3.1.1 \(\int \frac {(A+B x) (a+b x+c x^2)}{d+f x^2} \, dx\)
  3.1.2 \(\int \frac {(A+B x) (a+b x+c x^2)^2}{d+f x^2} \, dx\)
  3.1.3 \(\int \frac {(A+B x) (a+b x+c x^2)^3}{d+f x^2} \, dx\)
  3.1.4 \(\int \frac {A+B x}{(a+b x+c x^2) (d+f x^2)} \, dx\)
  3.1.5 \(\int \frac {A+B x}{(a+b x+c x^2)^2 (d+f x^2)} \, dx\)
  3.1.6 \(\int \frac {(A+B x) \sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
  3.1.7 \(\int \frac {A+B x}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
  3.1.8 \(\int \frac {A+B x}{(a+b x+c x^2)^{3/2} (d-f x^2)} \, dx\)
  3.1.9 \(\int \frac {A+B x}{(a+b x+c x^2)^{5/2} (d-f x^2)} \, dx\)
  3.1.10 \(\int \frac {1+2 x}{(-1+x^2) \sqrt {-1+x+x^2}} \, dx\)
  3.1.11 \(\int \frac {1+2 x}{(1+x^2) \sqrt {-1+x+x^2}} \, dx\)
  3.1.12 \(\int \frac {a-c+b x}{(1+x^2) \sqrt {a+b x+c x^2}} \, dx\)
  3.1.13 \(\int \frac {(A+B x) (a+b x+c x^2)}{d+e x+f x^2} \, dx\)
  3.1.14 \(\int \frac {(A+B x) (a+b x+c x^2)^2}{d+e x+f x^2} \, dx\)
  3.1.15 \(\int \frac {A+B x}{(a+b x+c x^2) (d+e x+f x^2)} \, dx\)
  3.1.16 \(\int \frac {A+B x}{(a+b x+c x^2)^2 (d+e x+f x^2)} \, dx\)
  3.1.17 \(\int \frac {g+h x}{(a+b x+c x^2) (a d+b d x+c d x^2)^2} \, dx\)
  3.1.18 \(\int \frac {g+h x}{(a+b x+c x^2)^2 (a d+b d x+c d x^2)} \, dx\)
  3.1.19 \(\int \frac {(A+B x) \sqrt {a+b x+c x^2}}{d+e x+f x^2} \, dx\)
  3.1.20 \(\int \frac {(A+B x) (a+b x+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
  3.1.21 \(\int \frac {A+B x}{(a+b x+c x^2) \sqrt {d+e x+f x^2}} \, dx\)
  3.1.22 \(\int \frac {A+B x}{(a+c x^2) \sqrt {d+e x+f x^2}} \, dx\)
  3.1.23 \(\int \frac {A+B x}{(a+b x+c x^2) \sqrt {d+f x^2}} \, dx\)
  3.1.24 \(\int \frac {A+B x}{(a+c x^2) \sqrt {d+f x^2}} \, dx\)
  3.1.25 \(\int \frac {2+x}{(2+4 x-3 x^2) \sqrt {1+3 x-2 x^2}} \, dx\)
  3.1.26 \(\int \frac {2+x}{(2+4 x-3 x^2) (1+3 x-2 x^2)^{3/2}} \, dx\)
  3.1.27 \(\int \frac {2+x}{(2+4 x-3 x^2) (1+3 x-2 x^2)^{5/2}} \, dx\)
  3.1.28 \(\int \frac {2+x}{(2+4 x-3 x^2) \sqrt {1+3 x+2 x^2}} \, dx\)
  3.1.29 \(\int \frac {2+x}{(2+4 x-3 x^2) (1+3 x+2 x^2)^{3/2}} \, dx\)
  3.1.30 \(\int \frac {2+x}{(2+4 x-3 x^2) (1+3 x+2 x^2)^{5/2}} \, dx\)
  3.1.31 \(\int \frac {1+x}{(4+2 x+x^2) \sqrt {5+2 x+x^2}} \, dx\)
  3.1.32 \(\int \frac {4+x}{(4+2 x+x^2) \sqrt {5+2 x+x^2}} \, dx\)
  3.1.33 \(\int \frac {1+2 x}{(3+x+x^2) \sqrt {5+x+x^2}} \, dx\)
  3.1.34 \(\int \frac {x}{(3+x+x^2) \sqrt {5+x+x^2}} \, dx\)
  3.1.35 \(\int \frac {A+B x}{\sqrt {d+e x+f x^2} (a e+b e x+b f x^2)^2} \, dx\)
  3.1.36 \(\int \frac {(g+h x) \sqrt {a+b x+c x^2}}{(a d+b d x+c d x^2)^2} \, dx\)
  3.1.37 \(\int \frac {3+2 x}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
  3.1.38 \(\int \frac {3+4 x}{\sqrt {-3-4 x-x^2} (3+4 x+2 x^2)} \, dx\)
  3.1.39 \(\int \frac {(g+h x) \sqrt {a+b x+c x^2}}{(a d+b d x+c d x^2)^{3/2}} \, dx\)
  3.1.40 \(\int x^2 \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2} \, dx\)
  3.1.41 \(\int x \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2} \, dx\)
  3.1.42 \(\int \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2} \, dx\)
  3.1.43 \(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2}}{x} \, dx\)
  3.1.44 \(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2}}{x^2} \, dx\)
  3.1.45 \(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+d x^2}}{x^3} \, dx\)
  3.1.46 \(\int x^2 \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2} \, dx\)
  3.1.47 \(\int x \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2} \, dx\)
  3.1.48 \(\int \sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2} \, dx\)
  3.1.49 \(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2}}{x} \, dx\)
  3.1.50 \(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2}}{x^2} \, dx\)
