3.22.1 \(\int \frac {(-1+x^4)^{3/4}}{-1+2 x^4+x^8} \, dx\)
  3.22.2 \(\int \frac {1+x^4}{(-1+x^4) \sqrt {1+\sqrt {1+x^2}}} \, dx\)
  3.22.3 \(\int \frac {1}{x^3 (-b+a x^2)^{3/4}} \, dx\)
  3.22.4 \(\int \frac {a b-2 b x+x^2}{\sqrt [4]{x (-a+x) (-b+x)^3} (b-(1+a d) x+d x^2)} \, dx\)
  3.22.5 \(\int \frac {1}{x^4 (-b+a x^3)^{3/4}} \, dx\)
  3.22.6 \(\int \frac {1}{x^4 \sqrt [4]{-b+a x^3}} \, dx\)
  3.22.7 \(\int \frac {(2+x) (-1-x+x^2) \sqrt [4]{\frac {1+x-2 x^2}{1+x+4 x^2}}}{2 x (1+2 x+x^2+x^4)} \, dx\)
  3.22.8 \(\int \frac {1+x^4}{(-1+x^4) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
  3.22.9 \(\int \frac {1}{x^5 (-b+a x^4)^{3/4}} \, dx\)
  3.22.10 \(\int \frac {a b^3-2 (3 a-b) b^2 x+3 (3 a-b) b x^2-4 a x^3+x^4}{\sqrt [4]{x (-a+x) (-b+x)^3} (a^3-(3 a^2+b^3 d) x+3 (a+b^2 d) x^2-(1+3 b d) x^3+d x^4)} \, dx\)
  3.22.11 \(\int \frac {1}{x^6 (-b+a x^5)^{3/4}} \, dx\)
  3.22.12 \(\int \frac {1}{x^7 (-b+a x^6)^{3/4}} \, dx\)
  3.22.13 \(\int \frac {b^6+a^6 x^6}{\sqrt {b^4+a^4 x^4} (-b^6+a^6 x^6)} \, dx\)
  3.22.14 \(\int \frac {\sqrt {-1+x^2} \sqrt {x^2+x \sqrt {-1+x^2}}}{1+x} \, dx\)
  3.22.15 \(\int \frac {(1+x^4) \sqrt {1+\sqrt {1+x^2}}}{-1+x^4} \, dx\)
  3.22.16 \(\int \frac {-b^2+a x^2}{(b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.22.17 \(\int \frac {x}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.22.18 \(\int \frac {-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} (b-b (1+k) x+(-1+b k) x^2)} \, dx\)
  3.22.19 \(\int \frac {(-b+a x^2) \sqrt {-b x+a x^3}}{x^2 (b+a x^2)} \, dx\)
  3.22.20 \(\int \frac {\sqrt [4]{-x^3+x^4}}{x (1+x^3)} \, dx\)
  3.22.21 \(\int \frac {\sqrt [4]{-x^3+x^4}}{x (1+x^3)} \, dx\)
  3.22.22 \(\int \frac {(-3+x^4) (1-x^3+x^4)^{2/3}}{x^3 (1+x^3+x^4)} \, dx\)
  3.22.23 \(\int \frac {(-4 b+a x^5) (b+a x^5)^{3/4}}{x^4 (2 b+c x^4+2 a x^5)} \, dx\)
  3.22.24 \(\int \frac {-1+x^6}{\sqrt [3]{x^2+x^4} (1+x^6)} \, dx\)
  3.22.25 \(\int \frac {\sqrt [4]{2+3 x^4} (4+6 x^4+x^8)}{x^6 (1+x^4) (1+2 x^4)} \, dx\)
  3.22.26 \(\int \frac {\sqrt [8]{256-256 x^2+96 x^4-16 x^6+x^8}}{-1+x^3} \, dx\)
  3.22.27 \(\int \frac {-36-6 x^2+6 x^3+x^6}{x (-6+x^3) \sqrt [6]{\frac {6+x^3}{-6+x^3}} (36-90 x+122 x^2-96 x^3+51 x^4-26 x^5+15 x^6-6 x^7+x^8)} \, dx\)
  3.22.28 \(\int \frac {2 b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-2 b+a x^4+x^8)} \, dx\)
  3.22.29 \(\int \frac {2 b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-2 b+a x^4+x^8)} \, dx\)
  3.22.30 \(\int \frac {-b+a x^8}{(b+a x^8) \sqrt [4]{b-c x^4+a x^8}} \, dx\)
  3.22.31 \(\int \frac {1}{x^2 \sqrt {-b x+a^2 x^2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.22.32 \(\int \frac {1+\sqrt {1+x^2}}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.22.33 \(\int \frac {-2+(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (b-b (1+k) x+(-1+b k) x^2)} \, dx\)
