3.19.1 \(\int \frac {\sqrt [4]{-b x^3+a x^4} (-d+c x^4)}{x^2} \, dx\)
  3.19.2 \(\int \frac {x^3 (5-4 (1+k) x+3 k x^2)}{((1-x) x (1-k x))^{2/3} (-b+b (1+k) x-b k x^2+x^5)} \, dx\)
  3.19.3 \(\int \frac {(-8+x^5) (2+x^5) \sqrt [4]{2-3 x^4+x^5}}{x^6 (4-3 x^4+2 x^5)} \, dx\)
  3.19.4 \(\int \frac {x^2}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.19.5 \(\int \frac {x^2}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.19.6 \(\int \frac {1+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.19.7 \(\int \frac {1+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.19.8 \(\int \frac {1-x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.19.9 \(\int \frac {1-x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.19.10 \(\int \frac {1+x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.19.11 \(\int \frac {1+x^2+x^4}{(-1+x^4) \sqrt [4]{x^2+x^6}} \, dx\)
  3.19.12 \(\int \frac {(-4+x^3) (-2+x^3) (-1+x^3)^{2/3}}{x^6 (-2+x^3+x^6)} \, dx\)
  3.19.13 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^8} \, dx\)
  3.19.14 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^8} \, dx\)
  3.19.15 \(\int \frac {-1+x^8}{\sqrt [4]{x^2+x^6} (1+x^8)} \, dx\)
  3.19.16 \(\int \frac {-1+x^8}{\sqrt [4]{x^2+x^6} (1+x^8)} \, dx\)
  3.19.17 \(\int \frac {x^5 (8-7 (1+k) x+6 k x^2)}{((1-x) x (1-k x))^{2/3} (-b+b (1+k) x-b k x^2+x^8)} \, dx\)
  3.19.18 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^4} \, dx\)
  3.19.19 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^4 \sqrt {b^2+a x^2}} \, dx\)
  3.19.20 \(\int \frac {(1+x^3) \sqrt {-2-x^3+x^6}}{x^4 (-1-2 x^3+x^6)} \, dx\)
  3.19.21 \(\int \frac {x^2 (-4+7 x^3)}{\sqrt [3]{-x+x^4} (-1-x^4+x^7)} \, dx\)
  3.19.22 \(\int \frac {\sqrt {1+2 x^2-x^4} (-1+x^4) (1+x^4)}{(-1-x^2+x^4) (1+3 x^2-x^4-3 x^6+x^8)} \, dx\)
  3.19.23 \(\int \frac {1}{(-1+x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.19.24 \(\int \frac {\sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}{\sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}} \, dx\)
  3.19.25 \(\int \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}} \sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}} \, dx\)
  3.19.26 \(\int \frac {(-3+x) (-2+x) (2-x+2 x^3)^{2/3}}{x^6 (-2+x+2 x^3)} \, dx\)
  3.19.27 \(\int \frac {(1+x^3)^{2/3} (2+x^3)}{x^6 (-2-x^3+x^6)} \, dx\)
  3.19.28 \(\int \frac {1}{(2+x) \sqrt [3]{1+x+x^2}} \, dx\)
  3.19.29 \(\int \frac {(-3+2 x) \sqrt [3]{-1+x+x^3}}{x^2 (2-2 x+x^3)} \, dx\)
  3.19.30 \(\int \frac {-((2 a-b) b^2)+(4 a-b) b x-(2 a+b) x^2+x^3}{(-a+x) \sqrt [4]{(-a+x) (-b+x)^2} (b^2+a d-(2 b+d) x+x^2)} \, dx\)
  3.19.31 \(\int \frac {(-b+a x^4) (b+a x^4)^{3/4}}{x^8 (b+2 a x^4)} \, dx\)
  3.19.32 \(\int \frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{x} \, dx\)
  3.19.33 \(\int \frac {-2 a b x+(a+b) x^2}{(x (-a+x) (-b+x))^{2/3} (a b d-(a+b) d x+(-1+d) x^2)} \, dx\)
