3.4.1 \(\int \frac {x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6+4 d f x^{2+2 m}} \, dx\)
  3.4.2 \(\int \frac {x^m (e (1+m)+2 f (-2+m) x^3)}{e^2+4 e f x^3+4 f^2 x^6-4 d f x^{2+2 m}} \, dx\)
  3.4.3 \(\int \frac {x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2+4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
  3.4.4 \(\int \frac {x^m (e (1+m)+2 f (1+m-n) x^n)}{e^2-4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
  3.4.5 \(\int \frac {x^5}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\)
  3.4.6 \(\int \frac {x^3}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\)
  3.4.7 \(\int \frac {x}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\)
  3.4.8 \(\int \frac {1}{x (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\)
  3.4.9 \(\int \frac {1}{x^3 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\)
  3.4.10 \(\int \frac {x^2}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\)
  3.4.11 \(\int \frac {1}{a c+b c x^2+d \sqrt {a+b x^2}} \, dx\)
  3.4.12 \(\int \frac {1}{x^2 (a c+b c x^2+d \sqrt {a+b x^2})} \, dx\)
  3.4.13 \(\int \frac {x^8}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\)
  3.4.14 \(\int \frac {x^5}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\)
  3.4.15 \(\int \frac {x^2}{a c+b c x^3+d \sqrt {a+b x^3}} \, dx\)
  3.4.16 \(\int \frac {1}{x (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\)
  3.4.17 \(\int \frac {1}{x^4 (a c+b c x^3+d \sqrt {a+b x^3})} \, dx\)
  3.4.18 \(\int \frac {x^{-1+n}}{a c+b c x^n+d \sqrt {a+b x^n}} \, dx\)
  3.4.19 \(\int \frac {1}{\sqrt {x}+4 x^{3/2}} \, dx\)
  3.4.20 \(\int \frac {1}{\sqrt {x}-x^{5/2}} \, dx\)
  3.4.21 \(\int \frac {1}{-\sqrt [4]{x}+\sqrt {x}} \, dx\)
  3.4.22 \(\int \frac {1}{\sqrt [3]{x}+\sqrt {x}} \, dx\)
  3.4.23 \(\int \frac {1}{\sqrt [4]{x}+\sqrt {x}} \, dx\)
  3.4.24 \(\int \frac {1}{-\sqrt [3]{x}+x^{2/3}} \, dx\)
  3.4.25 \(\int \frac {1}{\frac {1}{\sqrt [4]{x}}+\sqrt {x}} \, dx\)
  3.4.26 \(\int \frac {1}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\)
  3.4.27 \(\int \frac {1}{\frac {1}{\sqrt [3]{x}}+\frac {1}{\sqrt [4]{x}}} \, dx\)
  3.4.28 \(\int \frac {1}{-\frac {1}{\sqrt [3]{x}}+\sqrt {x}} \, dx\)
  3.4.29 \(\int \frac {\sqrt {x}}{x+x^2} \, dx\)
  3.4.30 \(\int \frac {x}{4 \sqrt {x}+x} \, dx\)
  3.4.31 \(\int \frac {\sqrt {x}}{\sqrt [3]{x}+x} \, dx\)
  3.4.32 \(\int \frac {\sqrt [3]{x}}{\sqrt [4]{x}+\sqrt {x}} \, dx\)
  3.4.33 \(\int \frac {\sqrt {x}}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\)
