3.17.1 \(\int \frac {-b+a x^3}{x^3 (b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\)
  3.17.2 \(\int \frac {-b+a x^4}{\sqrt [4]{b+a x^4} (-b+3 a x^4)} \, dx\)
  3.17.3 \(\int \frac {-2 b+a x^2}{\sqrt [4]{-b+a x^2} (-b+a x^2+c x^4)} \, dx\)
  3.17.4 \(\int \frac {(-q+p x^2) \sqrt {q^2+p^2 x^4}}{x^2 (a q+b x+a p x^2)} \, dx\)
  3.17.5 \(\int \frac {\sqrt [3]{1+x^5} (-3+2 x^5)}{x^2 (2-x^3+2 x^5)} \, dx\)
  3.17.6 \(\int \frac {x^2 (4 b+a x^5)}{(-b+a x^5)^{3/4} (-b+c x^4+a x^5)} \, dx\)
  3.17.7 \(\int \frac {(-1+x^6) (1+x^6)^{2/3}}{x^3 (2-x^3+2 x^6)} \, dx\)
  3.17.8 \(\int \frac {x^2 (2 b+a x^6)}{(-b+a x^6)^{3/4} (-b+c x^4+a x^6)} \, dx\)
  3.17.9 \(\int x^2 \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}} \, dx\)
  3.17.10 \(\int \sqrt {1+\sqrt {1+\sqrt {1+x}}} \, dx\)
  3.17.11 \(\int \frac {(-2+x^3) (1+x^3)^{2/3}}{x^6 (-1+2 x^3)} \, dx\)
  3.17.12 \(\int \frac {(-1+x+x^4) \sqrt [4]{-x^3+x^4}}{1+x} \, dx\)
  3.17.13 \(\int \frac {(-3+x^4) (1+x^4)^{2/3}}{x^3 (2+x^3+2 x^4)} \, dx\)
  3.17.14 \(\int \frac {(-4 b+a x^4) (b+a x^4)^{3/4}}{x^8 (4 b+a x^4)} \, dx\)
  3.17.15 \(\int \frac {(b+a x^4)^{3/4} (2 b+a x^4)}{x^8 (4 b+a x^4)} \, dx\)
  3.17.16 \(\int \frac {x^4 \sqrt [4]{b x^3+a x^4}}{b+a x} \, dx\)
  3.17.17 \(\int \frac {b+a x^2}{(-b+a x^2) \sqrt {b^2+a^2 x^4}} \, dx\)
  3.17.18 \(\int \frac {(1+x^2) \sqrt {1+\sqrt {1+x^2}}}{-1+x^2} \, dx\)
  3.17.19 \(\int \frac {1}{\sqrt [3]{-b+a x^3}} \, dx\)
  3.17.20 \(\int \frac {(a^2-2 a x+x^2) (-a b-a c+3 b c+2 (a-b-c) x+x^2)}{((-a+x) (-b+x) (-c+x))^{3/4} (-b c-a^3 d+(b+c+3 a^2 d) x-(1+3 a d) x^2+d x^3)} \, dx\)
  3.17.21 \(\int \frac {(-4+x^5) \sqrt [4]{1-2 x^4+x^5}}{x^2 (1+x^5)} \, dx\)
  3.17.22 \(\int \frac {b+a x^6}{x^6 \sqrt [3]{x+x^3}} \, dx\)
  3.17.23 \(\int \frac {b^2+a^2 x^2}{\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.17.24 \(\int \frac {x^2}{(b+a x^2)^{3/4} (2 b+a x^2)} \, dx\)
  3.17.25 \(\int \frac {x}{(-b+a x^3)^{2/3}} \, dx\)
  3.17.26 \(\int \frac {x \sqrt [3]{x^2+x^4}}{1+2 x^2} \, dx\)
  3.17.27 \(\int \frac {b+a x^3}{x^6 (-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.17.28 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^4+x^8} \, dx\)
  3.17.29 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^4+x^8} \, dx\)
  3.17.30 \(\int \frac {x \sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x}} \, dx\)
  3.17.31 \(\int \frac {(-1+a x) \sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x}} \, dx\)
  3.17.32 \(\int \frac {-2+x^4}{\sqrt [4]{1+x^4} (-1-x^4+2 x^8)} \, dx\)
  3.17.33 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{(b^2+a x^2)^{5/2}} \, dx\)
  3.17.34 \(\int \frac {\sqrt [4]{-b+a x^2}}{x} \, dx\)
