3.12.1 \(\int \frac {(4+3 x) (-1-x+x^4) \sqrt [4]{-1-x+2 x^4}}{x^6 (1+x+x^4)} \, dx\)
  3.12.2 \(\int \frac {\sqrt {1+3 x^4}}{-1+3 x^4} \, dx\)
  3.12.3 \(\int \frac {(b+a x^2) \sqrt [4]{-b x^2+a x^4}}{-b+a x^2} \, dx\)
  3.12.4 \(\int \frac {-b+2 a x^2}{(b+a x^2) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.12.5 \(\int \frac {(1+x^5)^{2/3}}{x^6} \, dx\)
  3.12.6 \(\int \frac {(1+x^5)^{2/3} (-3+2 x^5)}{x^3 (1-x^3+x^5)} \, dx\)
  3.12.7 \(\int \frac {(-1+x^5)^{2/3} (3+2 x^5)}{x^3 (-1-x^3+x^5)} \, dx\)
  3.12.8 \(\int \frac {\sqrt [4]{-1+x^6}}{x} \, dx\)
  3.12.9 \(\int \frac {1}{x^7 \sqrt [3]{1+x^6}} \, dx\)
  3.12.10 \(\int \frac {(1+x^6)^{2/3}}{x^7} \, dx\)
  3.12.11 \(\int \frac {(-3+k^2) x+2 k^2 x^3}{\sqrt [4]{(1-x^2) (1-k^2 x^2)} (-1+d+(3-d k^2) x^2-3 x^4+x^6)} \, dx\)
  3.12.12 \(\int \frac {(-1+x^7)^{2/3} (3+4 x^7)}{x^3 (-1+x^3+x^7)} \, dx\)
  3.12.13 \(\int \frac {x}{\sqrt {-b x+a^2 x^2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.12.14 \(\int \frac {-\sqrt {a b}+x}{\sqrt {x (a+x) (b+x)} (\sqrt {a b}+x)} \, dx\)
  3.12.15 \(\int \frac {1}{\sqrt [3]{-x^2+x^3}} \, dx\)
  3.12.16 \(\int \frac {3-x^2}{(1-x^2) \sqrt [4]{1-6 x^2+x^4}} \, dx\)
  3.12.17 \(\int \frac {-3+x^4}{(1+x^4) \sqrt [4]{-3 x+4 x^4-3 x^5}} \, dx\)
  3.12.18 \(\int \frac {\sqrt [3]{-1+x^6} (1+x^6)}{x^2 (-1+x^3+x^6)} \, dx\)
  3.12.19 \(\int \frac {(-1+x^4) \sqrt {1+x^4}}{1+x^2+3 x^4+x^6+x^8} \, dx\)
  3.12.20 \(\int \frac {-1+2 x^8}{\sqrt [4]{1+x^4} (-1+x^8)} \, dx\)
  3.12.21 \(\int \sqrt [4]{b x^5+a x^8} \, dx\)
  3.12.22 \(\int \frac {\sqrt {x-\sqrt {1+x^2}}}{1-\sqrt {1+x^2}} \, dx\)
  3.12.23 \(\int \frac {(-1+x) (3+x)}{(-1+x^2)^{2/3} (2-x+x^2)} \, dx\)
  3.12.24 \(\int \frac {\sqrt [3]{-1+x^3}}{x^4} \, dx\)
  3.12.25 \(\int \frac {(-1+x^3)^{2/3}}{x^4} \, dx\)
  3.12.26 \(\int \frac {\sqrt [3]{1+x^3}}{x^2} \, dx\)
  3.12.27 \(\int \frac {-1+x}{(1+x) \sqrt [3]{2+x^3}} \, dx\)
  3.12.28 \(\int \frac {1}{x^7 (b+a x^3)^{3/4}} \, dx\)
  3.12.29 \(\int \frac {(1+2 x+x^2) (-2-(-1+k) (1+k) x+2 k^2 x^2)}{((1-x^2) (1-k^2 x^2))^{3/4} (1-d-(1+3 d) x-(3 d+k^2) x^2+(-d+k^2) x^3)} \, dx\)
  3.12.30 \(\int \frac {1}{x^5 \sqrt [3]{-1+x^4}} \, dx\)
  3.12.31 \(\int \frac {x (-b+x) (a b-2 a x+x^2)}{\sqrt {x (-a+x) (-b+x)} (-a^2 d+2 a d x+(b^2-d) x^2-2 b x^3+x^4)} \, dx\)
  3.12.32 \(\int \frac {1}{x^9 (b+a x^4)^{3/4}} \, dx\)
  3.12.33 \(\int x^4 (b+a x^4)^{3/4} \, dx\)
  3.12.34 \(\int \frac {(-1+x^5)^{2/3}}{x^6} \, dx\)
  3.12.35 \(\int \frac {1}{x^{11} (b+a x^5)^{3/4}} \, dx\)
  3.12.36 \(\int \frac {1}{x^7 \sqrt [3]{-1+x^6}} \, dx\)
