3.19.1 \(\int \frac {(a+b x) (d+e x)^3}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
  3.19.2 \(\int \frac {(a+b x) (d+e x)^2}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
  3.19.3 \(\int \frac {(a+b x) (d+e x)}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
  3.19.4 \(\int \frac {a+b x}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
  3.19.5 \(\int \frac {a+b x}{(d+e x) (a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
  3.19.6 \(\int \frac {a+b x}{(d+e x)^2 (a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
  3.19.7 \(\int \frac {a+b x}{(d+e x)^3 (a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\)
  3.19.8 \(\int \frac {(a+b x) (d+e x)^5}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.9 \(\int \frac {(a+b x) (d+e x)^4}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.10 \(\int \frac {(a+b x) (d+e x)^3}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.11 \(\int \frac {(a+b x) (d+e x)^2}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.12 \(\int \frac {(a+b x) (d+e x)}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.13 \(\int \frac {a+b x}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.14 \(\int \frac {a+b x}{(d+e x) (a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.15 \(\int \frac {a+b x}{(d+e x)^2 (a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.16 \(\int \frac {a+b x}{(d+e x)^3 (a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\)
  3.19.17 \(\int (a+b x) (d+e x)^{7/2} (a^2+2 a b x+b^2 x^2) \, dx\)
  3.19.18 \(\int (a+b x) (d+e x)^{5/2} (a^2+2 a b x+b^2 x^2) \, dx\)
  3.19.19 \(\int (a+b x) (d+e x)^{3/2} (a^2+2 a b x+b^2 x^2) \, dx\)
  3.19.20 \(\int (a+b x) \sqrt {d+e x} (a^2+2 a b x+b^2 x^2) \, dx\)
  3.19.21 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)}{\sqrt {d+e x}} \, dx\)
  3.19.22 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)}{(d+e x)^{3/2}} \, dx\)
  3.19.23 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)}{(d+e x)^{5/2}} \, dx\)
  3.19.24 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)}{(d+e x)^{7/2}} \, dx\)
  3.19.25 \(\int (a+b x) (d+e x)^{7/2} (a^2+2 a b x+b^2 x^2)^2 \, dx\)
  3.19.26 \(\int (a+b x) (d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^2 \, dx\)
  3.19.27 \(\int (a+b x) (d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^2 \, dx\)
  3.19.28 \(\int (a+b x) \sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^2 \, dx\)
  3.19.29 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^2}{\sqrt {d+e x}} \, dx\)
  3.19.30 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^2}{(d+e x)^{3/2}} \, dx\)
  3.19.31 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^2}{(d+e x)^{5/2}} \, dx\)
  3.19.32 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^2}{(d+e x)^{7/2}} \, dx\)
  3.19.33 \(\int (a+b x) (d+e x)^{7/2} (a^2+2 a b x+b^2 x^2)^3 \, dx\)
  3.19.34 \(\int (a+b x) (d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^3 \, dx\)
  3.19.35 \(\int (a+b x) (d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^3 \, dx\)
  3.19.36 \(\int (a+b x) \sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^3 \, dx\)
  3.19.37 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^3}{\sqrt {d+e x}} \, dx\)
  3.19.38 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^3}{(d+e x)^{3/2}} \, dx\)
  3.19.39 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^3}{(d+e x)^{5/2}} \, dx\)
  3.19.40 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^3}{(d+e x)^{7/2}} \, dx\)
  3.19.41 \(\int \frac {(a+b x) (d+e x)^{7/2}}{a^2+2 a b x+b^2 x^2} \, dx\)
  3.19.42 \(\int \frac {(a+b x) (d+e x)^{5/2}}{a^2+2 a b x+b^2 x^2} \, dx\)
  3.19.43 \(\int \frac {(a+b x) (d+e x)^{3/2}}{a^2+2 a b x+b^2 x^2} \, dx\)
  3.19.44 \(\int \frac {(a+b x) \sqrt {d+e x}}{a^2+2 a b x+b^2 x^2} \, dx\)
  3.19.45 \(\int \frac {a+b x}{\sqrt {d+e x} (a^2+2 a b x+b^2 x^2)} \, dx\)
  3.19.46 \(\int \frac {a+b x}{(d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)} \, dx\)
  3.19.47 \(\int \frac {a+b x}{(d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)} \, dx\)
  3.19.48 \(\int \frac {a+b x}{(d+e x)^{7/2} (a^2+2 a b x+b^2 x^2)} \, dx\)