  3.19.34 \(\int \frac {\sqrt [4]{-b+a x^3}}{x^7} \, dx\)
  3.19.35 \(\int \frac {(b+2 a x^2) \sqrt [4]{b x^2+a x^4}}{-b+a x^2} \, dx\)
  3.19.36 \(\int \frac {-b^4+a^4 x^4}{\sqrt {-b^2 x+a^2 x^3} (b^4+a^4 x^4)} \, dx\)
  3.19.37 \(\int \frac {-b^6+a^6 x^6}{\sqrt {b^4+a^4 x^4} (b^6+a^6 x^6)} \, dx\)
  3.19.38 \(\int \frac {-2 a b+(a+b) x}{\sqrt [3]{x (-a+x) (-b+x)} (a b d-(a+b) d x+(-1+d) x^2)} \, dx\)
  3.19.39 \(\int \frac {1}{x^7 (-b+a x^3)^{3/4}} \, dx\)
  3.19.40 \(\int \frac {1}{x^7 \sqrt [4]{-b+a x^3}} \, dx\)
  3.19.41 \(\int \frac {1+x^2}{(-1+x^2) \sqrt [3]{x^2+x^4}} \, dx\)
  3.19.42 \(\int \frac {(-1+x^4)^{2/3} (3+x^4) (-2-x^3+2 x^4)}{x^6 (-2+3 x^3+2 x^4)} \, dx\)
  3.19.43 \(\int \frac {1}{x^9 (-b+a x^4)^{3/4}} \, dx\)
  3.19.44 \(\int \frac {b^2+c x^2+a^2 x^4}{\sqrt {b x+a x^3} (-b^2+a^2 x^4)} \, dx\)
  3.19.45 \(\int \frac {1}{x^{11} (-b+a x^5)^{3/4}} \, dx\)
  3.19.46 \(\int \frac {1+x^6}{\sqrt [3]{-x^2+x^4} (-1+x^6)} \, dx\)
  3.19.47 \(\int \frac {-b^6+a^6 x^6}{\sqrt {b^2 x+a^2 x^3} (b^6+a^6 x^6)} \, dx\)
  3.19.48 \(\int \frac {\sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}{x^2 \sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}} \, dx\)
  3.19.49 \(\int \frac {(-2 q+p x^3) \sqrt {q+p x^3}}{b x^4+a (q+p x^3)^2} \, dx\)
  3.19.50 \(\int x^4 \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}} \, dx\)
  3.19.51 \(\int \frac {\sqrt {q+p x^5} (-2 q+3 p x^5)}{b x^4+a (q+p x^5)^2} \, dx\)
  3.19.52 \(\int \frac {-3+x}{\sqrt [3]{1-x^2} (3+x^2)} \, dx\)
  3.19.53 \(\int \frac {x^3 (-3 a b+(a+2 b) x)}{(-a+x) (-b+x) \sqrt [4]{x (-a+x) (-b+x)^2} (-a b^2 d+b (2 a+b) d x-(a+2 b) d x^2+(-1+d) x^3)} \, dx\)
  3.19.54 \(\int \frac {a x+\sqrt {b^2+a^2 x^2}}{b+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.19.55 \(\int \frac {1}{(3+x^2) \sqrt [3]{1+3 x^2}} \, dx\)
  3.19.56 \(\int \frac {(1+x^2) \sqrt [4]{x^3+x^5}}{x^2 (-1+x^2)} \, dx\)
  3.19.57 \(\int \frac {(4+x^2+x^5) \sqrt [4]{-2-x^2-2 x^4+2 x^5}}{x^2 (-2-x^2+2 x^5)} \, dx\)
  3.19.58 \(\int \frac {(-1+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}}{(1+x^4)^2} \, dx\)
  3.19.59 \(\int (\frac {1}{\sqrt {1-\sqrt {x}}}-\sqrt {1-\sqrt {x}-x}) \, dx\)
  3.19.60 \(\int \frac {-5+x}{\sqrt [3]{-2-x+x^2} (-3+4 x+x^2)} \, dx\)
  3.19.61 \(\int \frac {(-a+x) (-2 a+b+x)}{((-a+x) (-b+x)^2)^{3/4} (a+b^2 d-(1+2 b d) x+d x^2)} \, dx\)
  3.19.62 \(\int \frac {1+x}{(1+4 x+x^2) \sqrt [3]{1-x^3}} \, dx\)
  3.19.63 \(\int \frac {x^8}{\sqrt {-1+x^4} (-1+x^{16})} \, dx\)
  3.19.64 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{(b^2+a x^2)^4} \, dx\)
  3.19.65 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{1+x^2} \, dx\)
  3.19.66 \(\int \frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x^2}}}}}{x} \, dx\)
  3.19.67 \(\int \frac {1}{(1+x) \sqrt [3]{1-x^3}} \, dx\)
