3.19.1 \(\int \frac {(-b+a x^4) \sqrt [4]{b x^2+a x^4}}{x^2} \, dx\)
  3.19.2 \(\int \frac {(b+a x^4) \sqrt [4]{b x^2+a x^4}}{x^2} \, dx\)
  3.19.3 \(\int \frac {b+2 a x^4}{(-b+a x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.19.4 \(\int \frac {b+2 a x^4}{(-b+a x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.19.5 \(\int \frac {-b-2 a x^4+2 x^8}{\sqrt [4]{-b+a x^4}} \, dx\)
  3.19.6 \(\int \frac {-1+x}{(-4-2 x+x^2) \sqrt [3]{-2-2 x+x^2}} \, dx\)
  3.19.7 \(\int \frac {1}{(1+x) \sqrt [3]{3+2 x+x^2}} \, dx\)
  3.19.8 \(\int \frac {1}{x (-b+a x^2)^{3/4}} \, dx\)
  3.19.9 \(\int \frac {1}{x \sqrt [3]{-b+a x^3}} \, dx\)
  3.19.10 \(\int \frac {-b^3+a^3 x^3}{\sqrt {b^2 x+a^2 x^3} (b^3+a^3 x^3)} \, dx\)
  3.19.11 \(\int \frac {b^3+a^3 x^3}{\sqrt {b^2 x+a^2 x^3} (-b^3+a^3 x^3)} \, dx\)
  3.19.12 \(\int \frac {\sqrt [4]{x^3+x^4}}{-2+x+2 x^2} \, dx\)
  3.19.13 \(\int \frac {(-4 b+a x^3) (b-a x^3+x^4)}{x^4 \sqrt [4]{-b+a x^3} (-b+a x^3+x^4)} \, dx\)
  3.19.14 \(\int \frac {(-2+x^2) (-1+x^2) \sqrt [4]{-1+x^2+x^4}}{x^6 (-1+x^2+2 x^4)} \, dx\)
  3.19.15 \(\int x^2 \sqrt [4]{b x^3+a x^4} \, dx\)
  3.19.16 \(\int \frac {1+x^6}{\sqrt {x+x^2+x^3} (1-x^6)} \, dx\)
  3.19.17 \(\int \frac {1-3 x^3+3 x^6}{x^6 (-1+2 x^3) \sqrt [4]{-x+x^4}} \, dx\)
  3.19.18 \(\int \frac {b+a x^6}{x^3 (b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.19.19 \(\int \frac {(-1-x-x^2+x^4) (2+x+2 x^4)}{\sqrt {-1-x+x^4} (4+8 x+3 x^2-x^3-7 x^4-8 x^5+x^6+4 x^8)} \, dx\)
  3.19.20 \(\int \frac {(1+x^6)^2 (-1+2 x^6)}{(1-x^2+x^6)^{3/2} (1-x^2-x^4+2 x^6-x^8+x^{12})} \, dx\)
  3.19.21 \(\int \frac {1}{(2 \sqrt {x}+\sqrt {1+x})^2} \, dx\)
  3.19.22 \(\int \frac {1}{x^3 \sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}} \, dx\)
  3.19.23 \(\int \frac {1}{x \sqrt [4]{-b+a x^2}} \, dx\)
  3.19.24 \(\int \frac {1+k^{3/2} x^3}{\sqrt {(1-x^2) (1-k^2 x^2)} (-1+k^{3/2} x^3)} \, dx\)
  3.19.25 \(\int \frac {(-d+2 c x) \sqrt [4]{b x^3+a x^4}}{x} \, dx\)
  3.19.26 \(\int \frac {-1+x^6}{(1+x^6) \sqrt [3]{1+a^3 x^3+x^6}} \, dx\)
  3.19.27 \(\int \frac {(2+x^3+4 x^6) \sqrt [3]{x+2 x^3-x^4-x^7}}{(-1-2 x^2+x^3+x^6) (-1-x^2+x^3+x^6)} \, dx\)
  3.19.28 \(\int \frac {x^2}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\)
  3.19.29 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^{3/2}} \, dx\)
  3.19.30 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^{3/2}} \, dx\)
  3.19.31 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^{3/2}} \, dx\)
  3.19.32 \(\int \frac {1}{(-1+x) \sqrt [3]{-3-2 x+x^2}} \, dx\)
  3.19.33 \(\int \frac {1}{(-1+x) \sqrt [3]{-1-2 x+x^2}} \, dx\)
  3.19.34 \(\int \frac {1}{(1+x) \sqrt [3]{-1+2 x+x^2}} \, dx\)
