3.1.1 \(\int \sqrt {1-d x} \sqrt {1+d x} (e+f x)^3 (A+B x+C x^2) \, dx\)
  3.1.2 \(\int \sqrt {1-d x} \sqrt {1+d x} (e+f x)^2 (A+B x+C x^2) \, dx\)
  3.1.3 \(\int \sqrt {1-d x} \sqrt {1+d x} (e+f x) (A+B x+C x^2) \, dx\)
  3.1.4 \(\int \sqrt {1-d x} \sqrt {1+d x} (A+B x+C x^2) \, dx\)
  3.1.5 \(\int \frac {A+B x+C x^2}{\sqrt {1-d x} \sqrt {1+d x} (e+f x)} \, dx\)
  3.1.6 \(\int \frac {A+B x+C x^2}{\sqrt {1-d x} \sqrt {1+d x} (e+f x)^2} \, dx\)
  3.1.7 \(\int \frac {A+B x+C x^2}{\sqrt {1-d x} \sqrt {1+d x} (e+f x)^3} \, dx\)
  3.1.8 \(\int \frac {(e+f x)^3 (A+B x+C x^2)}{\sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.9 \(\int \frac {(e+f x)^2 (A+B x+C x^2)}{\sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.10 \(\int \frac {(e+f x) (A+B x+C x^2)}{\sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.11 \(\int \frac {A+B x+C x^2}{\sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.12 \(\int \frac {A+B x+C x^2}{\sqrt {1-d x} \sqrt {1+d x} (e+f x)} \, dx\)
  3.1.13 \(\int \frac {A+B x+C x^2}{\sqrt {1-d x} \sqrt {1+d x} (e+f x)^2} \, dx\)
  3.1.14 \(\int \frac {A+B x+C x^2}{\sqrt {1-d x} \sqrt {1+d x} (e+f x)^3} \, dx\)
  3.1.15 \(\int \frac {x (a+b x+c x^2)}{\sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.16 \(\int \frac {a+b x+c x^2}{\sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.17 \(\int \frac {a+b x+c x^2}{x \sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.18 \(\int \frac {a+b x+c x^2}{x^2 \sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.19 \(\int \frac {a+b x+c x^2}{x^3 \sqrt {1-d x} \sqrt {1+d x}} \, dx\)
  3.1.20 \(\int \sqrt {a+b x} \sqrt {a c-b c x} (e+f x)^3 (A+B x+C x^2) \, dx\)
  3.1.21 \(\int \sqrt {a+b x} \sqrt {a c-b c x} (e+f x)^2 (A+B x+C x^2) \, dx\)
  3.1.22 \(\int \sqrt {a+b x} \sqrt {a c-b c x} (e+f x) (A+B x+C x^2) \, dx\)
  3.1.23 \(\int \sqrt {a+b x} \sqrt {a c-b c x} (A+B x+C x^2) \, dx\)
  3.1.24 \(\int \frac {A+B x+C x^2}{\sqrt {a+b x} \sqrt {a c-b c x} (e+f x)} \, dx\)
  3.1.25 \(\int \frac {A+B x+C x^2}{\sqrt {a+b x} \sqrt {a c-b c x} (e+f x)^2} \, dx\)
  3.1.26 \(\int \frac {A+B x+C x^2}{\sqrt {a+b x} \sqrt {a c-b c x} (e+f x)^3} \, dx\)
  3.1.27 \(\int \frac {(e+f x)^3 (A+B x+C x^2)}{\sqrt {a+b x} \sqrt {a c-b c x}} \, dx\)
  3.1.28 \(\int \frac {(e+f x)^2 (A+B x+C x^2)}{\sqrt {a+b x} \sqrt {a c-b c x}} \, dx\)
  3.1.29 \(\int \frac {(e+f x) (A+B x+C x^2)}{\sqrt {a+b x} \sqrt {a c-b c x}} \, dx\)
  3.1.30 \(\int \frac {A+B x+C x^2}{\sqrt {a+b x} \sqrt {a c-b c x}} \, dx\)
