3.21.1 \(\int \frac {-1+2 x^4}{\sqrt [4]{1+x^4} (-1+x^4+x^8)} \, dx\)
  3.21.2 \(\int \frac {(-2 x+(1+k) x^2) (a-a (1+k) x+(1+a k) x^2)}{(-1+x) ((1-x) x (1-k x))^{2/3} (-1+k x) (b-b (1+k) x+(-1+b k) x^2)} \, dx\)
  3.21.3 \(\int \frac {-3 k+2 (1+k^2) x+k (1+k^2) x^2-4 k^2 x^3+k^3 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d-(2+d) k x+(d+k^2) x^2+d k x^3)} \, dx\)
  3.21.4 \(\int \frac {x (4 a b-3 (a+b) x+2 x^2)}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a b+(a+b) x-x^2+d x^4)} \, dx\)
  3.21.5 \(\int \frac {x^2}{(x^2 (-a+x))^{2/3} (-a^2+2 a x+(-1+d) x^2)} \, dx\)
  3.21.6 \(\int \frac {(-2+(1+k) x) (1-(1+k) x+(a+k) x^2)}{x ((1-x) x (1-k x))^{2/3} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.21.7 \(\int \frac {-2 a^2 b x+a (3 a+2 b) x^2-4 a x^3+x^4}{(x^2 (-a+x) (-b+x))^{2/3} (-a^2+2 a x-(1+b d) x^2+d x^3)} \, dx\)
  3.21.8 \(\int \frac {1}{\sqrt [3]{-8+12 x+54 x^2-135 x^3+81 x^4}} \, dx\)
  3.21.9 \(\int \frac {1+x^2}{(-1-x+x^2) \sqrt [3]{-1+x^6}} \, dx\)
  3.21.10 \(\int \frac {1+x^2}{(-1-x+x^2) \sqrt [3]{-1+x^6}} \, dx\)
  3.21.11 \(\int \frac {(2-2 x^4+3 x^5+4 x^6) \sqrt [3]{-x+2 x^3-x^5+x^6+x^7}}{(-1+x^2-x^4+x^5+x^6)^2} \, dx\)
  3.21.12 \(\int \frac {-1+(-1+2 k) x}{\sqrt [3]{(1-x) x (1-k x)} (b-(1+2 b) x+(b+k) x^2)} \, dx\)
  3.21.13 \(\int \frac {\sqrt {b^2+a^2 x^3} (2 b^2+c x^3+a^2 x^6)}{x^7 (-b^2+a^2 x^6)} \, dx\)
  3.21.14 \(\int \frac {x^7 (-4 a+3 x)}{(x^2 (-a+x))^{2/3} (-a^2+2 a x-x^2+d x^8)} \, dx\)
  3.21.15 \(\int \frac {-1+2 x+(-2 k+k^2) x^2}{((1-x) x (1-k x))^{2/3} (b-(1+2 b k) x+(1+b k^2) x^2)} \, dx\)
  3.21.16 \(\int \frac {\sqrt [3]{-x^2+x^4}}{x (1+x^2)} \, dx\)
  3.21.17 \(\int \frac {b+a x^6}{x^3 (-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.21.18 \(\int \frac {3+x}{\sqrt [3]{-1+x^2} (5-x+2 x^2)} \, dx\)
  3.21.19 \(\int \frac {(-2+(1+k) x) (1-(1+k) x+(a+k) x^2)}{x^2 \sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.21.20 \(\int \frac {(-2+x^3) \sqrt [3]{x+x^3+x^4}}{(1+x^3) (1-x^2+x^3)} \, dx\)
  3.21.21 \(\int \frac {(1+x^3)^{2/3} (-1+2 x^6)}{x^6 (-1+2 x^3)} \, dx\)
  3.21.22 \(\int \frac {-b+a x^4}{(b+a x^4) \sqrt [4]{b^2+c x^4+a^2 x^8}} \, dx\)
  3.21.23 \(\int \frac {(2+x)^2 \sqrt [3]{-19+66 x-30 x^2+9 x^3}}{(-3+2 x)^2 (-5+6 x-6 x^2+x^3)} \, dx\)
  3.21.24 \(\int \frac {1+x^3}{(-1+x^3) \sqrt [3]{x^2+x^4}} \, dx\)
  3.21.25 \(\int \frac {x (4 a b-3 (a+b) x+2 x^2)}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a b d+(a+b) d x-d x^2+x^4)} \, dx\)
  3.21.26 \(\int \frac {\sqrt {b+a x^4}}{-b+a x^4} \, dx\)