  3.22.34 \(\int \frac {\sqrt [4]{-b+a x^4} (-8 b+a x^8)}{x^{10} (b+a x^4)} \, dx\)
  3.22.35 \(\int \frac {x}{x+\sqrt {x+\sqrt {1+x}}} \, dx\)
  3.22.36 \(\int \frac {x}{x+\sqrt {x+\sqrt {1+x}}} \, dx\)
  3.22.37 \(\int \frac {(-6+x^2) (-2+x^2) (2-x^2+x^3) \sqrt [3]{-2+x^2+2 x^3}}{x^5 (-2+x^2+x^3)^2} \, dx\)
  3.22.38 \(\int \frac {(-1+x) \sqrt [4]{-x^3+x^4}}{x (1+x^3)} \, dx\)
  3.22.39 \(\int \frac {(-1+x) \sqrt [4]{-x^3+x^4}}{x (1+x^3)} \, dx\)
  3.22.40 \(\int \frac {(1+x) \sqrt [4]{x^3+x^5}}{x (-1+x^3)} \, dx\)
  3.22.41 \(\int \frac {x^3}{\sqrt [3]{-b x^2+a x^3} (-b^2+a^2 x^6)} \, dx\)
  3.22.42 \(\int \frac {1+x^2}{(-1+x^2) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.22.43 \(\int \frac {1+x^2}{(-1+x^2) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.22.44 \(\int \frac {-1+x+x^3}{(1-x+x^3) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.22.45 \(\int \frac {-1+x+x^3}{(1-x+x^3) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.22.46 \(\int \frac {(1+2 x^3)^{4/3} (1+3 x^3)}{x^8 (1+4 x^3)} \, dx\)
  3.22.47 \(\int \frac {-1+x^2}{(1+x^2) \sqrt [3]{-x^2+x^4}} \, dx\)
  3.22.48 \(\int \frac {\sqrt [4]{-b x^2+a x^4} (-b+2 a x^4)}{b+a x^4} \, dx\)
  3.22.49 \(\int \frac {\sqrt [4]{-b x^2+a x^4} (-b+2 a x^4)}{b+a x^4} \, dx\)
  3.22.50 \(\int \frac {x^3 (-4 a+3 x)}{(x^2 (-a+x))^{2/3} (a-x+d x^4)} \, dx\)
  3.22.51 \(\int \frac {b+a x^6}{x^6 (b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\)
  3.22.52 \(\int \frac {-1+x^2}{\sqrt {1+x} (1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\)
  3.22.53 \(\int \frac {-1+x^2}{\sqrt {1+x} (1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\)
  3.22.54 \(\int x^2 \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\)
  3.22.55 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [3]{a x+\sqrt {-b+a^2 x^2}} \sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.22.56 \(\int \frac {(2 a-3 b+x) (-a^3+3 a^2 x-3 a x^2+x^3)}{(-b+x) \sqrt [4]{(-a+x) (-b+x)^2} (-a^3-b^2 d+(3 a^2+2 b d) x-(3 a+d) x^2+x^3)} \, dx\)
  3.22.57 \(\int \frac {(2-x+2 x^2) \sqrt [4]{-x^3+x^4}}{-2-2 x+x^2} \, dx\)
  3.22.58 \(\int \frac {(2-x+2 x^2) \sqrt [4]{-x^3+x^4}}{-2-2 x+x^2} \, dx\)
  3.22.59 \(\int \frac {\sqrt {1-3 x^2-2 x^4} (1+2 x^4)}{(-1+x^2+2 x^4) (-1+2 x^2+2 x^4)} \, dx\)
  3.22.60 \(\int \frac {\sqrt [4]{b x^2+a x^4} (-b+2 a x^4)}{-2 b+a x^4} \, dx\)
  3.22.61 \(\int \frac {\sqrt [4]{b x^2+a x^4} (-b+2 a x^4)}{-2 b+a x^4} \, dx\)
  3.22.62 \(\int \frac {x (-4 a+3 x)}{\sqrt [3]{x^2 (-a+x)} (a-x+d x^4)} \, dx\)
  3.22.63 \(\int \frac {-b-2 a x^4+2 x^8}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\)
  3.22.64 \(\int \frac {-b-2 a x^4+2 x^8}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\)
  3.22.65 \(\int \frac {1}{(-1+x^2) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.22.66 \(\int \frac {-b^2+a^2 x^4}{\sqrt {-b x+a x^3} (b^2+c x^2+a^2 x^4)} \, dx\)
