 x-2 e^{5+x} x) \log (x)}{80 x+20 e^{10+2 x} x+e^5 (-360 x+40 x^2)+e^{10} (405 x-90 x^2+5 x^3)+(40 e^5 x+e^{10} (-90 x+10 x^2)) \log (2)+5 e^{10} x \log ^2(2)+e^x (80 e^5 x+e^{10} (-180 x+20 x^2)+20 e^{10} x \log (2))} \, dx\) [2059]
\(\int \genfrac {}{}{}{}{1}{5} (e^{x/5} (20+14 x)+e^{x/5} (10 x+x^2) \log (2 x^2)) \, dx\) [2060]
\(\int \genfrac {}{}{}{}{4}{3 e^5} \, dx\) [2061]
\(\int \genfrac {}{}{}{}{5+e+e^{-2+2 x} (5+e)-120 x^2+e^{-1+x} (10+2 e-120 x^2+40 x^3)}{1+2 e^{-1+x}+e^{-2+2 x}} \, dx\) [2062]
\(\int \genfrac {}{}{}{}{-6 x^3+2 x^7+(4 x^4+8 x^6+4 x^8) \log (5)+(6-8 x^4+2 x^8) \log (5) \log (3-x^4)}{-3 x^3+x^7} \, dx\) [2063]
\(\int \genfrac {}{}{}{}{78-48 x+390 x^2+(-48 x+5004 x^2-3072 x^3+384 x^4) \log (x)+(16224 x^2-19968 x^3+8640 x^4-1536 x^5+96 x^6) \log ^2(x)}{4 x+(52 x-32 x^2+4 x^3) \log (x)+(169 x-208 x^2+90 x^3-16 x^4+x^5) \log ^2(x)} \, dx\) [2064]
\(\int \genfrac {}{}{}{}{x^2+e^{e^{12}+\genfrac {}{}{}{}{17+x}{x}} (425+170 x+7 x^2-2 x^3)}{x^2} \, dx\) [2065]
\(\int \genfrac {}{}{}{}{75-5 x+18 x^2-5 x^3+(-15+3 x-4 x^2+x^3) \log (x)}{25 x^2-5 x^3+(-5 x^2+x^3) \log (x)} \, dx\) [2066]
\(\int \genfrac {}{}{}{}{e^{5 e^{-\genfrac {}{}{}{}{-2-3 x+x^2}{-3+x}}} (-275+150 x-25 x^2)}{e^{5 e^{-\genfrac {}{}{}{}{-2-3 x+x^2}{-3+x}}+\genfrac {}{}{}{}{-2-3 x+x^2}{-3+x}} (9-6 x+x^2)+e^{\genfrac {}{}{}{}{-2-3 x+x^2}{-3+x}} (63-42 x+7 x^2)} \, dx\) [2067]
\(\int \genfrac {}{}{}{}{-x+2 x^3+e^x (-1+2 x^2)+(e^x+x) \log (x)+(6 x^3+e^x (4 x^2+2 x^3)+(e^x (-2-x)-3 x) \log (x)) \log (\genfrac {}{}{}{}{x}{-10 x^2+5 \log (x)})}{-6 e^{2 x} x^5-12 e^x x^6-6 x^7+(3 e^{2 x} x^3+6 e^x x^4+3 x^5) \log (x)} \, dx\) [2068]
\(\int \genfrac {}{}{}{}{x^3-4 e x^3-4 x^4+e^{2 e^{-x^2+x \log (x)}} (4+e^{-x^2+x \log (x)} (-4 x+8 x^2-4 x \log (x)))+e^{e^{-x^2+x \log (x)}} (4 e x+e^{-x^2+x \log (x)} (-4 x^3+8 x^4+e (-4 x^2+8 x^3)+(-4 e x^2-4 x^3) \log (x)))}{2 x^3} \, dx\) [2069]