  3.19.49 \(\int \frac {(a+b x) (d+e x)^{9/2}}{(a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.50 \(\int \frac {(a+b x) (d+e x)^{7/2}}{(a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.51 \(\int \frac {(a+b x) (d+e x)^{5/2}}{(a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.52 \(\int \frac {(a+b x) (d+e x)^{3/2}}{(a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.53 \(\int \frac {(a+b x) \sqrt {d+e x}}{(a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.54 \(\int \frac {a+b x}{\sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.55 \(\int \frac {a+b x}{(d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.56 \(\int \frac {a+b x}{(d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.57 \(\int \frac {a+b x}{(d+e x)^{7/2} (a^2+2 a b x+b^2 x^2)^2} \, dx\)
  3.19.58 \(\int \frac {(a+b x) (d+e x)^{11/2}}{(a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.59 \(\int \frac {(a+b x) (d+e x)^{9/2}}{(a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.60 \(\int \frac {(a+b x) (d+e x)^{7/2}}{(a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.61 \(\int \frac {(a+b x) (d+e x)^{5/2}}{(a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.62 \(\int \frac {(a+b x) (d+e x)^{3/2}}{(a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.63 \(\int \frac {(a+b x) \sqrt {d+e x}}{(a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.64 \(\int \frac {a+b x}{\sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.65 \(\int \frac {a+b x}{(d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.66 \(\int \frac {a+b x}{(d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^3} \, dx\)
  3.19.67 \(\int (a+b x) (d+e x)^{7/2} \sqrt {a^2+2 a b x+b^2 x^2} \, dx\)
  3.19.68 \(\int (a+b x) (d+e x)^{5/2} \sqrt {a^2+2 a b x+b^2 x^2} \, dx\)
  3.19.69 \(\int (a+b x) (d+e x)^{3/2} \sqrt {a^2+2 a b x+b^2 x^2} \, dx\)
  3.19.70 \(\int (a+b x) \sqrt {d+e x} \sqrt {a^2+2 a b x+b^2 x^2} \, dx\)
  3.19.71 \(\int \frac {(a+b x) \sqrt {a^2+2 a b x+b^2 x^2}}{\sqrt {d+e x}} \, dx\)
  3.19.72 \(\int \frac {(a+b x) \sqrt {a^2+2 a b x+b^2 x^2}}{(d+e x)^{3/2}} \, dx\)
  3.19.73 \(\int \frac {(a+b x) \sqrt {a^2+2 a b x+b^2 x^2}}{(d+e x)^{5/2}} \, dx\)
  3.19.74 \(\int \frac {(a+b x) \sqrt {a^2+2 a b x+b^2 x^2}}{(d+e x)^{7/2}} \, dx\)
  3.19.75 \(\int (a+b x) (d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\)
  3.19.76 \(\int (a+b x) (d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\)
  3.19.77 \(\int (a+b x) \sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\)
  3.19.78 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{\sqrt {d+e x}} \, dx\)
  3.19.79 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{3/2}} \, dx\)
  3.19.80 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{5/2}} \, dx\)
  3.19.81 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{7/2}} \, dx\)
  3.19.82 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{9/2}} \, dx\)
  3.19.83 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{11/2}} \, dx\)
  3.19.84 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{3/2}}{(d+e x)^{13/2}} \, dx\)
  3.19.85 \(\int (a+b x) (d+e x)^{5/2} (a^2+2 a b x+b^2 x^2)^{5/2} \, dx\)
  3.19.86 \(\int (a+b x) (d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^{5/2} \, dx\)
  3.19.87 \(\int (a+b x) \sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^{5/2} \, dx\)
  3.19.88 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{\sqrt {d+e x}} \, dx\)
  3.19.89 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{3/2}} \, dx\)
  3.19.90 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{5/2}} \, dx\)
  3.19.91 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{7/2}} \, dx\)
  3.19.92 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{9/2}} \, dx\)
  3.19.93 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{11/2}} \, dx\)
  3.19.94 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{13/2}} \, dx\)
  3.19.95 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{15/2}} \, dx\)
  3.19.96 \(\int \frac {(a+b x) (a^2+2 a b x+b^2 x^2)^{5/2}}{(d+e x)^{17/2}} \, dx\)
  3.19.97 \(\int \frac {(a+b x) (d+e x)^{7/2}}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\)
  3.19.98 \(\int \frac {(a+b x) (d+e x)^{5/2}}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\)
  3.19.99 \(\int \frac {(a+b x) (d+e x)^{3/2}}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\)
  3.19.100 \(\int \frac {(a+b x) \sqrt {d+e x}}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\)