  3.4.34 \(\int \frac {\sqrt {x}}{-\frac {1}{\sqrt [3]{x}}+\sqrt {x}} \, dx\)
  3.4.35 \(\int \frac {\sqrt {b-\frac {a}{x}} x^m}{\sqrt {a-b x}} \, dx\)
  3.4.36 \(\int \frac {\sqrt {b-\frac {a}{x}} x^2}{\sqrt {a-b x}} \, dx\)
  3.4.37 \(\int \frac {\sqrt {b-\frac {a}{x}} x}{\sqrt {a-b x}} \, dx\)
  3.4.38 \(\int \frac {\sqrt {b-\frac {a}{x}}}{\sqrt {a-b x}} \, dx\)
  3.4.39 \(\int \frac {\sqrt {b-\frac {a}{x}}}{x \sqrt {a-b x}} \, dx\)
  3.4.40 \(\int \frac {\sqrt {b-\frac {a}{x}}}{x^2 \sqrt {a-b x}} \, dx\)
  3.4.41 \(\int \frac {\sqrt {b-\frac {a}{x^2}} x^m}{\sqrt {a-b x^2}} \, dx\)
  3.4.42 \(\int \frac {\sqrt {b-\frac {a}{x^2}} x^2}{\sqrt {a-b x^2}} \, dx\)
  3.4.43 \(\int \frac {\sqrt {b-\frac {a}{x^2}} x}{\sqrt {a-b x^2}} \, dx\)
  3.4.44 \(\int \frac {\sqrt {b-\frac {a}{x^2}}}{\sqrt {a-b x^2}} \, dx\)
  3.4.45 \(\int \frac {\sqrt {b-\frac {a}{x^2}}}{x \sqrt {a-b x^2}} \, dx\)
  3.4.46 \(\int \frac {\sqrt {b-\frac {a}{x^2}}}{x^2 \sqrt {a-b x^2}} \, dx\)
  3.4.47 \(\int \frac {-1+x^3}{(-4 x+x^4)^{2/3}} \, dx\)
  3.4.48 \(\int (2-x^2) \sqrt [4]{6 x-x^3} \, dx\)
  3.4.49 \(\int (1+x^4) \sqrt {5 x+x^5} \, dx\)
  3.4.50 \(\int (2+5 x^4) \sqrt {2 x+x^5} \, dx\)
  3.4.51 \(\int \frac {x+3 x^2}{\sqrt {x^2+2 x^3}} \, dx\)
  3.4.52 \(\int \frac {2+\sqrt [3]{1-5 x}}{3+\sqrt [3]{1-5 x}} \, dx\)
  3.4.53 \(\int \frac {1+\sqrt {x}}{-1+\sqrt {x}} \, dx\)
  3.4.54 \(\int \frac {1-\sqrt {2+3 x}}{1+\sqrt {2+3 x}} \, dx\)
  3.4.55 \(\int \frac {-1+\sqrt {a+b x}}{1+\sqrt {a+b x}} \, dx\)
  3.4.56 \(\int \frac {a+b n x^{-1+n}}{a x+b x^n} \, dx\)
  3.4.57 \(\int \frac {x^{-n} (a+b n x^{-1+n})}{b+a x^{1-n}} \, dx\)
  3.4.58 \(\int x (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (2 a d+(3 b d+3 a e+b d m+a e n) x+(4 c d+4 b e+4 a f+2 c d m+b e m+b e n+2 a f n) x^2+(5 c e+5 b f+5 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(6 c f+6 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (7+2 m+3 n) x^5) \, dx\)
  3.4.59 \(\int (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (a d+(2 b d+2 a e+b d m+a e n) x+(3 c d+3 b e+3 a f+2 c d m+b e m+b e n+2 a f n) x^2+(4 c e+4 b f+4 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(5 c f+5 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (6+2 m+3 n) x^5) \, dx\)
  3.4.60 \(\int (a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4) \, dx\)