\(\int \genfrac {}{}{}{}{\log ^{\genfrac {}{}{}{}{2}{x}}(\genfrac {}{}{}{}{1}{9} x \log ^2(e^{-x} x)) (32-32 x+16 \log (e^{-x} x)-16 \log (e^{-x} x) \log (\genfrac {}{}{}{}{1}{9} x \log ^2(e^{-x} x)) \log (\log (\genfrac {}{}{}{}{1}{9} x \log ^2(e^{-x} x))))+\log ^{\genfrac {}{}{}{}{4}{x}}(\genfrac {}{}{}{}{1}{9} x \log ^2(e^{-x} x)) (32-32 x+16 \log (e^{-x} x)-16 \log (e^{-x} x) \log (\genfrac {}{}{}{}{1}{9} x \log ^2(e^{-x} x)) \log (\log (\genfrac {}{}{}{}{1}{9} x \log ^2(e^{-x} x))))}{x^2 \log (e^{-x} x) \log (\genfrac {}{}{}{}{1}{9} x \log ^2(e^{-x} x))} \, dx\) [2070]
\(\int \genfrac {}{}{}{}{70+40 x-30 x^2+e^x (15 x-5 x^2)+e^x (30+30 x-5 x^2-5 x^3) \log (2+2 x)}{49 x^3+21 x^4-24 x^5+4 x^6+e^x (42 x^3+16 x^4-22 x^5+4 x^6) \log (2+2 x)+e^{2 x} (9 x^3+3 x^4-5 x^5+x^6) \log ^2(2+2 x)} \, dx\) [2071]
\(\int \genfrac {}{}{}{}{51 x+17 e^{2 e^2} x}{-8+12 x-6 x^2+x^3} \, dx\) [2072]
\(\int \genfrac {}{}{}{}{1}{320} e^{-x} (-10000+10400 x+(400 x-204 x^2) \log (x^2)+(-3 x^2+x^3) \log ^2(x^2)) \, dx\) [2073]
\(\int \genfrac {}{}{}{}{-400-105 x+(-200-50 x) \log (-4-x)+(-80-20 x+(-40-10 x) \log (-4-x)) \log (2+\log (-4-x))}{200 x^3+50 x^4+(100 x^3+25 x^4) \log (-4-x)+(80 x^3+20 x^4+(40 x^3+10 x^4) \log (-4-x)) \log (2+\log (-4-x))+(8 x^3+2 x^4+(4 x^3+x^4) \log (-4-x)) \log ^2(2+\log (-4-x))} \, dx\) [2074]
\(\int (2 e^{2 e^x+x}+e^{2 x} (4 x^3+2 x^4)-72 x^2 \log (4)+96 x^5 \log ^2(4)+e^x (12 x+6 x^2+(-40 x^4-8 x^5) \log (4))+e^{e^x} (-2 e^{2 x} x^2+24 x^2 \log (4)+e^x (-6-4 x-2 x^2+8 x^3 \log (4)))) \, dx\) [2075]
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{25+10 x^3 \log (x)+(-5 x^4+x^6) \log ^2(x)}{x^4 \log ^2(x)}} (-50+(-100-10 x^3) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x))}{(-100 x^5 \log ^3(x)+20 e^{\genfrac {}{}{}{}{25+10 x^3 \log (x)+(-5 x^4+x^6) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log (5-e^{\genfrac {}{}{}{}{25+10 x^3 \log (x)+(-5 x^4+x^6) \log ^2(x)}{x^4 \log ^2(x)}}) (-5 x^5 \log ^3(x)+e^{\genfrac {}{}{}{}{25+10 x^3 \log (x)+(-5 x^4+x^6) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x))) \log (20+\log (5-e^{\genfrac {}{}{}{}{25+10 x^3 \log (x)+(-5 x^4+x^6) \log ^2(x)}{x^4 \log ^2(x)}}))} \, dx\) [2076]
\(\int \genfrac {}{}{}{}{-3 e^{5+x}-3 x+(2 x+e^{5+x} (1+x)) \log (2 x^3)}{e^{10+2 x} x^2+2 e^{5+x} x^3+x^4} \, dx\) [2077]