  3.19.68 \(\int \frac {(a b-2 b x+x^2) (b^2-2 b x+x^2)}{(x (-a+x) (-b+x)^3)^{3/4} (b d-(a+d) x+x^2)} \, dx\)
  3.19.69 \(\int \frac {-2 a b+(a+b) x}{\sqrt [3]{x (-a+x) (-b+x)} (-a b+(a+b) x+(-1+d) x^2)} \, dx\)
  3.19.70 \(\int \frac {(-1+x^3)^{2/3} (1+x^3)}{x^6 (2+x^3)} \, dx\)
  3.19.71 \(\int \frac {1}{(1+x) (-2+3 x-2 x^2+3 x^3-2 x^4)^{3/2}} \, dx\)
  3.19.72 \(\int \frac {\sqrt {-x+x^4}}{-b+a x^6} \, dx\)
  3.19.73 \(\int \frac {(1+2 x^8) \sqrt [4]{-1-2 x^4+2 x^8} (1-3 x^8+4 x^{16})}{x^{10} (-1+2 x^8)} \, dx\)
  3.19.74 \(\int \frac {(b^2+a x^2)^{3/2}}{\sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.19.75 \(\int \frac {x (-2 q+p x^6) \sqrt {q+p x^6}}{b x^8+a (q+p x^6)^2} \, dx\)
  3.19.76 \(\int \frac {\sqrt [3]{-1-2 x+6 x^2}}{-1+6 x} \, dx\)
  3.19.77 \(\int \frac {-2 a b x+(a+b) x^2}{(x (-a+x) (-b+x))^{2/3} (-a b+(a+b) x+(-1+d) x^2)} \, dx\)
  3.19.78 \(\int \frac {x (-a b+x^2)}{(x^2 (-a+x) (-b+x))^{2/3} (a b d-(1+a d+b d) x+d x^2)} \, dx\)
  3.19.79 \(\int \frac {(-2+x^3) (-1+x^3)^{2/3}}{x^3 (-1+2 x^3)} \, dx\)
  3.19.80 \(\int \frac {(-b+a x^2) \sqrt [4]{-b x^2+a x^4}}{b+a x^2} \, dx\)
  3.19.81 \(\int \frac {1+x^3}{(-1+x^3) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.19.82 \(\int \frac {1}{\sqrt {d+\sqrt {c+\sqrt {b+a x}}}} \, dx\)
  3.19.83 \(\int \frac {1}{x \sqrt [3]{3+3 x+x^2}} \, dx\)
  3.19.84 \(\int \frac {-a b+x^2}{\sqrt [3]{x^2 (-a+x) (-b+x)} (a b d-(1+a d+b d) x+d x^2)} \, dx\)
  3.19.85 \(\int \frac {(-3+2 x) (1-x+x^3)^{2/3}}{x^3 (-2+2 x+x^3)} \, dx\)
  3.19.86 \(\int \frac {(-3+4 x) (-1+2 x+x^3)^{2/3}}{x^3 (2-4 x+x^3)} \, dx\)
  3.19.87 \(\int \frac {\sqrt {-81+27 x+135 x^2-150 x^3+65 x^4-13 x^5+x^6}}{-1+x} \, dx\)
  3.19.88 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^2 (a q+b x+a p x^3)} \, dx\)
  3.19.89 \(\int \frac {(1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{(-1+x^2) \sqrt {1+x^4}} \, dx\)
  3.19.90 \(\int \frac {2+x}{(-3+x) \sqrt [4]{1-x^2} (1+x^2)} \, dx\)
  3.19.91 \(\int \frac {\sqrt {b^2+a^2 x^3} (2 b^2+c x^3+a^2 x^6)}{x (-b^2+a^2 x^6)} \, dx\)
  3.19.92 \(\int \frac {1-x^4+2 x^8}{\sqrt [4]{1+x^4} (-1-2 x^4+x^8)} \, dx\)
  3.19.93 \(\int \frac {(-1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{(1+x^2) \sqrt {1+x^4}} \, dx\)
  3.19.94 \(\int \frac {1}{(1+x) \sqrt [3]{1-x+x^2}} \, dx\)
  3.19.95 \(\int \frac {\sqrt [3]{b x+a x^3} (b+a x^4)}{x^4} \, dx\)
  3.19.96 \(\int \frac {b^4+a^4 x^4}{\sqrt {-b^2 x+a^2 x^3} (-b^4+a^4 x^4)} \, dx\)
  3.19.97 \(\int \frac {c x^6 (-4 b+a x^5)}{(b+a x^5)^{3/4} (b^2+2 a b x^5-c^2 x^8+a^2 x^{10})} \, dx\)
  3.19.98 \(\int \frac {x^2 \sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x}} \, dx\)
  3.19.99 \(\int \frac {a+b x^2+a k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^4 x^4)} \, dx\)
  3.19.100 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (a q^2+2 a p q x^3+b x^4+a p^2 x^6)}{x^9} \, dx\)