3.14.1 \(\int \frac {-a^2 b+a (2 a+b) x-3 a x^2+x^3}{\sqrt {x (-a+x) (-b+x)} (-a^2 d+2 a d x+(b^2-d) x^2-2 b x^3+x^4)} \, dx\)
  3.14.2 \(\int \frac {-2 b+a x^4}{x^4 \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.14.3 \(\int \frac {2 b+a x^4}{x^4 \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.14.4 \(\int \frac {-1+x}{(1+x) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.14.5 \(\int \frac {1+x}{(-1+x) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.14.6 \(\int \frac {x^2}{\sqrt {(1-x^2) (1-k^2 x^2)} (-1+k^2 x^4)} \, dx\)
  3.14.7 \(\int \frac {(-1+x^6)^{2/3} (1+x^6)}{x^3 (-1-x^3+x^6)} \, dx\)
  3.14.8 \(\int \frac {(-1+x^6) (1+x^6)^{2/3}}{x^3 (1-x^3+x^6)} \, dx\)
  3.14.9 \(\int \frac {-1+x^8}{\sqrt [4]{-x^2+x^4} (1+x^8)} \, dx\)
  3.14.10 \(\int \frac {-1+x^8}{\sqrt [4]{-x^2+x^4} (1+x^8)} \, dx\)
  3.14.11 \(\int \frac {1+3 x^4+x^8}{x^2 (1+x^4)^{3/4} (1+3 x^4+3 x^8)} \, dx\)
  3.14.12 \(\int \frac {\sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}}}{b+a^2 x^2} \, dx\)
  3.14.13 \(\int \frac {\sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}}}{b+a^2 x^2} \, dx\)
  3.14.14 \(\int \frac {-1+x}{x^4 \sqrt [3]{1+x^3}} \, dx\)
  3.14.15 \(\int \frac {(3+2 x) \sqrt [3]{1+x+x^3}}{x^2 (1+x)} \, dx\)
  3.14.16 \(\int \frac {(a^2-2 a x+x^2) (-a b+2 (a-b) x+x^2)}{(x (-a+x) (-b+x))^{3/4} (-a^3 d+(b+3 a^2 d) x-(1+3 a d) x^2+d x^3)} \, dx\)
  3.14.17 \(\int \frac {(1+x^2)^2}{(1-x^2) (1-6 x^2+x^4)^{3/4}} \, dx\)
  3.14.18 \(\int \frac {(-4+x^3) (1-x^3+x^4)}{x^2 (-1+x^3)^{3/4} (-1+x^3+x^4)} \, dx\)
  3.14.19 \(\int \frac {(-1+x^4) (3+x^4) (-1-x^3+x^4)}{x^6 (-1-2 x^3+x^4) \sqrt [4]{-x+x^5}} \, dx\)
  3.14.20 \(\int \frac {(4 b+a x^5) (-b+c x^4+a x^5)}{x^2 (-b+a x^5)^{3/4} (-b-c x^4+a x^5)} \, dx\)
  3.14.21 \(\int \frac {(-2+x^6) (1-x^4+x^6)}{x^4 \sqrt [4]{1+x^6} (1+x^4+x^6)} \, dx\)
  3.14.22 \(\int \frac {x^4 (2 b+a x^6)}{\sqrt [4]{-b+a x^6} (-b-x^4+a x^6)^2} \, dx\)
  3.14.23 \(\int \frac {(2 b+a x^6) (-b-x^4+a x^6)}{x^4 \sqrt [4]{-b+a x^6} (-b-2 x^4+a x^6)} \, dx\)
  3.14.24 \(\int \frac {\sqrt {-1-2 x^2-2 x^3-x^8} (-1+x^3+3 x^8)}{(1+2 x^3+x^8) (1+x^2+2 x^3+x^8)} \, dx\)
  3.14.25 \(\int \frac {(1+x^6) \sqrt {-2-x^2+x^6}}{4-3 x^4-4 x^6+x^{12}} \, dx\)
  3.14.26 \(\int x \sqrt [3]{-1+x^3} \, dx\)
  3.14.27 \(\int x \sqrt [3]{1+x^3} \, dx\)
  3.14.28 \(\int \frac {\sqrt [3]{x+x^3}}{x^2} \, dx\)
  3.14.29 \(\int \frac {(-1+x) (-1+k x) (3-2 (1+k) x+k x^2)}{x ((1-x) x (1-k x))^{3/4} (-1+(1+k) x-k x^2+d x^3)} \, dx\)
  3.14.30 \(\int \frac {(1-2 x+x^2) (-2+(-1+k) (1+k) x+2 k^2 x^2)}{((1-x^2) (1-k^2 x^2))^{3/4} (-1+d-(1+3 d) x+(3 d+k^2) x^2+(-d+k^2) x^3)} \, dx\)
  3.14.31 \(\int \frac {x^2}{(-b+a x^2) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.14.32 \(\int \frac {\sqrt {q+p x^5} (-2 q+3 p x^5) (a q+b x^2+a p x^5)}{x^4 (c q+d x^2+c p x^5)} \, dx\)