\(\int \genfrac {}{}{}{}{1}{4} ((-400 x-800 x^2-400 x^3) \log (-\genfrac {}{}{}{}{12}{x})+(400 x+1200 x^2+800 x^3) \log ^2(-\genfrac {}{}{}{}{12}{x})+(-x^3-4 x^4-6 x^5-4 x^6-x^7) \log ^3(-\genfrac {}{}{}{}{12}{x})+(x^3+5 x^4+9 x^5+7 x^6+2 x^7) \log ^4(-\genfrac {}{}{}{}{12}{x})) \, dx\) [2078]
\(\int \genfrac {}{}{}{}{92 e^{\genfrac {}{}{}{}{30 x^2}{23}}+e^{\genfrac {}{}{}{}{30 x^2}{23}} (-92+240 x^2) \log (4 x)}{23 x^2} \, dx\) [2079]
\(\int \genfrac {}{}{}{}{4+(320+60 x-5 x^2) \log ^2(\genfrac {}{}{}{}{4+x}{x})+\log ^2(2 x) (4+(-20 x-5 x^2) \log ^2(\genfrac {}{}{}{}{4+x}{x}))+\log (2 x) (-8+(40 x+10 x^2) \log ^2(\genfrac {}{}{}{}{4+x}{x}))}{(20 x+5 x^2) \log ^2(\genfrac {}{}{}{}{4+x}{x})+(-40 x-10 x^2) \log (2 x) \log ^2(\genfrac {}{}{}{}{4+x}{x})+(20 x+5 x^2) \log ^2(2 x) \log ^2(\genfrac {}{}{}{}{4+x}{x})} \, dx\) [2080]
\(\int \genfrac {}{}{}{}{e^{\genfrac {}{}{}{}{1}{2} (-2 x-x^2)} (3 x^2+3 x^3+45 e^{1+\genfrac {}{}{}{}{1}{2} (2 x+x^2)} \log (3))}{5 x^2} \, dx\) [2081]
\(\int \genfrac {}{}{}{}{2-x-20 x^2+25 x^3+25 e^{2 x} x^3+e^x (5 x+20 x^2-50 x^3)+(5 x+e^x (-5 x-5 x^2)) \log (x)}{4 x-20 x^2+25 x^3+25 e^{2 x} x^3+e^x (20 x^2-50 x^3)} \, dx\) [2082]
\(\int \genfrac {}{}{}{}{240 x-24 x \log (4)}{16 x^4-24 x^2 \log (5)+9 \log ^2(5)} \, dx\) [2083]
\(\int \genfrac {}{}{}{}{256-10000 x^5+(-256+10000 x^5) \log (x)+(-256-40000 x^5) \log (x) \log (\genfrac {}{}{}{}{5 x}{\log (x)})}{(256-20000 x^5+390625 x^{10}) \log (x)} \, dx\) [2084]
\(\int \genfrac {}{}{}{}{15-21 x+21 x \log (x)}{x \log ^2(x)} \, dx\) [2085]
\(\int \genfrac {}{}{}{}{-270-232 x-24 x^2+4 x^3+1800 x^4+2520 x^5+1242 x^6+252 x^7+18 x^8}{90 x+53 x^2+2 x^3-x^4+1800 x^5+2520 x^6+1242 x^7+252 x^8+18 x^9} \, dx\) [2086]
\(\int \genfrac {}{}{}{}{5+e^{5/4} (-240+15 x^2)}{e^{17/4} x^2 \log (5)} \, dx\) [2087]
\(\int (-3-3 x+9 x^2+2 x \log (x)) \, dx\) [2088]
\(\int \genfrac {}{}{}{}{1}{18} e^{\genfrac {}{}{}{}{1}{18} (-288+7 x+3 x^2)} (7+6 x) \, dx\) [2089]
\(\int \genfrac {}{}{}{}{21+e^x (7 x+7 x^2+(4+4 x) \log (2))}{7 x+4 \log (2)} \, dx\) [2090]
\(\int \genfrac {}{}{}{}{5-20 x-20 x \log (x)+e^x x (2 x^2+5 x^3+4 x^3 \log (x))}{-20 x+4 e^x x^4} \, dx\) [2091]
\(\int \genfrac {}{}{}{}{36-120 e^{2 x}+100 e^{4 x}+(9+e^{2 x} (-15+30 x)) (i \pi +\log (-5+5 e^3))}{36-120 e^{2 x}+100 e^{4 x}} \, dx\) [2092]