  3.21.27 \(\int \frac {1+x^2}{(-1+x+x^2) \sqrt [3]{-1+x^6}} \, dx\)
  3.21.28 \(\int \frac {1+x^2}{(-1+x+x^2) \sqrt [3]{-1+x^6}} \, dx\)
  3.21.29 \(\int \frac {(-b^2+a x^2)^2}{(b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.21.30 \(\int \frac {(-2+(1+k) x) (a-a (1+k) x+(1+a k) x^2)}{(-1+x) \sqrt [3]{(1-x) x (1-k x)} (-1+k x) (b-b (1+k) x+(-1+b k) x^2)} \, dx\)
  3.21.31 \(\int \frac {(b+x^3)^3}{\sqrt [3]{a+x^3}} \, dx\)
  3.21.32 \(\int \frac {-3+(1-2 k^2) x+3 k^2 x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d-(2+d) x-(1+d k^2) x^2+d k^2 x^3)} \, dx\)
  3.21.33 \(\int \frac {x^2}{(-b+a x^4) \sqrt {b+a x^4}} \, dx\)
  3.21.34 \(\int \frac {(-1+x) (-1+k x) (-2+(1+k) x)}{\sqrt [3]{(1-x) x (1-k x)} (b-2 (b+b k) x+(b+4 b k+b k^2) x^2-2 b k (1+k) x^3+(-1+b k^2) x^4)} \, dx\)
  3.21.35 \(\int \frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{x^2} \, dx\)
  3.21.36 \(\int \frac {\sqrt [3]{x^2+x^4}}{x (-1+x^2)} \, dx\)
  3.21.37 \(\int \frac {1}{(c+d x) \sqrt {b+a^2 x^2} \sqrt {a x-\sqrt {b+a^2 x^2}}} \, dx\)
  3.21.38 \(\int \frac {\sqrt {1+x} \sqrt {1+\sqrt {1+x}}}{x^2 \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.21.39 \(\int \frac {-1+(2-k) x}{\sqrt [3]{(1-x) x (1-k x)} (b-(1+2 b k) x+(1+b k^2) x^2)} \, dx\)
  3.21.40 \(\int \frac {3+(1-2 k^2) x-3 k^2 x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d-(2+d) x+(1+d k^2) x^2+d k^2 x^3)} \, dx\)
  3.21.41 \(\int \frac {(1+x^3)^{2/3} (8-4 x^3+x^6)}{x^6 (2+x^3)} \, dx\)
  3.21.42 \(\int \frac {(-1+x^3)^{2/3} (8+2 x^3+x^6)}{x^6 (-2+x^3)} \, dx\)
  3.21.43 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (c x^4+b x^2 (q+p x^3)+a (q+p x^3)^2)}{x^9} \, dx\)
  3.21.44 \(\int \frac {-b+a x^2}{\sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.21.45 \(\int \frac {b+a x^2}{\sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.21.46 \(\int \frac {-a^2 b+4 a b x-(2 a+3 b) x^2+2 x^3}{\sqrt [4]{x (-a+x)^2 (-b+x)^3} (b+(-1+a^2 d) x-2 a d x^2+d x^3)} \, dx\)
  3.21.47 \(\int \frac {a b^3-(6 a-b) b^2 x+9 a b x^2-(4 a+3 b) x^3+2 x^4}{\sqrt [4]{x (-a+x)^2 (-b+x)^3} (-a^2+(2 a-b^3 d) x+(-1+3 b^2 d) x^2-3 b d x^3+d x^4)} \, dx\)
  3.21.48 \(\int \frac {1}{(d+c x) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.21.49 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b q x+c x^2+b p x^4+a (q+p x^3)^2)}{x^5} \, dx\)
  3.21.50 \(\int \frac {-a (a-2 b)-2 b x+x^2}{((-a+x) (-b+x))^{2/3} (a^2+b d-(2 a+d) x+x^2)} \, dx\)
