3.1.1 \(\int \frac {c+d x^2}{a+b x^4} \, dx\)
  3.1.2 \(\int \frac {c-d x^2}{a+b x^4} \, dx\)
  3.1.3 \(\int \frac {c+d x^2}{a-b x^4} \, dx\)
  3.1.4 \(\int \frac {c-d x^2}{a-b x^4} \, dx\)
  3.1.5 \(\int \frac {2+3 x^2}{4+9 x^4} \, dx\)
  3.1.6 \(\int \frac {2-3 x^2}{4+9 x^4} \, dx\)
  3.1.7 \(\int \frac {2+3 x^2}{4-9 x^4} \, dx\)
  3.1.8 \(\int \frac {2-3 x^2}{4-9 x^4} \, dx\)
  3.1.9 \(\int \frac {\sqrt {a} \sqrt {b}+b x^2}{a+b x^4} \, dx\)
  3.1.10 \(\int \frac {\sqrt {a} \sqrt {b}-b x^2}{a+b x^4} \, dx\)
  3.1.11 \(\int \frac {d+e x^2}{d^2+e^2 x^4} \, dx\)
  3.1.12 \(\int \frac {d-e x^2}{d^2+e^2 x^4} \, dx\)
  3.1.13 \(\int \frac {5+2 x^2}{-1+x^4} \, dx\)
  3.1.14 \(\int \frac {d+e x^2}{d^2+b x^2+e^2 x^4} \, dx\)
  3.1.15 \(\int \frac {d+e x^2}{d^2+f x^2+e^2 x^4} \, dx\)
  3.1.16 \(\int \frac {d+e x^2}{d^2-b x^2+e^2 x^4} \, dx\)
  3.1.17 \(\int \frac {d+e x^2}{d^2-f x^2+e^2 x^4} \, dx\)
  3.1.18 \(\int \frac {d-e x^2}{d^2+b x^2+e^2 x^4} \, dx\)
  3.1.19 \(\int \frac {d-e x^2}{d^2+f x^2+e^2 x^4} \, dx\)
  3.1.20 \(\int \frac {d-e x^2}{d^2-b x^2+e^2 x^4} \, dx\)
  3.1.21 \(\int \frac {d-e x^2}{d^2-f x^2+e^2 x^4} \, dx\)
  3.1.22 \(\int \frac {d-e x^2}{\frac {c d^2}{e^2}+b x^2+c x^4} \, dx\)
  3.1.23 \(\int \frac {d+e x^2}{\frac {c d^2}{e^2}+b x^2+c x^4} \, dx\)
  3.1.24 \(\int \frac {d+e x^2}{b x^2+c (\frac {d^2}{e^2}+x^4)} \, dx\)
  3.1.25 \(\int \frac {a-b x^2}{a^2+(-1+2 a b) x^2+b^2 x^4} \, dx\)
  3.1.26 \(\int \frac {a+b x^2}{a^2+(-1+2 a b) x^2+b^2 x^4} \, dx\)
  3.1.27 \(\int \frac {1+2 x^2}{1+b x^2+4 x^4} \, dx\)
  3.1.28 \(\int \frac {1+2 x^2}{1-b x^2+4 x^4} \, dx\)
  3.1.29 \(\int \frac {1+2 x^2}{1+6 x^2+4 x^4} \, dx\)
  3.1.30 \(\int \frac {1+2 x^2}{1+5 x^2+4 x^4} \, dx\)
  3.1.31 \(\int \frac {1+2 x^2}{1+4 x^2+4 x^4} \, dx\)
  3.1.32 \(\int \frac {1+2 x^2}{1+3 x^2+4 x^4} \, dx\)
  3.1.33 \(\int \frac {1+2 x^2}{1+2 x^2+4 x^4} \, dx\)
  3.1.34 \(\int \frac {1+2 x^2}{1+x^2+4 x^4} \, dx\)
  3.1.35 \(\int \frac {1+2 x^2}{1+4 x^4} \, dx\)
  3.1.36 \(\int \frac {1+2 x^2}{1-x^2+4 x^4} \, dx\)
  3.1.37 \(\int \frac {1+2 x^2}{1-2 x^2+4 x^4} \, dx\)
  3.1.38 \(\int \frac {1+2 x^2}{1-3 x^2+4 x^4} \, dx\)
  3.1.39 \(\int \frac {1+2 x^2}{1-4 x^2+4 x^4} \, dx\)
  3.1.40 \(\int \frac {1+2 x^2}{1-5 x^2+4 x^4} \, dx\)
  3.1.41 \(\int \frac {1+2 x^2}{1-6 x^2+4 x^4} \, dx\)
  3.1.42 \(\int \frac {1-2 x^2}{1+b x^2+4 x^4} \, dx\)
  3.1.43 \(\int \frac {1-2 x^2}{1+6 x^2+4 x^4} \, dx\)
  3.1.44 \(\int \frac {1-2 x^2}{1+5 x^2+4 x^4} \, dx\)
  3.1.45 \(\int \frac {1-2 x^2}{1+4 x^2+4 x^4} \, dx\)
  3.1.46 \(\int \frac {1-2 x^2}{1+3 x^2+4 x^4} \, dx\)
  3.1.47 \(\int \frac {1-2 x^2}{1+2 x^2+4 x^4} \, dx\)
  3.1.48 \(\int \frac {1-2 x^2}{1+x^2+4 x^4} \, dx\)
  3.1.49 \(\int \frac {1-2 x^2}{1+4 x^4} \, dx\)