  3.4.61 \(\int \frac {(a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (-a d+(b d m+a e n) x+(c d+b e+a f+2 c d m+b e m+b e n+2 a f n) x^2+(2 c e+2 b f+2 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(3 c f+3 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (4+2 m+3 n) x^5)}{x^2} \, dx\)
  3.4.62 \(\int \frac {(a+b x+c x^2)^m (d+e x+f x^2+g x^3)^n (-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5)}{x^3} \, dx\)
  3.4.63 \(\int x^3 (a+b \sqrt {c+d x})^2 \, dx\)
  3.4.64 \(\int x^2 (a+b \sqrt {c+d x})^2 \, dx\)
  3.4.65 \(\int x (a+b \sqrt {c+d x})^2 \, dx\)
  3.4.66 \(\int (a+b \sqrt {c+d x})^2 \, dx\)
  3.4.67 \(\int \frac {(a+b \sqrt {c+d x})^2}{x} \, dx\)
  3.4.68 \(\int \frac {(a+b \sqrt {c+d x})^2}{x^2} \, dx\)
  3.4.69 \(\int \frac {(a+b \sqrt {c+d x})^2}{x^3} \, dx\)
  3.4.70 \(\int x^3 \sqrt {a+b \sqrt {c+d x}} \, dx\)
  3.4.71 \(\int x^2 \sqrt {a+b \sqrt {c+d x}} \, dx\)
  3.4.72 \(\int x \sqrt {a+b \sqrt {c+d x}} \, dx\)
  3.4.73 \(\int \sqrt {a+b \sqrt {c+d x}} \, dx\)
  3.4.74 \(\int \frac {\sqrt {a+b \sqrt {c+d x}}}{x} \, dx\)
  3.4.75 \(\int \frac {\sqrt {a+b \sqrt {c+d x}}}{x^2} \, dx\)
  3.4.76 \(\int \frac {\sqrt {a+b \sqrt {c+d x}}}{x^3} \, dx\)
  3.4.77 \(\int \frac {x^3}{a+b \sqrt {c+d x}} \, dx\)
  3.4.78 \(\int \frac {x^2}{a+b \sqrt {c+d x}} \, dx\)
  3.4.79 \(\int \frac {x}{a+b \sqrt {c+d x}} \, dx\)
  3.4.80 \(\int \frac {1}{a+b \sqrt {c+d x}} \, dx\)
  3.4.81 \(\int \frac {1}{x (a+b \sqrt {c+d x})} \, dx\)
  3.4.82 \(\int \frac {1}{x^2 (a+b \sqrt {c+d x})} \, dx\)
  3.4.83 \(\int \frac {1}{x^3 (a+b \sqrt {c+d x})} \, dx\)
  3.4.84 \(\int \frac {x^3}{(a+b \sqrt {c+d x})^2} \, dx\)
  3.4.85 \(\int \frac {x^2}{(a+b \sqrt {c+d x})^2} \, dx\)
  3.4.86 \(\int \frac {x}{(a+b \sqrt {c+d x})^2} \, dx\)
  3.4.87 \(\int \frac {1}{(a+b \sqrt {c+d x})^2} \, dx\)
  3.4.88 \(\int \frac {1}{x (a+b \sqrt {c+d x})^2} \, dx\)
  3.4.89 \(\int \frac {1}{x^2 (a+b \sqrt {c+d x})^2} \, dx\)
  3.4.90 \(\int \frac {1}{x^3 (a+b \sqrt {c+d x})^2} \, dx\)
  3.4.91 \(\int \frac {x^3}{\sqrt {a+b \sqrt {c+d x}}} \, dx\)
  3.4.92 \(\int \frac {x^2}{\sqrt {a+b \sqrt {c+d x}}} \, dx\)
  3.4.93 \(\int \frac {x}{\sqrt {a+b \sqrt {c+d x}}} \, dx\)
  3.4.94 \(\int \frac {1}{\sqrt {a+b \sqrt {c+d x}}} \, dx\)
  3.4.95 \(\int \frac {1}{x \sqrt {a+b \sqrt {c+d x}}} \, dx\)
  3.4.96 \(\int \frac {1}{x^2 \sqrt {a+b \sqrt {c+d x}}} \, dx\)
  3.4.97 \(\int \frac {1}{x^3 \sqrt {a+b \sqrt {c+d x}}} \, dx\)
  3.4.98 \(\int x^3 (a+b \sqrt {c+d x})^p \, dx\)
  3.4.99 \(\int x^2 (a+b \sqrt {c+d x})^p \, dx\)
  3.4.100 \(\int x (a+b \sqrt {c+d x})^p \, dx\)