  3.17.35 \(\int \frac {(b+a x^2) \sqrt [3]{-x+x^3}}{x^2} \, dx\)
  3.17.36 \(\int \frac {-b+a x}{x \sqrt [3]{b^3+a^3 x^3}} \, dx\)
  3.17.37 \(\int \frac {x^2 \sqrt [4]{-x^3+x^4}}{2+x} \, dx\)
  3.17.38 \(\int \frac {(-1+x) (-3+8 x-8 x^2+12 x^4)}{x (\frac {1-2 x^2}{1+2 x^2})^{2/3} (1+2 x^2) (3-7 x+7 x^2-6 x^3+2 x^4)} \, dx\)
  3.17.39 \(\int \frac {(-1+x^3)^{2/3} (1+x^3+x^6)}{x^6 (-1+x^6)} \, dx\)
  3.17.40 \(\int \frac {x}{(x^2 (-a+x))^{2/3} (-a d+(-1+d) x)} \, dx\)
  3.17.41 \(\int \frac {(-b+a x^2)^{3/4}}{x} \, dx\)
  3.17.42 \(\int \frac {-2 x+x^2}{(1-x+x^2) \sqrt [4]{1+x^4}} \, dx\)
  3.17.43 \(\int \frac {1+k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^4 x^4)} \, dx\)
  3.17.44 \(\int \frac {(-1+x^8) (1+x^8)}{\sqrt [4]{-1-x^4+x^8} (1-3 x^8+x^{16})} \, dx\)
  3.17.45 \(\int \frac {1}{\sqrt [3]{x^2 (-a+x)} (-a d+(-1+d) x)} \, dx\)
  3.17.46 \(\int \frac {\sqrt [3]{6+2 x+x^2}}{1+x} \, dx\)
  3.17.47 \(\int \frac {-1+x}{x \sqrt [3]{-1+x^3}} \, dx\)
  3.17.48 \(\int \frac {(-1+x^3)^{2/3} (1+x^3)}{x^6 (-2+x^3)} \, dx\)
  3.17.49 \(\int \frac {(-4+x^2) \sqrt [3]{x+x^3}}{x^4 (2+x^2)} \, dx\)
  3.17.50 \(\int \frac {x}{(b+a x^2) \sqrt {-b x+a x^3}} \, dx\)
  3.17.51 \(\int \frac {-b+a x^2}{(b+a x^2) \sqrt {-b x+a x^3}} \, dx\)
  3.17.52 \(\int \frac {\sqrt {-b x+a x^3}}{-b^2+a^2 x^4} \, dx\)
  3.17.53 \(\int \frac {(1+x^5)^{2/3} (-3+2 x^5) (2+x^3+2 x^5)}{x^6 (2-x^3+2 x^5)} \, dx\)
  3.17.54 \(\int \frac {b+a x^6}{(-b+a x^6) \sqrt [3]{-b+a^3 x^3+a x^6}} \, dx\)
  3.17.55 \(\int \frac {(1+x^2) (1+x^8) \sqrt {1+x^2+x^4+x^6+x^8}}{x^7 (-1+x^2)} \, dx\)
  3.17.56 \(\int \frac {x^2 \sqrt {x+x^2}}{\sqrt {x^2+x \sqrt {x+x^2}}} \, dx\)
  3.17.57 \(\int \frac {\sqrt [3]{-6-2 x+x^2}}{-1+x} \, dx\)
  3.17.58 \(\int \frac {-1+x}{\sqrt [3]{1-x-x^2+x^3}} \, dx\)
  3.17.59 \(\int \frac {x}{\sqrt [3]{-1-x+x^2+x^3}} \, dx\)
  3.17.60 \(\int \frac {(3+2 x) (1+x+3 x^3)^{2/3}}{x^3 (1+x+x^3)} \, dx\)
  3.17.61 \(\int \frac {x^2 (-3 a b^3+2 b^2 (3 a+b) x-3 b (a+b) x^2+x^4)}{(x (-a+x) (-b+x)^3)^{3/4} (a b^3-b^2 (3 a+b) x+3 b (a+b) x^2-(a+3 b+d) x^3+x^4)} \, dx\)
  3.17.62 \(\int \frac {x^6}{(-b+a x^4)^{3/4} (b+a x^4)} \, dx\)
  3.17.63 \(\int \frac {-b+2 a x^2}{(-b+a x^2) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.17.64 \(\int \frac {-3 b+2 a x^4}{(-2 b+a x^4) \sqrt [4]{b+a x^4}} \, dx\)
  3.17.65 \(\int \frac {b+a x^4}{\sqrt [4]{-b+a x^4} (b+3 a x^4)} \, dx\)
  3.17.66 \(\int \frac {(2+x^6) (-1-x^4+x^6)}{\sqrt [4]{1-x^4-x^6} (-1+x^6)^2} \, dx\)
  3.17.67 \(\int \frac {(-2 b+a x^6) (b-c x^4+a x^6)}{x^2 (b+a x^6)^{3/4} (b+c x^4+a x^6)} \, dx\)