  3.1.50 \(\int \frac {1-2 x^2}{1-x^2+4 x^4} \, dx\)
  3.1.51 \(\int \frac {1-2 x^2}{1-2 x^2+4 x^4} \, dx\)
  3.1.52 \(\int \frac {1-2 x^2}{1-3 x^2+4 x^4} \, dx\)
  3.1.53 \(\int \frac {1-2 x^2}{1-4 x^2+4 x^4} \, dx\)
  3.1.54 \(\int \frac {1-2 x^2}{1-5 x^2+4 x^4} \, dx\)
  3.1.55 \(\int \frac {1-2 x^2}{1-6 x^2+4 x^4} \, dx\)
  3.1.56 \(\int \frac {1+x^2}{1+b x^2+x^4} \, dx\)
  3.1.57 \(\int \frac {1+x^2}{1+5 x^2+x^4} \, dx\)
  3.1.58 \(\int \frac {1+x^2}{1+4 x^2+x^4} \, dx\)
  3.1.59 \(\int \frac {1+x^2}{1+3 x^2+x^4} \, dx\)
  3.1.60 \(\int \frac {1+x^2}{1+2 x^2+x^4} \, dx\)
  3.1.61 \(\int \frac {1+x^2}{1+x^2+x^4} \, dx\)
  3.1.62 \(\int \frac {1+x^2}{1+x^4} \, dx\)
  3.1.63 \(\int \frac {1+x^2}{1-x^2+x^4} \, dx\)
  3.1.64 \(\int \frac {1+x^2}{1-2 x^2+x^4} \, dx\)
  3.1.65 \(\int \frac {1+x^2}{1-3 x^2+x^4} \, dx\)
  3.1.66 \(\int \frac {1+x^2}{1-4 x^2+x^4} \, dx\)
  3.1.67 \(\int \frac {1+x^2}{1-5 x^2+x^4} \, dx\)
  3.1.68 \(\int \frac {1-x^2}{1+b x^2+x^4} \, dx\)
  3.1.69 \(\int \frac {1-x^2}{1+5 x^2+x^4} \, dx\)
  3.1.70 \(\int \frac {1-x^2}{1+4 x^2+x^4} \, dx\)
  3.1.71 \(\int \frac {1-x^2}{1+3 x^2+x^4} \, dx\)
  3.1.72 \(\int \frac {1-x^2}{1+2 x^2+x^4} \, dx\)
  3.1.73 \(\int \frac {1-x^2}{1+x^2+x^4} \, dx\)
  3.1.74 \(\int \frac {1-x^2}{1+x^4} \, dx\)
  3.1.75 \(\int \frac {1-x^2}{1-x^2+x^4} \, dx\)
  3.1.76 \(\int \frac {1-x^2}{1-2 x^2+x^4} \, dx\)
  3.1.77 \(\int \frac {1-x^2}{1-3 x^2+x^4} \, dx\)
  3.1.78 \(\int \frac {1-x^2}{1-4 x^2+x^4} \, dx\)
  3.1.79 \(\int \frac {1-x^2}{1-5 x^2+x^4} \, dx\)
  3.1.80 \(\int \frac {-1-3 x^2}{1+2 x^2+9 x^4} \, dx\)
  3.1.81 \(\int \frac {1+3 x^2}{-1-2 x^2-9 x^4} \, dx\)
  3.1.82 \(\int \frac {3+2 x^2}{1-2 x^2+x^4} \, dx\)
  3.1.83 \(\int \frac {2+3 x^2}{5-8 x^2+3 x^4} \, dx\)
  3.1.84 \(\int \frac {d+e x^2}{5-8 x^2+3 x^4} \, dx\)
  3.1.85 \(\int \frac {3+x^2}{1+3 x^2+x^4} \, dx\)
  3.1.86 \(\int \frac {a+b x^2}{1+x^2+x^4} \, dx\)
  3.1.87 \(\int \frac {a+b x^2}{(1+x^2+x^4)^2} \, dx\)
  3.1.88 \(\int \frac {a+b x^2}{2+x^2+x^4} \, dx\)
  3.1.89 \(\int \frac {a+b x^2}{(2+x^2+x^4)^2} \, dx\)
  3.1.90 \(\int \frac {\sqrt {2}-x^2}{1-\sqrt {2} x^2+x^4} \, dx\)
  3.1.91 \(\int \frac {\sqrt {2}+x^2}{1+\sqrt {2} x^2+x^4} \, dx\)
  3.1.92 \(\int \frac {\sqrt {2}-x^2}{1+b x^2+x^4} \, dx\)
  3.1.93 \(\int \frac {\sqrt {2}+x^2}{1+b x^2+x^4} \, dx\)
  3.1.94 \(\int \frac {2 a-x^2}{a^2-a x^2+x^4} \, dx\)
  3.1.95 \(\int \frac {2 \sqrt {a}-x^2}{a-\sqrt {a} x^2+x^4} \, dx\)
  3.1.96 \(\int \frac {2 b^{2/3}+x^2}{b^{4/3}+b^{2/3} x^2+x^4} \, dx\)
  3.1.97 \(\int \frac {A+B x^2}{a^2-a x^2+x^4} \, dx\)
  3.1.98 \(\int \frac {A+B x^2}{a-\sqrt {a} x^2+x^4} \, dx\)
  3.1.99 \(\int \frac {A+B x^2}{a-\sqrt {a c} x^2+c x^4} \, dx\)
  3.1.100 \(\int \frac {A+B x^2}{a-\sqrt {a} \sqrt {c} x^2+c x^4} \, dx\)