  3.1.31 \(\int \frac {A+B x+C x^2}{\sqrt {a+b x} \sqrt {a c-b c x} (e+f x)} \, dx\)
  3.1.32 \(\int \frac {A+B x+C x^2}{\sqrt {a+b x} \sqrt {a c-b c x} (e+f x)^2} \, dx\)
  3.1.33 \(\int \frac {A+B x+C x^2}{\sqrt {a+b x} \sqrt {a c-b c x} (e+f x)^3} \, dx\)
  3.1.34 \(\int \frac {x (a+b x+c x^2)}{\sqrt {-1+d x} \sqrt {1+d x}} \, dx\)
  3.1.35 \(\int \frac {a+b x+c x^2}{\sqrt {-1+d x} \sqrt {1+d x}} \, dx\)
  3.1.36 \(\int \frac {a+b x+c x^2}{x \sqrt {-1+d x} \sqrt {1+d x}} \, dx\)
  3.1.37 \(\int \frac {a+b x+c x^2}{x^2 \sqrt {-1+d x} \sqrt {1+d x}} \, dx\)
  3.1.38 \(\int \frac {a+b x+c x^2}{x^3 \sqrt {-1+d x} \sqrt {1+d x}} \, dx\)
  3.1.39 \(\int \frac {a+b x+c x^2}{x^4 \sqrt {-1+d x} \sqrt {1+d x}} \, dx\)
  3.1.40 \(\int \frac {a+b x+c x^2}{\sqrt {-1+x} \sqrt {1+x} (d+e x)^3} \, dx\)
  3.1.41 \(\int (a+b x)^2 \sqrt {c+d x} \sqrt {e+f x} (A+B x+C x^2) \, dx\)
  3.1.42 \(\int (a+b x) \sqrt {c+d x} \sqrt {e+f x} (A+B x+C x^2) \, dx\)
  3.1.43 \(\int \sqrt {c+d x} \sqrt {e+f x} (A+B x+C x^2) \, dx\)
  3.1.44 \(\int \frac {\sqrt {c+d x} \sqrt {e+f x} (A+B x+C x^2)}{a+b x} \, dx\)
  3.1.45 \(\int \frac {\sqrt {c+d x} \sqrt {e+f x} (A+B x+C x^2)}{(a+b x)^2} \, dx\)
  3.1.46 \(\int \frac {\sqrt {c+d x} \sqrt {e+f x} (A+B x+C x^2)}{(a+b x)^3} \, dx\)
  3.1.47 \(\int \frac {(a+b x)^2 \sqrt {c+d x} (A+B x+C x^2)}{\sqrt {e+f x}} \, dx\)
  3.1.48 \(\int \frac {(a+b x) \sqrt {c+d x} (A+B x+C x^2)}{\sqrt {e+f x}} \, dx\)
  3.1.49 \(\int \frac {\sqrt {c+d x} (A+B x+C x^2)}{\sqrt {e+f x}} \, dx\)
  3.1.50 \(\int \frac {\sqrt {c+d x} (A+B x+C x^2)}{(a+b x) \sqrt {e+f x}} \, dx\)
  3.1.51 \(\int \frac {\sqrt {c+d x} (A+B x+C x^2)}{(a+b x)^2 \sqrt {e+f x}} \, dx\)
  3.1.52 \(\int \frac {\sqrt {c+d x} (A+B x+C x^2)}{(a+b x)^3 \sqrt {e+f x}} \, dx\)
  3.1.53 \(\int \frac {\sqrt {c+d x} (A+B x+C x^2)}{(a+b x)^4 \sqrt {e+f x}} \, dx\)
  3.1.54 \(\int \frac {(a+b x)^2 (A+B x+C x^2)}{\sqrt {c+d x} \sqrt {e+f x}} \, dx\)
  3.1.55 \(\int \frac {(a+b x) (A+B x+C x^2)}{\sqrt {c+d x} \sqrt {e+f x}} \, dx\)
  3.1.56 \(\int \frac {A+B x+C x^2}{\sqrt {c+d x} \sqrt {e+f x}} \, dx\)
  3.1.57 \(\int \frac {A+B x+C x^2}{(a+b x) \sqrt {c+d x} \sqrt {e+f x}} \, dx\)
  3.1.58 \(\int \frac {A+B x+C x^2}{(a+b x)^2 \sqrt {c+d x} \sqrt {e+f x}} \, dx\)
  3.1.59 \(\int \frac {A+B x+C x^2}{(a+b x)^3 \sqrt {c+d x} \sqrt {e+f x}} \, dx\)
  3.1.60 \(\int \frac {A+B x+C x^2}{(a+b x)^4 \sqrt {c+d x} \sqrt {e+f x}} \, dx\)