  3.19.35 \(\int \frac {-2 a b x^2+(a+b) x^3}{(-a+x) (-b+x) \sqrt [4]{x^2 (-a+x) (-b+x)} (-a b d+(a+b) d x+(1-d) x^2)} \, dx\)
  3.19.36 \(\int \frac {(a^2-2 a x+x^2) (a b^2-2 (2 a-b) b x+(3 a-2 b) x^2)}{(x (-a+x) (-b+x)^2)^{3/4} (a^3 d+(b^2-3 a^2 d) x+(-2 b+3 a d) x^2+(1-d) x^3)} \, dx\)
  3.19.37 \(\int \frac {-1+k^{3/2} x^3}{\sqrt {(1-x^2) (1-k^2 x^2)} (1+k^{3/2} x^3)} \, dx\)
  3.19.38 \(\int \frac {\sqrt {-x-x^2+x^3}}{-1+x^4} \, dx\)
  3.19.39 \(\int \frac {(b+a x^3) \sqrt {x+x^4}}{-d+c x^3} \, dx\)
  3.19.40 \(\int \frac {1-2 x+2 x^4}{x \sqrt [4]{-1+x^4}} \, dx\)
  3.19.41 \(\int \frac {x^2 (-4 b+a x^5)}{(b+a x^5)^{3/4} (b+c x^4+a x^5)} \, dx\)
  3.19.42 \(\int \frac {1}{\sqrt [6]{1+2 x-x^2-4 x^3-x^4+2 x^5+x^6}} \, dx\)
  3.19.43 \(\int \frac {x^2 (-2 b+a x^6)}{(b+a x^6)^{3/4} (b+c x^4+a x^6)} \, dx\)
  3.19.44 \(\int \frac {(4+x^3) (1+2 x^3+x^6+x^8)}{x^4 \sqrt [4]{1+x^3} (-1-2 x^3-x^6+x^8)} \, dx\)
  3.19.45 \(\int \frac {2-x^4+2 x^8}{\sqrt [4]{1+x^4} (-2+x^4+x^8)} \, dx\)
  3.19.46 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{(b^2+a x^2)^2} \, dx\)
  3.19.47 \(\int \frac {(b+a x^3) \sqrt {-x+x^4}}{-d+c x^3} \, dx\)
  3.19.48 \(\int \frac {b+a x^3}{x^3 (-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.19.49 \(\int \frac {(1+2 x^6) \sqrt [3]{x+x^3-x^7}}{(-1+x^6)^2} \, dx\)
  3.19.50 \(\int \frac {-((2 a-b) b^2)+(4 a-b) b x-(2 a+b) x^2+x^3}{((-a+x) (-b+x)^2)^{3/4} (a+b^2 d-(1+2 b d) x+d x^2)} \, dx\)
  3.19.51 \(\int \frac {2+x^4}{\sqrt [4]{x^2+x^4} (-1-x^4+2 x^8)} \, dx\)
  3.19.52 \(\int \frac {2+x^4}{\sqrt [4]{x^2+x^4} (-1-x^4+2 x^8)} \, dx\)
  3.19.53 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{x^2} \, dx\)
  3.19.54 \(\int \frac {(-1+x) \sqrt {x+\sqrt {1+x^2}}}{1+x} \, dx\)
  3.19.55 \(\int \frac {(1+x) \sqrt {x+\sqrt {1+x^2}}}{-1+x} \, dx\)
  3.19.56 \(\int \frac {6+2 x+x^2}{(1+x) \sqrt [3]{2+x+x^2} (2-x+2 x^2)} \, dx\)
  3.19.57 \(\int \frac {1}{x (-b+a x^3)^{3/4}} \, dx\)
  3.19.58 \(\int \frac {1}{x \sqrt [4]{-b+a x^3}} \, dx\)
  3.19.59 \(\int \frac {(-3 b+a x^2) (b-a x^2+x^3)}{x^3 (-b+a x^2+x^3) \sqrt [4]{-b x+a x^3}} \, dx\)
  3.19.60 \(\int \frac {1}{x (-b+a x^4)^{3/4}} \, dx\)
  3.19.61 \(\int \frac {1}{x \sqrt [4]{-b+a x^4}} \, dx\)
  3.19.62 \(\int \frac {1-x^5}{\sqrt {a+b x} (1+x^5)} \, dx\)
  3.19.63 \(\int \frac {1}{x (-b+a x^5)^{3/4}} \, dx\)
  3.19.64 \(\int \frac {1}{x (-b+a x^6)^{3/4}} \, dx\)
  3.19.65 \(\int \frac {(1+x^4) (-1+x^2+x^4)^{3/2}}{(-1+x^4) (1+x^2-x^4-x^6+x^8)} \, dx\)
  3.19.66 \(\int \frac {(-1+x^6) (1+x^3+x^6)^{2/3}}{1+x^6+x^{12}} \, dx\)
  3.19.67 \(\int \frac {(-1+x^3)^3 (1+x^3) \sqrt {2+3 x^6+2 x^{12}}}{x^7 (1+x^6)} \, dx\)
  3.19.68 \(\int \frac {\sqrt {a x-\sqrt {b+a^2 x^2}}}{a^2 x^2+\sqrt {b+a^2 x^2}} \, dx\)