  3.22.67 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x (b x^2+a (q+p x^3)^2)} \, dx\)
  3.22.68 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x (b x^4+a (q+p x^3)^2)} \, dx\)
  3.22.69 \(\int \frac {x^2-\sqrt {1+x^2}}{x^2+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.22.70 \(\int \frac {x^2-\sqrt {1+x^2}}{x^2+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.22.71 \(\int \frac {\sqrt {1+\sqrt {1-\sqrt {1+\frac {1}{x^2}}}}}{x} \, dx\)
  3.22.72 \(\int \frac {-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.22.73 \(\int \frac {2-(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx\)
  3.22.74 \(\int \frac {-2+(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.22.75 \(\int \frac {(3+2 x^2) (1+2 x^2+2 x^3)^{2/3}}{x^3 (-1-2 x^2+x^3)} \, dx\)
  3.22.76 \(\int \frac {-b+c x+a x^2}{(b+a x^2) \sqrt {-b x+a x^3}} \, dx\)
  3.22.77 \(\int \frac {-4-2 x+2 x^2+x^4}{x (-2+x^2) \sqrt [4]{\frac {2+x^2}{-2+x^2}} (8-10 x+4 x^2+4 x^3-4 x^4+x^5)} \, dx\)
  3.22.78 \(\int \frac {\sqrt {1+x} (-1+x^4) \sqrt {1+\sqrt {1+x}}}{1+x^4} \, dx\)
  3.22.79 \(\int \frac {\sqrt {1+x} (-1+x^4) \sqrt {1+\sqrt {1+x}}}{1+x^4} \, dx\)
  3.22.80 \(\int \frac {-d+c x}{x^4 \sqrt [3]{-b+a x^3}} \, dx\)
  3.22.81 \(\int \frac {\sqrt [4]{-b x^3+a x^4} (-d+c x^4)}{x^2} \, dx\)
  3.22.82 \(\int \frac {x^3 (5-4 (1+k) x+3 k x^2)}{((1-x) x (1-k x))^{2/3} (-b+b (1+k) x-b k x^2+x^5)} \, dx\)
  3.22.83 \(\int \frac {(-8+x^5) (2+x^5) \sqrt [4]{2-3 x^4+x^5}}{x^6 (4-3 x^4+2 x^5)} \, dx\)
  3.22.84 \(\int \frac {x^2}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.22.85 \(\int \frac {x^2}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.22.86 \(\int \frac {1+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.22.87 \(\int \frac {1+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.22.88 \(\int \frac {1-x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.22.89 \(\int \frac {1-x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.22.90 \(\int \frac {1+x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.22.91 \(\int \frac {1+x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.22.92 \(\int \frac {(-4+x^3) (-2+x^3) (-1+x^3)^{2/3}}{x^6 (-2+x^3+x^6)} \, dx\)
  3.22.93 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^8} \, dx\)
  3.22.94 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^8} \, dx\)
  3.22.95 \(\int \frac {-1+x^8}{\sqrt [4]{x^2+x^6} (1+x^8)} \, dx\)
  3.22.96 \(\int \frac {-1+x^8}{\sqrt [4]{x^2+x^6} (1+x^8)} \, dx\)
  3.22.97 \(\int \frac {x^5 (8-7 (1+k) x+6 k x^2)}{((1-x) x (1-k x))^{2/3} (-b+b (1+k) x-b k x^2+x^8)} \, dx\)
  3.22.98 \(\int \frac {-2 b-a x^4+2 x^8}{\sqrt [4]{-b+a x^4} (-2 b-a x^4+x^8)} \, dx\)
  3.22.99 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^4} \, dx\)
  3.22.100 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^4 \sqrt {b^2+a x^2}} \, dx\)