  3.14.33 \(\int \frac {x}{\sqrt [3]{x^2+x^6}} \, dx\)
  3.14.34 \(\int \frac {-1+x^4}{(1+x^2+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.14.35 \(\int \frac {-1+x^4}{(1+x^2+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.14.36 \(\int \frac {x^2 (2 b+a x^6)}{(-b+a x^6)^{3/4} (-b-2 c x^4+a x^6)} \, dx\)
  3.14.37 \(\int \frac {1}{\sqrt [4]{b+a x^4} (-2 b-2 a x^4+x^8)} \, dx\)
  3.14.38 \(\int \frac {1}{\sqrt [4]{b+a x^4} (-2 b-2 a x^4+x^8)} \, dx\)
  3.14.39 \(\int \frac {-2 b+a x^4}{\sqrt [4]{b+a x^4} (-b-a x^4+2 x^8)} \, dx\)
  3.14.40 \(\int \frac {1+b x+k^2 x^2}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^2 x^2)} \, dx\)
  3.14.41 \(\int \frac {\sqrt [3]{-1+x^3}}{x^7} \, dx\)
  3.14.42 \(\int \frac {\sqrt [3]{1+x^3}}{x^7} \, dx\)
  3.14.43 \(\int \frac {(-1+x^3) \sqrt [3]{1+x^3}}{x^4} \, dx\)
  3.14.44 \(\int \frac {1+x}{(-1-x+x^3) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.14.45 \(\int \frac {1+x}{(-1-x+x^3) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.14.46 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {-x-x^2+x^3}} \, dx\)
  3.14.47 \(\int \frac {\sqrt [3]{x^2+x^3}}{x} \, dx\)
  3.14.48 \(\int \frac {(1+x^3)^{2/3} (2+x^3)}{x^6 (1+2 x^3)} \, dx\)
  3.14.49 \(\int \frac {(-3+x^4) \sqrt [3]{1+x^4}}{x^9} \, dx\)
  3.14.50 \(\int \frac {-b+a x^3}{x^3 \sqrt [4]{b x+a x^4}} \, dx\)
  3.14.51 \(\int \frac {b+a x^3}{x^3 \sqrt [4]{b x+a x^4}} \, dx\)
  3.14.52 \(\int \frac {1}{x^{13} \sqrt [3]{1+x^6}} \, dx\)
  3.14.53 \(\int \frac {-3+5 x^8}{(1+x^8) \sqrt [3]{1-x^3+x^8}} \, dx\)
  3.14.54 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{1+\sqrt {1+x}} \, dx\)
  3.14.55 \(\int \frac {x+\sqrt {1+x^2}}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.14.56 \(\int \frac {x^2}{(-2 b+a x^2) (-b+a x^2)^{3/4}} \, dx\)
  3.14.57 \(\int \frac {(-2 k-(-1+k) (1+k) x+2 k x^2) (1-2 k x+k^2 x^2)}{((1-x^2) (1-k^2 x^2))^{3/4} (1-d+(1+3 d) k x-(1+3 d k^2) x^2+k (-1+d k^2) x^3)} \, dx\)
  3.14.58 \(\int \frac {(-1+x^2) (1+x^2) \sqrt {1+3 x^2+x^4}}{x^2 (1+x+x^2)^2} \, dx\)
  3.14.59 \(\int \frac {(2+x^2) (-4+x+2 x^2) \sqrt {8-7 x^2+2 x^4}}{x^4} \, dx\)
  3.14.60 \(\int x^4 (-b+a x^4)^{3/4} \, dx\)
  3.14.61 \(\int \frac {(-2 b+a x^2) \sqrt [4]{b x^2+a x^4}}{x^2} \, dx\)
  3.14.62 \(\int \frac {(2 b+a x^2) \sqrt [4]{b x^2+a x^4}}{x^2} \, dx\)
  3.14.63 \(\int \frac {(1-3 k^2) x+2 k^2 x^3}{\sqrt [4]{(1-x^2) (1-k^2 x^2)} (-1+d+(-d+3 k^2) x^2-3 k^4 x^4+k^6 x^6)} \, dx\)
  3.14.64 \(\int \frac {-b+a x^4}{\sqrt [4]{b+a x^4} (b-a x^4+x^8)} \, dx\)
  3.14.65 \(\int \frac {-b+a x^4}{\sqrt [4]{b+a x^4} (b-a x^4+x^8)} \, dx\)
  3.14.66 \(\int \frac {(4+x^5) (1-x^4-2 x^5+x^8+x^9+x^{10})}{x^2 (-1+x^5)^{3/4} (1+x^4-2 x^5-x^8-x^9+x^{10})} \, dx\)