  3.21.51 \(\int \frac {a-2 b+x}{\sqrt [3]{(-a+x) (-b+x)} (b+a^2 d+(-1-2 a d) x+d x^2)} \, dx\)
  3.21.52 \(\int \frac {a-2 b+x}{\sqrt [3]{(-a+x) (-b+x)} (b+a^2 d-(1+2 a d) x+d x^2)} \, dx\)
  3.21.53 \(\int \frac {-1+2 k x+(1-2 k) x^2}{((1-x) x (1-k x))^{2/3} (b-(1+2 b) x+(b+k) x^2)} \, dx\)
  3.21.54 \(\int \frac {-1+x}{(1+x) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.21.55 \(\int \frac {(-1+x+x^3+x^6)^{2/3} (3-2 x+3 x^6)}{(-1+x+x^6) (-1+x-x^3+x^6)} \, dx\)
  3.21.56 \(\int \frac {-1-2 x^4+2 x^8}{\sqrt [4]{-1+x^4} (-1-x^4+x^8)} \, dx\)
  3.21.57 \(\int \frac {-1+2 x^4+2 x^8}{\sqrt [4]{1+x^4} (-1+x^4+x^8)} \, dx\)
  3.21.58 \(\int \frac {-a b+(2 a-b) x}{\sqrt [3]{x (-a+x) (-b+x)} (-a^2+(2 a-b d) x+(-1+d) x^2)} \, dx\)
  3.21.59 \(\int \frac {x}{(1+x) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.21.60 \(\int \frac {\sqrt [3]{-x^2+x^3}}{-1+x^2} \, dx\)
  3.21.61 \(\int x^2 \sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\)
  3.21.62 \(\int \frac {(-b x+a^2 x^2)^{3/2}}{(a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.21.63 \(\int \frac {-3 k+(-2+k^2) x+3 k x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d-(2+d) k x-(d+k^2) x^2+d k x^3)} \, dx\)
  3.21.64 \(\int \frac {a+b x}{x (-d+c x) \sqrt [4]{-x^3+x^4}} \, dx\)
  3.21.65 \(\int \frac {(-4+3 x) \sqrt [4]{\frac {-a+a x+b x^4}{-c+c x+d x^4}}}{(-1+x) x} \, dx\)
  3.21.66 \(\int \frac {(1+x^3)^{2/3} (1-2 x^3+2 x^6)}{x^6 (-1-x^3+2 x^6)} \, dx\)
  3.21.67 \(\int \frac {2}{(3+x) (2-8 x+8 x^2)^{2/3}} \, dx\)
  3.21.68 \(\int \frac {1-(-3+2 k) x-(4+k) x^2+3 k x^3}{\sqrt [3]{(1-x) x (1-k x)} (-1+(5+b) x-(10+b k) x^2+10 x^3-5 x^4+x^5)} \, dx\)
  3.21.69 \(\int \frac {1}{x \sqrt [3]{(1+x) (q+2 q x+x^2)}} \, dx\)
  3.21.70 \(\int \frac {-1+2 x+(-2 k+k^2) x^2}{((1-x) x (1-k x))^{2/3} (1-(b+2 k) x+(b+k^2) x^2)} \, dx\)
  3.21.71 \(\int \frac {3 k+(-2+k^2) x-3 k x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d-(2+d) k x+(d+k^2) x^2+d k x^3)} \, dx\)
  3.21.72 \(\int \frac {3+2 (1+k^2) x-(1+k^2) x^2-4 k^2 x^3-k^2 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d-(1+2 d) x-(d+k^2) x^2+k^2 x^3)} \, dx\)
  3.21.73 \(\int \frac {\sqrt [4]{\frac {-1+x}{1+2 x}}-3 (\frac {-1+x}{1+2 x})^{3/4}}{(-1+x) (1+x)^2 (-1+2 x)} \, dx\)
  3.21.74 \(\int \frac {(-1+x^2)^2}{(1+x^2)^2 \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.21.75 \(\int \frac {-3+2 (1+k^2) x+(1+k^2) x^2-4 k^2 x^3+k^2 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d+(-1-2 d) x+(d+k^2) x^2+k^2 x^3)} \, dx\)