  3.17.68 \(\int \frac {\sqrt [4]{1+2 x^4} (-1-x^4+2 x^8)}{x^6 (2+x^4)} \, dx\)
  3.17.69 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.17.70 \(\int \frac {(1+x^2) \sqrt [3]{x+2 x^3}}{x^4 (-1+x^2)} \, dx\)
  3.17.71 \(\int \frac {(-b+a^3 x^3) \sqrt [3]{b+a^3 x^3}}{x^5} \, dx\)
  3.17.72 \(\int \frac {-3 b+a x^2}{\sqrt [4]{3 b-2 a x^2} (3 b-2 a x^2+3 x^4)} \, dx\)
  3.17.73 \(\int \frac {(-4 b+a x^5) (b-c x^4+a x^5)}{x^2 (b+a x^5)^{3/4} (b+c x^4+a x^5)} \, dx\)
  3.17.74 \(\int \frac {(-1+x^3) (1+x^6)^{2/3} (1-x^3+x^6)}{x^6 (1+x^3)} \, dx\)
  3.17.75 \(\int \frac {(-b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}}}{(b^2+a x^2)^2} \, dx\)
  3.17.76 \(\int \frac {(2+x^3) (1+2 x^3)^{2/3}}{x^6 (-1+x^3)} \, dx\)
  3.17.77 \(\int \frac {(-4+x^2) \sqrt [4]{2-x^2-2 x^4}}{x^2 (-2+x^2)} \, dx\)
  3.17.78 \(\int \frac {1}{(1+x) (-2+2 x+x^2-x^4)^{3/2}} \, dx\)
  3.17.79 \(\int \frac {(-3+2 x^4) (1+2 x^4)^{2/3}}{x^3 (2-x^3+4 x^4)} \, dx\)
  3.17.80 \(\int \frac {-b+a x^3}{x^6 (b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\)
  3.17.81 \(\int \frac {(-1+x^3)^{2/3} (4+4 x^3+x^6)}{x^9 (1+x^3)} \, dx\)
  3.17.82 \(\int \frac {(1+x^3)^{2/3} (-1-2 x^3+2 x^6)}{x^9 (-1+x^3)} \, dx\)
  3.17.83 \(\int \frac {x-\sqrt {1+x^2}}{\sqrt {1+\sqrt {1+x^2}}} \, dx\)
  3.17.84 \(\int \frac {(-4+x^3) (-2+x^3) (-1+x^3)^{2/3}}{x^9 (-2+3 x^3)} \, dx\)
  3.17.85 \(\int \frac {1}{(-1+x) (-2 x^2-3 x^3+x^4)^{3/2}} \, dx\)
  3.17.86 \(\int \frac {1}{(b+2 a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.17.87 \(\int \frac {\sqrt [3]{1-x^7} (-2+x^3+2 x^7) (3+4 x^7)}{x^2 (-1+x^7) (-4+x^3+4 x^7)} \, dx\)
  3.17.88 \(\int \frac {1}{x^2 \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.17.89 \(\int \frac {\sqrt [4]{-b+a x^3}}{x} \, dx\)
  3.17.90 \(\int \frac {(-b+a x^3)^{3/4}}{x} \, dx\)
  3.17.91 \(\int \frac {(-1+x^4)^{2/3} (3+x^4) (-1-x^3+x^4)}{x^6 (-2-x^3+2 x^4)} \, dx\)
  3.17.92 \(\int \frac {(-b+a x^4)^{3/4}}{x} \, dx\)
  3.17.93 \(\int \frac {-3 a b^3+2 b^2 (3 a+b) x-3 b (a+b) x^2+x^4}{\sqrt [4]{x (-a+x) (-b+x)^3} (a b^3 d-b^2 (3 a+b) d x+3 b (a+b) d x^2-(1+a d+3 b d) x^3+d x^4)} \, dx\)
  3.17.94 \(\int \frac {(-b+a x^5)^{3/4}}{x} \, dx\)
  3.17.95 \(\int \frac {(-1+x^3)^{2/3} (4+x^3+x^6)}{x^9 (-2+x^3)} \, dx\)
  3.17.96 \(\int \frac {-3-4 x+3 x^6}{(1+2 x+x^6) \sqrt [3]{1+2 x+2 x^3+x^6}} \, dx\)
  3.17.97 \(\int \frac {(-b+a x^6)^{3/4}}{x} \, dx\)
  3.17.98 \(\int \frac {b+a x^6}{\sqrt [3]{-x+x^3}} \, dx\)
  3.17.99 \(\int \frac {\sqrt [4]{a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}}{\sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}} \, dx\)
  3.17.100 \(\int \frac {1}{\sqrt [3]{x^2 (-a+x)} (a+(-1+d) x)} \, dx\)