  3.12.37 \(\int \frac {(-1+x^6)^{2/3}}{x^7} \, dx\)
  3.12.38 \(\int \frac {(-1+x^4+2 x^6) \sqrt [3]{x+x^5+x^7}}{(1+x^4+x^6) (1-x^2+x^4+x^6)} \, dx\)
  3.12.39 \(\int \frac {\sqrt {1+\sqrt {1+x}}}{x-\sqrt {1+x}} \, dx\)
  3.12.40 \(\int \frac {1}{x^3 (-1+x^2)^{3/4}} \, dx\)
  3.12.41 \(\int \frac {(-1+x^3)^{2/3}}{x^3} \, dx\)
  3.12.42 \(\int \frac {2+x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.12.43 \(\int \frac {(1+x^3)^{2/3}}{x^3} \, dx\)
  3.12.44 \(\int \frac {2 a b x+(-3 a+b) x^2}{\sqrt [4]{x^2 (-a+x) (-b+x)} (a^3-3 a^2 x+(3 a-b d) x^2+(-1+d) x^3)} \, dx\)
  3.12.45 \(\int \frac {\sqrt [4]{-1+x^4}}{x^5} \, dx\)
  3.12.46 \(\int \frac {1+x^2}{(-1+x+x^2) \sqrt [3]{-x^2+x^4}} \, dx\)
  3.12.47 \(\int \frac {(-1+2 x) (2-x+x^2) \sqrt {-2+x^2-2 x^3+x^4}}{3-2 x+2 x^2} \, dx\)
  3.12.48 \(\int \frac {\sqrt [4]{-x^3+x^4}}{x (1+x)} \, dx\)
  3.12.49 \(\int \frac {1+2 x^3}{(-1+x+x^3) \sqrt [3]{-x^2+x^5}} \, dx\)
  3.12.50 \(\int \frac {\sqrt [4]{-1+x^6}}{x^7} \, dx\)
  3.12.51 \(\int \frac {1+3 x^4}{(-1+x+x^4) \sqrt [3]{-x^2+x^6}} \, dx\)
  3.12.52 \(\int \frac {(2+x^3) \sqrt {-1-x^2+x^3}}{1-x^2-2 x^3-x^4+x^5+x^6} \, dx\)
  3.12.53 \(\int \frac {(1+x^4) \sqrt {-1-x^2+x^4}}{1-x^2-3 x^4+x^6+x^8} \, dx\)
  3.12.54 \(\int \frac {x^2 \sqrt {x+\sqrt {1+x}}}{\sqrt {1+x}} \, dx\)
  3.12.55 \(\int (-1+x^3)^{2/3} \, dx\)
  3.12.56 \(\int (1+x^3)^{2/3} \, dx\)
  3.12.57 \(\int \frac {-1+x^3}{\sqrt [3]{2+x^3}} \, dx\)
  3.12.58 \(\int \sqrt [3]{x+x^3} \, dx\)
  3.12.59 \(\int \frac {(-2 k+(-1+k) (1+k) x+2 k x^2) (1+2 k x+k^2 x^2)}{((1-x^2) (1-k^2 x^2))^{3/4} (-1+d+(1+3 d) k x+(1+3 d k^2) x^2+k (-1+d k^2) x^3)} \, dx\)
  3.12.60 \(\int \frac {(-1+x^4)^{3/4} (4+x^4)}{x^8 (-4+x^4)} \, dx\)
  3.12.61 \(\int \frac {4 b+a x^3}{\sqrt [4]{b+a x^3} (b+a x^3+x^4)} \, dx\)
  3.12.62 \(\int \frac {-a^2 b+a (2 a+b) x-3 a x^2+x^3}{\sqrt {x (-a+x) (-b+x)} (-a^2 d+2 a d x+(b^2-d) x^2-2 b x^3+x^4)} \, dx\)
  3.12.63 \(\int \frac {-2 b+a x^4}{x^4 \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.12.64 \(\int \frac {2 b+a x^4}{x^4 \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.12.65 \(\int \frac {-1+x}{(1+x) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.12.66 \(\int \frac {1+x}{(-1+x) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.12.67 \(\int \frac {x^2}{\sqrt {(1-x^2) (1-k^2 x^2)} (-1+k^2 x^4)} \, dx\)
  3.12.68 \(\int \frac {(-1+x^6)^{2/3} (1+x^6)}{x^3 (-1-x^3+x^6)} \, dx\)
  3.12.69 \(\int \frac {(-1+x^6) (1+x^6)^{2/3}}{x^3 (1-x^3+x^6)} \, dx\)
  3.12.70 \(\int \frac {1+3 x^4+x^8}{x^2 (1+x^4)^{3/4} (1+3 x^4+3 x^8)} \, dx\)