  3.19.69 \(\int \frac {d+c x}{\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.19.70 \(\int \frac {1}{\sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.19.71 \(\int \frac {(-b+a x^2) \sqrt [3]{x+x^3}}{x^2} \, dx\)
  3.19.72 \(\int \frac {1}{x^3 \sqrt [3]{-b x^2+a x^3} (d+c x^3)} \, dx\)
  3.19.73 \(\int \frac {-1+x^4}{\sqrt {-x-x^2+x^3} (1+x^4)} \, dx\)
  3.19.74 \(\int \sqrt {-1-11 x-36 x^2-27 x^3+16 x^4+9 x^5+x^6} \, dx\)
  3.19.75 \(\int \frac {(-q+2 p x^3) (a q+b x+a p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^4} \, dx\)
  3.19.76 \(\int \frac {-2-x^4+2 x^8}{\sqrt [4]{-1+x^4} (-2-x^4+x^8)} \, dx\)
  3.19.77 \(\int \frac {(-1+x^4) \sqrt {1+\sqrt {1+x}}}{1+x^4} \, dx\)
  3.19.78 \(\int \frac {(-1+x^4) \sqrt {1+\sqrt {1+x}}}{1+x^4} \, dx\)
  3.19.79 \(\int \frac {(b+a x^2) \sqrt {b x+a x^3}}{x^2 (-b+a x^2)} \, dx\)
  3.19.80 \(\int \frac {(-2 a b+(3 a-b) x) (-a^3+3 a^2 x-3 a x^2+x^3)}{x (-b+x) \sqrt [4]{x^2 (-a+x) (-b+x)} (a^3-3 a^2 x+(3 a-b d) x^2+(-1+d) x^3)} \, dx\)
  3.19.81 \(\int \frac {2 b+a x^2}{\sqrt [4]{b+a x^2} (b n+a n x^2+2 x^4)} \, dx\)
  3.19.82 \(\int \frac {\sqrt {1+x} (-1+x^2)}{(1+x^2) \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.19.83 \(\int \frac {\sqrt {1+x} (-1+x^2)}{(1+x^2) \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.19.84 \(\int \frac {(-1+x^4) \sqrt {1+\sqrt {1+x}}}{\sqrt {1+x} (1+x^4)} \, dx\)
  3.19.85 \(\int \frac {(-1+x^4) \sqrt {1+\sqrt {1+x}}}{\sqrt {1+x} (1+x^4)} \, dx\)
  3.19.86 \(\int \frac {1+a x^2}{(-1+a x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.19.87 \(\int \frac {x \sqrt {x+x^2}}{\sqrt {x^2+x \sqrt {x+x^2}}} \, dx\)
  3.19.88 \(\int \frac {\sqrt {1+x}}{1+\sqrt {x+\sqrt {1+x}}} \, dx\)
  3.19.89 \(\int \frac {1+x}{(-1+x) (1+2 x) \sqrt [3]{-1+3 x^2}} \, dx\)
  3.19.90 \(\int \frac {-b+a x^2}{x^2 \sqrt [3]{-x+x^3}} \, dx\)
  3.19.91 \(\int \frac {1+x^4}{\sqrt {-x-x^2+x^3} (-1+x^4)} \, dx\)
  3.19.92 \(\int \frac {(-1+x^3) \sqrt [3]{1+x^6}}{x^2 (1+x^3)} \, dx\)
  3.19.93 \(\int \frac {(-2+x^6) \sqrt [3]{2+x^6}}{x^2 (2+2 x^3+x^6)} \, dx\)
  3.19.94 \(\int \frac {(1+x^3)^{2/3} (-1-2 x^3+2 x^6)}{x^6 (-1+x^3+2 x^6)} \, dx\)
  3.19.95 \(\int \frac {(1+x^3) \sqrt {x-x^4}}{2+4 x^3+3 x^6} \, dx\)
  3.19.96 \(\int \frac {-2+a x^4}{\sqrt [4]{b+a x^4} (-b+a x^4+2 x^8)} \, dx\)
  3.19.97 \(\int \frac {-1+x}{(1+x) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.19.98 \(\int \frac {1+x}{(-1+x) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.19.99 \(\int \frac {\sqrt {-x+x^2}}{\sqrt {x^2-x \sqrt {-x+x^2}}} \, dx\)
  3.19.100 \(\int \frac {6+2 x+x^2}{(2+x) (2+x^2) \sqrt [3]{2+x+x^2}} \, dx\)