  3.21.76 \(\int \frac {x^3 (-2+(1+k) x)}{((1-x) x (1-k x))^{2/3} (1-(2+2 k) x+(1+4 k+k^2) x^2-(2 k+2 k^2) x^3+(-b+k^2) x^4)} \, dx\)
  3.21.77 \(\int \frac {(1+x^2)^2}{(-1+x^2)^2 \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.21.78 \(\int \frac {(-1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}}{(1+x^2)^2 \sqrt {1+x^4}} \, dx\)
  3.21.79 \(\int \frac {(-2+x) \sqrt [3]{x-x^2+x^3}}{(-1+x) (-1+x+x^2)} \, dx\)
  3.21.80 \(\int \frac {(1+x^2) \sqrt [3]{x^2+x^3}}{-1+x^2} \, dx\)
  3.21.81 \(\int \frac {-b+a x}{x \sqrt [3]{-b^3+a^3 x^3}} \, dx\)
  3.21.82 \(\int \frac {(-2+x^3) \sqrt [3]{x+2 x^3+x^4}}{(1+x^3) (1+x^2+x^3)} \, dx\)
  3.21.83 \(\int \frac {x^4}{\sqrt [4]{-1+x^4} (1-2 x^4+2 x^8)} \, dx\)
  3.21.84 \(\int \frac {(-1+x^4)^{3/4}}{1-2 x^4+2 x^8} \, dx\)
  3.21.85 \(\int \frac {x^4}{\sqrt [4]{1+x^4} (1+2 x^4+2 x^8)} \, dx\)
  3.21.86 \(\int \frac {(1+x^4)^{3/4}}{1+2 x^4+2 x^8} \, dx\)
  3.21.87 \(\int \frac {x^2 \sqrt {-b x+a^2 x^2}}{(a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.21.88 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{(1+x) \sqrt {1+x^4}} \, dx\)
  3.21.89 \(\int \frac {2 a b x-3 a x^2+x^3}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a^2+2 a x-(1+b d) x^2+d x^3)} \, dx\)
  3.21.90 \(\int \frac {(-2+k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d+(-2+d k^2) x^2+x^4)} \, dx\)
  3.21.91 \(\int \frac {(1+2 x) \sqrt [4]{x^3+x^4}}{-1+x+x^2} \, dx\)
  3.21.92 \(\int \frac {(-1+2 k^2) x-2 k^4 x^3+k^4 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d+(1-2 d k^2) x^2+d k^4 x^4)} \, dx\)
  3.21.93 \(\int \frac {(-a+x) (-b+x) (-2 a b+(a+b) x)}{\sqrt [3]{x (-a+x) (-b+x)} (a^2 b^2 d-2 a b (a+b) d x+(a^2+4 a b+b^2) d x^2-2 (a+b) d x^3+(-1+d) x^4)} \, dx\)
  3.21.94 \(\int \frac {\sqrt {b^2+a^2 x^3} (2 b^2+c x^3+a^2 x^6)}{x (b^2+a^2 x^6)} \, dx\)
  3.21.95 \(\int \frac {\sqrt {x+x^4} (b+a x^6)}{-d+c x^6} \, dx\)
  3.21.96 \(\int \frac {x (-1+k x) (1-2 k x+(-1+2 k) x^2)}{((1-x) x (1-k x))^{2/3} (-1+4 x+(-6+b) x^2+(4-2 b k) x^3+(-1+b k^2) x^4)} \, dx\)
  3.21.97 \(\int \frac {-3 a q+4 b p x^3+a p x^4}{\sqrt [3]{q+p x^4} (b^3 d+c q+3 a b^2 d x+3 a^2 b d x^2+a^3 d x^3+c p x^4)} \, dx\)
  3.21.98 \(\int \frac {3+(-1+2 k^2) x-3 k^2 x^2-k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d-(1+2 d) x-(d+k^2) x^2+k^2 x^3)} \, dx\)
  3.21.99 \(\int \frac {3+(1-2 k^2) x-3 k^2 x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d-(1+2 d) x+(d+k^2) x^2+k^2 x^3)} \, dx\)
  3.21.100 \(\int \frac {\sqrt {-b^4+a^4 x^4} (b^4+a^4 x^4)}{b^8-c x^4+a^8 x^8} \, dx\)