  3.12.71 \(\int \frac {-1+x}{x^4 \sqrt [3]{1+x^3}} \, dx\)
  3.12.72 \(\int \frac {(3+2 x) \sqrt [3]{1+x+x^3}}{x^2 (1+x)} \, dx\)
  3.12.73 \(\int \frac {(a^2-2 a x+x^2) (-a b+2 (a-b) x+x^2)}{(x (-a+x) (-b+x))^{3/4} (-a^3 d+(b+3 a^2 d) x-(1+3 a d) x^2+d x^3)} \, dx\)
  3.12.74 \(\int \frac {(1+x^2)^2}{(1-x^2) (1-6 x^2+x^4)^{3/4}} \, dx\)
  3.12.75 \(\int \frac {(-4+x^3) (1-x^3+x^4)}{x^2 (-1+x^3)^{3/4} (-1+x^3+x^4)} \, dx\)
  3.12.76 \(\int \frac {(-1+x^4) (3+x^4) (-1-x^3+x^4)}{x^6 (-1-2 x^3+x^4) \sqrt [4]{-x+x^5}} \, dx\)
  3.12.77 \(\int \frac {(4 b+a x^5) (-b+c x^4+a x^5)}{x^2 (-b+a x^5)^{3/4} (-b-c x^4+a x^5)} \, dx\)
  3.12.78 \(\int \frac {(-2+x^6) (1-x^4+x^6)}{x^4 \sqrt [4]{1+x^6} (1+x^4+x^6)} \, dx\)
  3.12.79 \(\int \frac {x^4 (2 b+a x^6)}{\sqrt [4]{-b+a x^6} (-b-x^4+a x^6)^2} \, dx\)
  3.12.80 \(\int \frac {(2 b+a x^6) (-b-x^4+a x^6)}{x^4 \sqrt [4]{-b+a x^6} (-b-2 x^4+a x^6)} \, dx\)
  3.12.81 \(\int \frac {\sqrt {-1-2 x^2-2 x^3-x^8} (-1+x^3+3 x^8)}{(1+2 x^3+x^8) (1+x^2+2 x^3+x^8)} \, dx\)
  3.12.82 \(\int \frac {(1+x^6) \sqrt {-2-x^2+x^6}}{4-3 x^4-4 x^6+x^{12}} \, dx\)
  3.12.83 \(\int x \sqrt [3]{-1+x^3} \, dx\)
  3.12.84 \(\int x \sqrt [3]{1+x^3} \, dx\)
  3.12.85 \(\int \frac {\sqrt [3]{x+x^3}}{x^2} \, dx\)
  3.12.86 \(\int \frac {(-1+x) (-1+k x) (3-2 (1+k) x+k x^2)}{x ((1-x) x (1-k x))^{3/4} (-1+(1+k) x-k x^2+d x^3)} \, dx\)
  3.12.87 \(\int \frac {(1-2 x+x^2) (-2+(-1+k) (1+k) x+2 k^2 x^2)}{((1-x^2) (1-k^2 x^2))^{3/4} (-1+d-(1+3 d) x+(3 d+k^2) x^2+(-d+k^2) x^3)} \, dx\)
  3.12.88 \(\int \frac {x^2}{(-b+a x^2) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.12.89 \(\int \frac {\sqrt {q+p x^5} (-2 q+3 p x^5) (a q+b x^2+a p x^5)}{x^4 (c q+d x^2+c p x^5)} \, dx\)
  3.12.90 \(\int \frac {x}{\sqrt [3]{x^2+x^6}} \, dx\)
  3.12.91 \(\int \frac {-1+x^4}{(1+x^2+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.12.92 \(\int \frac {-1+x^4}{(1+x^2+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.12.93 \(\int \frac {x^2 (2 b+a x^6)}{(-b+a x^6)^{3/4} (-b-2 c x^4+a x^6)} \, dx\)
  3.12.94 \(\int \frac {1+b x+k^2 x^2}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^2 x^2)} \, dx\)
  3.12.95 \(\int \frac {\sqrt [3]{-1+x^3}}{x^7} \, dx\)
  3.12.96 \(\int \frac {\sqrt [3]{1+x^3}}{x^7} \, dx\)
  3.12.97 \(\int \frac {(-1+x^3) \sqrt [3]{1+x^3}}{x^4} \, dx\)
  3.12.98 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {-x-x^2+x^3}} \, dx\)
  3.12.99 \(\int \frac {\sqrt [3]{x^2+x^3}}{x} \, dx\)
  3.12.100 \(\int \frac {(1+x^3)^{2/3} (2+x^3)}{x^6 (1+2 x^3)} \, dx\)