  3.14.67 \(\int \frac {(4+x^5) (1-x^4-2 x^5+x^8+x^9+x^{10})}{x^2 (-1+x^5)^{3/4} (1+x^4-2 x^5-x^8-x^9+x^{10})} \, dx\)
  3.14.68 \(\int \frac {1}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\)
  3.14.69 \(\int \frac {(-3 b+2 a x^2) (b^2+a^2 x^2)^{3/4}}{x} \, dx\)
  3.14.70 \(\int \frac {-1+x}{(-2-2 x+x^2) \sqrt {-1+x^3}} \, dx\)
  3.14.71 \(\int \frac {3-x+x^2}{(-2-2 x+x^2) \sqrt {-1+x^3}} \, dx\)
  3.14.72 \(\int \frac {2 x+x^2}{(-2-2 x+x^2) \sqrt {-1+x^3}} \, dx\)
  3.14.73 \(\int \frac {\sqrt [3]{-1+x^3} (1+x^3)}{x^7} \, dx\)
  3.14.74 \(\int \frac {\sqrt [3]{-1+x^3} (-1+2 x^3)}{x^7} \, dx\)
  3.14.75 \(\int \frac {(a^2-2 a x+x^2) (-2 a b x+(3 a-b) x^2)}{(x^2 (-a+x) (-b+x))^{3/4} (a^3 d-3 a^2 d x+(-b+3 a d) x^2+(1-d) x^3)} \, dx\)
  3.14.76 \(\int \frac {1+x^2}{\sqrt {\frac {-2-x+2 x^2}{-1+x+x^2}} (1-x^2+x^4)} \, dx\)
  3.14.77 \(\int \frac {-2 b+a x^4}{x^4 (b+a x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.14.78 \(\int \frac {-2 b+a x^4}{x^4 (b+a x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.14.79 \(\int \sqrt [4]{b x^3+a x^4} \, dx\)
  3.14.80 \(\int \frac {1}{x^{13} \sqrt [3]{-1+x^6}} \, dx\)
  3.14.81 \(\int \frac {b+2 a x^4}{\sqrt [4]{b+a x^4} (-2 b-a x^4+x^8)} \, dx\)
  3.14.82 \(\int \frac {2 b+a x^4}{\sqrt [4]{b x^2+a x^4} (-b-a x^4+2 x^8)} \, dx\)
  3.14.83 \(\int \frac {2 b+a x^4}{\sqrt [4]{b x^2+a x^4} (-b-a x^4+2 x^8)} \, dx\)
  3.14.84 \(\int \frac {(-1+2 x^2) (-1+4 x-4 x^2+4 x^4)}{\sqrt {\frac {1-2 x^2}{1+2 x^2}} (1+2 x^2) (-1-8 x+32 x^2-40 x^3+46 x^4-64 x^5+56 x^6-32 x^7+8 x^8)} \, dx\)
  3.14.85 \(\int \frac {\sqrt {1+x^2}}{x^2+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.14.86 \(\int \frac {\sqrt {1+x^2}}{x^2+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.14.87 \(\int \frac {1+k x^2}{(-1+c k x+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.14.88 \(\int \frac {-1+k x^2}{(1+c k x+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.14.89 \(\int x^2 \sqrt [3]{x+x^3} \, dx\)
  3.14.90 \(\int \frac {6+2 x+x^2}{\sqrt [3]{2+x^2} (1+3 x-2 x^2+x^3)} \, dx\)
  3.14.91 \(\int \frac {\sqrt [3]{x^2+x^3}}{x^2} \, dx\)
  3.14.92 \(\int \frac {\sqrt [3]{1+x^4} (3+x^4)}{x^{13}} \, dx\)
  3.14.93 \(\int \frac {(-1+x^4)^{2/3} (3+x^4) (-1+x^3+x^4)}{x^6 (-1-x^3+x^4)} \, dx\)
  3.14.94 \(\int \frac {(-3+x^4) (1+x^4)^{2/3} (1+x^3+x^4)}{x^6 (1-x^3+x^4)} \, dx\)
  3.14.95 \(\int \frac {-b+a x^2}{(b+a x^2+x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.14.96 \(\int \frac {-b+a x^2}{(b+a x^2+x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.14.97 \(\int \frac {(-1+x^3) (1+x^3)^{2/3}}{x^3 (-1-x^3+x^6)} \, dx\)
  3.14.98 \(\int \frac {(-1+x^3) (1+x^3)^{2/3}}{x^3 (-1-x^3+x^6)} \, dx\)
  3.14.99 \(\int \frac {\sqrt [3]{1+2 x^7} (-3+8 x^7)}{x^2 (1+x^3+2 x^7)} \, dx\)
  3.14.100 \(\int \frac {-b+2 a x^4}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\)