3.1 Integrals 1 to 76

\(\int \genfrac {}{}{}{}{1-3 x^4}{(-2+x) (1+x^2)^2} \, dx\) [1]
\(\int \genfrac {}{}{}{}{-9-9 x+2 x^2}{-9 x+x^3} \, dx\) [2]
\(\int \genfrac {}{}{}{}{1+2 x^2+x^5}{-x+x^3} \, dx\) [3]
\(\int \genfrac {}{}{}{}{3+2 x^2}{(-1+x)^2 x} \, dx\) [4]
\(\int \genfrac {}{}{}{}{-1+2 x^2}{(-1+4 x) (1+x^2)} \, dx\) [5]
\(\int \genfrac {}{}{}{}{-3+2 x-3 x^2+x^3}{1+x^2} \, dx\) [6]
\(\int \genfrac {}{}{}{}{x+10 x^2+6 x^3+x^4}{10+6 x+x^2} \, dx\) [7]
\(\int \genfrac {}{}{}{}{1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx\) [8]
\(\int \genfrac {}{}{}{}{1+x^3}{-2+x} \, dx\) [9]
\(\int \genfrac {}{}{}{}{3 x-4 x^2+3 x^3}{1+x^2} \, dx\) [10]
\(\int \genfrac {}{}{}{}{5+3 x}{1-x-x^2+x^3} \, dx\) [11]
\(\int \genfrac {}{}{}{}{-1-x-x^3+x^4}{-x^2+x^3} \, dx\) [12]
\(\int \genfrac {}{}{}{}{2+x+x^2+x^3}{2+3 x^2+x^4} \, dx\) [13]
\(\int \genfrac {}{}{}{}{-4+8 x-4 x^2+4 x^3-x^4+x^5}{(2+x^2)^3} \, dx\) [14]
\(\int \genfrac {}{}{}{}{-1-3 x+x^2}{-2 x+x^2+x^3} \, dx\) [15]
\(\int \genfrac {}{}{}{}{3-x+3 x^2-2 x^3+x^4}{3 x-2 x^2+x^3} \, dx\) [16]
\(\int \genfrac {}{}{}{}{-1+x+x^3}{(1+x^2)^2} \, dx\) [17]
\(\int \genfrac {}{}{}{}{1+2 x-x^2+8 x^3+x^4}{(x+x^2) (1+x^3)} \, dx\) [18]
\(\int \genfrac {}{}{}{}{15-5 x+x^2+x^3}{(5+x^2) (3+2 x+x^2)} \, dx\) [19]
\(\int \genfrac {}{}{}{}{-3+25 x+23 x^2+32 x^3+15 x^4+7 x^5+x^6}{(1+x^2)^2 (2+x+x^2)^2} \, dx\) [20]
\(\int \genfrac {}{}{}{}{1}{(1+x^2) (4+x^2)} \, dx\) [21]
\(\int \genfrac {}{}{}{}{a+b x^3}{1+x^2} \, dx\) [22]
\(\int \genfrac {}{}{}{}{x+x^2}{(4+x) (-4+x^2)} \, dx\) [23]
\(\int \genfrac {}{}{}{}{4+x^2}{(1+x^2) (2+x^2)} \, dx\) [24]
\(\int \genfrac {}{}{}{}{5-4 x+3 x^2+x^4}{(-1+x)^2 (1+x^2)} \, dx\) [25]
\(\int \genfrac {}{}{}{}{1+x^4}{2+x^2} \, dx\) [26]
\(\int \genfrac {}{}{}{}{2+2 x+x^4}{x^4+x^5} \, dx\) [27]
\(\int \genfrac {}{}{}{}{-1-5 x+2 x^2}{2-x-2 x^2+x^3} \, dx\) [28]
\(\int \genfrac {}{}{}{}{2+x+x^3}{1+2 x^2+x^4} \, dx\) [29]
\(\int \genfrac {}{}{}{}{1+2 x+x^2+x^3}{1+2 x^2+x^4} \, dx\) [30]
\(\int \genfrac {}{}{}{}{3+4 x}{(1+x^2) (2+x^2)} \, dx\) [31]
\(\int \genfrac {}{}{}{}{2+x}{(1+x^2) (4+x^2)} \, dx\) [32]
\(\int \genfrac {}{}{}{}{2-x+x^3}{-7-6 x+x^2} \, dx\) [33]
\(\int \genfrac {}{}{}{}{-1+x^5}{-1+x^2} \, dx\) [34]
\(\int \genfrac {}{}{}{}{5+2 x-x^2+x^3}{1+x+x^2} \, dx\) [35]
\(\int \genfrac {}{}{}{}{-3+x-2 x^3+x^4}{10-8 x+2 x^2} \, dx\) [36]
\(\int \genfrac {}{}{}{}{1+2 x+3 x^2+x^3}{(-3+x) (-2+x) (-1+x)} \, dx\) [37]
\(\int \genfrac {}{}{}{}{2-7 x+x^2-x^3+x^4}{-24-14 x+x^2+x^3} \, dx\) [38]
\(\int \genfrac {}{}{}{}{2+x^2}{(-1+x)^2 x (1+x)} \, dx\) [39]