  3.1.51 \(\int \frac {\sqrt {a^2+2 a b x+b^2 x^2} \sqrt {c+e x+d x^2}}{x^3} \, dx\)
  3.1.52 \(\int \frac {x^2 \sqrt {a+c x^2}}{d+e x+f x^2} \, dx\)
  3.1.53 \(\int \frac {x \sqrt {a+c x^2}}{d+e x+f x^2} \, dx\)
  3.1.54 \(\int \frac {\sqrt {a+c x^2}}{d+e x+f x^2} \, dx\)
  3.1.55 \(\int \frac {\sqrt {a+c x^2}}{x (d+e x+f x^2)} \, dx\)
  3.1.56 \(\int \frac {\sqrt {a+c x^2}}{x^2 (d+e x+f x^2)} \, dx\)
  3.1.57 \(\int \frac {\sqrt {a+c x^2}}{x^3 (d+e x+f x^2)} \, dx\)
  3.1.58 \(\int \frac {x^2 (a+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
  3.1.59 \(\int \frac {x (a+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
  3.1.60 \(\int \frac {(a+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
  3.1.61 \(\int \frac {(a+c x^2)^{3/2}}{x (d+e x+f x^2)} \, dx\)
  3.1.62 \(\int \frac {(a+c x^2)^{3/2}}{x^2 (d+e x+f x^2)} \, dx\)
  3.1.63 \(\int \frac {(a+c x^2)^{3/2}}{x^3 (d+e x+f x^2)} \, dx\)
  3.1.64 \(\int \frac {x^3}{\sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
  3.1.65 \(\int \frac {x^2}{\sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
  3.1.66 \(\int \frac {x}{\sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
  3.1.67 \(\int \frac {1}{\sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
  3.1.68 \(\int \frac {1}{x \sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
  3.1.69 \(\int \frac {1}{x^2 \sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
  3.1.70 \(\int \frac {1}{x^3 \sqrt {a+c x^2} (d+e x+f x^2)} \, dx\)
  3.1.71 \(\int \frac {x^3}{(a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
  3.1.72 \(\int \frac {x^2}{(a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
  3.1.73 \(\int \frac {x}{(a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
  3.1.74 \(\int \frac {1}{(a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
  3.1.75 \(\int \frac {1}{x (a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
  3.1.76 \(\int \frac {1}{x^2 (a+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
  3.1.77 \(\int \frac {x^3 \sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
  3.1.78 \(\int \frac {x^2 \sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
  3.1.79 \(\int \frac {x \sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
  3.1.80 \(\int \frac {\sqrt {a+b x+c x^2}}{d-f x^2} \, dx\)
  3.1.81 \(\int \frac {\sqrt {a+b x+c x^2}}{x (d-f x^2)} \, dx\)
  3.1.82 \(\int \frac {\sqrt {a+b x+c x^2}}{x^2 (d-f x^2)} \, dx\)
  3.1.83 \(\int \frac {\sqrt {a+b x+c x^2}}{x^3 (d-f x^2)} \, dx\)
  3.1.84 \(\int \frac {x^3 (a+b x+c x^2)^{3/2}}{d-f x^2} \, dx\)
  3.1.85 \(\int \frac {x^2 (a+b x+c x^2)^{3/2}}{d-f x^2} \, dx\)
  3.1.86 \(\int \frac {x (a+b x+c x^2)^{3/2}}{d-f x^2} \, dx\)
  3.1.87 \(\int \frac {(a+b x+c x^2)^{3/2}}{d-f x^2} \, dx\)
  3.1.88 \(\int \frac {(a+b x+c x^2)^{3/2}}{x (d-f x^2)} \, dx\)
  3.1.89 \(\int \frac {(a+b x+c x^2)^{3/2}}{x^2 (d-f x^2)} \, dx\)
  3.1.90 \(\int \frac {(a+b x+c x^2)^{3/2}}{x^3 (d-f x^2)} \, dx\)
  3.1.91 \(\int \frac {(a+b x+c x^2)^{3/2}}{1-x^2} \, dx\)
  3.1.92 \(\int \frac {\sqrt {-1-x+x^2}}{1-x^2} \, dx\)
  3.1.93 \(\int \frac {(x+x^2)^{3/2}}{1+x^2} \, dx\)
  3.1.94 \(\int \frac {x^4}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
  3.1.95 \(\int \frac {x^3}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
  3.1.96 \(\int \frac {x^2}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
  3.1.97 \(\int \frac {x}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
  3.1.98 \(\int \frac {1}{\sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
  3.1.99 \(\int \frac {1}{x \sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)
  3.1.100 \(\int \frac {1}{x^2 \sqrt {a+b x+c x^2} (d-f x^2)} \, dx\)