\(\int \genfrac {}{}{}{}{-4 x^2+e^{2 x^2} (6-8 x^2)}{x^4} \, dx\) [2093]
\(\int \genfrac {}{}{}{}{3735552+6291456 x-638976 x^2-5160960 x^3-815616 x^4+1257472 x^5+97216 x^6+232352 x^7+171568 x^8-233522 x^9-67735 x^{10}+68780 x^{11}+7886 x^{12}-10118 x^{13}+276 x^{14}+624 x^{15}-87 x^{16}+(2621440+4456448 x-458752 x^2-3784704 x^3-626176 x^4+1043456 x^5+130368 x^6+76992 x^7+91442 x^8-135460 x^9-40964 x^{10}+42400 x^{11}+4938 x^{12}-6396 x^{13}+176 x^{14}+400 x^{15}-56 x^{16}) \log (x)+(458752+786432 x-81920 x^2-688128 x^3-118272 x^4+207872 x^5+32704 x^6+11423 x^8-19248 x^9-6132 x^{10}+6496 x^{11}+770 x^{12}-1008 x^{13}+28 x^{14}+64 x^{15}-9 x^{16}) \log ^2(x)}{x^8} \, dx\) [2094]
\(\int \genfrac {}{}{}{}{188-95 x-96 x^2-72 x^3+9 x^4+16 x^5-3 x^6+(4-2 x) \log (x)}{16 x^2-8 x^3+x^4} \, dx\) [2095]
\(\int \genfrac {}{}{}{}{e^{50} (-8-4 x)-18 x-16 x^2-4 x^3+e^{25} (-16-24 x-8 x^2)+(e^{50} (-4-2 x)-8 x-8 x^2-2 x^3+e^{25} (-8-12 x-4 x^2)) \log (\genfrac {}{}{}{}{20+10 e^{25}+10 x}{e^{25}+x})+(2 e^{50}+4 x+2 x^2+e^{25} (4+4 x)+(e^{50}+2 x+x^2+e^{25} (2+2 x)) \log (\genfrac {}{}{}{}{20+10 e^{25}+10 x}{e^{25}+x})) \log (4 x+2 x \log (\genfrac {}{}{}{}{20+10 e^{25}+10 x}{e^{25}+x}))}{2 e^{50}+4 x+2 x^2+e^{25} (4+4 x)+(e^{50}+2 x+x^2+e^{25} (2+2 x)) \log (\genfrac {}{}{}{}{20+10 e^{25}+10 x}{e^{25}+x})} \, dx\) [2096]
\(\int \genfrac {}{}{}{}{-4 x^2+x^2 (i \pi +\log (3))}{60 \log ^2(5)} \, dx\) [2097]
\(\int \genfrac {}{}{}{}{2000-2000 x+(-x+x^2)^{\genfrac {}{}{}{}{1}{400} (-400 x^2+x^3)} (400 x-801 x^2+2 x^3+(800 x-803 x^2+3 x^3) \log (-x+x^2))}{-2000+2000 x} \, dx\) [2098]
\(\int -\genfrac {}{}{}{}{3 e^{e^2} \log (2) \log (5)}{9 e^{2 e^2} x^2+6 e^{e^2} x \log (2)+\log ^2(2)} \, dx\) [2099]
\(\int \genfrac {}{}{}{}{4+8 x+(8 x+4 x^2) \log (x)+(-2+(-2-2 x) \log (x)) \log (\genfrac {}{}{}{}{1}{1+(2+2 x) \log (x)+(1+2 x+x^2) \log ^2(x)})}{5 x^4+(5 x^4+5 x^5) \log (x)+(-10 x^3+(-10 x^3-10 x^4) \log (x)) \log (\genfrac {}{}{}{}{1}{1+(2+2 x) \log (x)+(1+2 x+x^2) \log ^2(x)})+(5 x^2+(5 x^2+5 x^3) \log (x)) \log ^2(\genfrac {}{}{}{}{1}{1+(2+2 x) \log (x)+(1+2 x+x^2) \log ^2(x)})} \, dx\) [2100]