\(\int \genfrac {}{}{}{}{3+x^2+x^3}{(2+x^2)^2} \, dx\) [40]
\(\int \genfrac {}{}{}{}{-35+70 x-4 x^2+2 x^3}{(26-10 x+x^2) (17-2 x+x^2)} \, dx\) [41]
\(\int \genfrac {}{}{}{}{2+x^2}{(-5+x) (-3+x) (4+x)} \, dx\) [42]
\(\int \genfrac {}{}{}{}{x^4}{(-1+x) (2+x^2)} \, dx\) [43]
\(\int \genfrac {}{}{}{}{-1+7 x+2 x^2}{-1-x+x^2+x^3} \, dx\) [44]
\(\int \genfrac {}{}{}{}{1+2 x}{-1+3 x-3 x^2+x^3} \, dx\) [45]
\(\int \genfrac {}{}{}{}{5-5 x+7 x^2+x^3}{(-1+x)^2 (1+x)^3} \, dx\) [46]
\(\int \genfrac {}{}{}{}{1+3 x+3 x^2}{1+2 x+2 x^2+x^3} \, dx\) [47]
\(\int \genfrac {}{}{}{}{-1+2 x+x^2}{-2 x+3 x^2+2 x^3} \, dx\) [48]
\(\int \genfrac {}{}{}{}{1+4 x-2 x^2+x^4}{1-x-x^2+x^3} \, dx\) [49]
\(\int \genfrac {}{}{}{}{4-x+2 x^2}{4 x+x^3} \, dx\) [50]
\(\int \genfrac {}{}{}{}{1+x^2+x^3}{(-1+x) x (1+x^2)^3 (1+x+x^2)} \, dx\) [51]
\(\int \genfrac {}{}{}{}{1-3 x+2 x^2-x^3}{(1+x^2)^2} \, dx\) [52]
\(\int \genfrac {}{}{}{}{1-3 x+2 x^2-x^3}{x (1+x^2)^2} \, dx\) [53]
\(\int \genfrac {}{}{}{}{1-x-x^2+x^3+x^4}{-x+x^3} \, dx\) [54]
\(\int \genfrac {}{}{}{}{2-4 x^2+x^3}{(1+x^2) (2+x^2)} \, dx\) [55]
\(\int \genfrac {}{}{}{}{1+x^2+x^4}{(1+x^2) (4+x^2)^2} \, dx\) [56]
\(\int \genfrac {}{}{}{}{1+x^2+x^3}{2 x^2+x^3+x^4} \, dx\) [57]
\(\int \genfrac {}{}{}{}{1-12 x+x^2+x^3}{-12+x+x^2} \, dx\) [58]
\(\int \genfrac {}{}{}{}{-3+5 x+6 x^2}{-3 x+2 x^2+x^3} \, dx\) [59]
\(\int \genfrac {}{}{}{}{-2+3 x+5 x^2}{2 x^2+x^3} \, dx\) [60]
\(\int \genfrac {}{}{}{}{18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx\) [61]
\(\int \genfrac {}{}{}{}{1+x-2 x^2+x^3}{4+5 x^2+x^4} \, dx\) [62]
\(\int \genfrac {}{}{}{}{-32+5 x-27 x^2+4 x^3}{-70-299 x-286 x^2+50 x^3-13 x^4+30 x^5} \, dx\) [63]
\(\int \genfrac {}{}{}{}{8-13 x^2-7 x^3+12 x^5}{4-20 x+41 x^2-80 x^3+116 x^4-80 x^5+100 x^6} \, dx\) [64]
\(\int \genfrac {}{}{}{}{9+x^4}{x^2 (9+x^2)} \, dx\) [65]
\(\int \genfrac {}{}{}{}{2 x+x^4}{1+x^2} \, dx\) [66]
\(\int \genfrac {}{}{}{}{-x+x^3}{(-1+x)^2 (1+x^2)} \, dx\) [67]
\(\int \genfrac {}{}{}{}{2+5 x+3 x^2+2 x^3}{1+x+x^2} \, dx\) [68]
\(\int \genfrac {}{}{}{}{3-4 x-5 x^2+3 x^3}{x^3 (-1+x+x^2)} \, dx\) [69]
\(\int \genfrac {}{}{}{}{4+8 x+5 x^2+2 x^3}{(2+2 x+x^2)^2} \, dx\) [70]
\(\int \genfrac {}{}{}{}{(-1+x)^4 x^4}{1+x^2} \, dx\) [71]
\(\int \genfrac {}{}{}{}{-20 x+4 x^2}{9-10 x^2+x^4} \, dx\) [72]
\(\int \genfrac {}{}{}{}{-1+x+4 x^3}{(-1+x) x^2 (1+x^2)} \, dx\) [73]
\(\int \genfrac {}{}{}{}{1-3 x+2 x^2-4 x^3+x^4}{(1+x^2)^3} \, dx\) [74]
\(\int \genfrac {}{}{}{}{1-3 x+2 x^2-4 x^3+x^4}{1+3 x^2+3 x^4+x^6} \, dx\) [75]
\(\int \genfrac {}{}{}{}{1+x+2 x^2+2 x^3}{x^2+x^3+x^4} \, dx\) [76]