3.20.1 \(\int \frac {-1+x}{x \sqrt [3]{1+2 x+2 x^2+x^3}} \, dx\)
  3.20.2 \(\int \frac {(-2 q+p x^3) (a q+b x^2+a p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^7} \, dx\)
  3.20.3 \(\int \frac {x^2}{(1+x^2) \sqrt [10]{243-5265 x+47250 x^2-225810 x^3+615255 x^4-954733 x^5+820340 x^6-401440 x^7+112000 x^8-16640 x^9+1024 x^{10}}} \, dx\)
  3.20.4 \(\int \frac {1}{x \sqrt {-b x+a^2 x^2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.20.5 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{(-1+x^2) \sqrt {1+x^4}} \, dx\)
  3.20.6 \(\int \frac {1}{(1+2 x) \sqrt [3]{-1+4 x+4 x^2}} \, dx\)
  3.20.7 \(\int \frac {1}{x^3 (-b+a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.20.8 \(\int \frac {1}{x^3 (-b+a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.20.9 \(\int \frac {x^3 (-b+x) (-2 a b+(3 a-b) x)}{(-a+x) (x^2 (-a+x) (-b+x))^{3/4} (-a^3 d+3 a^2 d x+(b-3 a d) x^2+(-1+d) x^3)} \, dx\)
  3.20.10 \(\int \frac {x^2}{\sqrt {-x-x^2+x^3} (-1+x^4)} \, dx\)
  3.20.11 \(\int \frac {(-1+x^2) \sqrt {1+x^2+x^4}}{(1+x^2) (1+x+x^2+x^3+x^4)} \, dx\)
  3.20.12 \(\int \frac {x^6}{(-b+a x^4) (b+a x^4)^{3/4}} \, dx\)
  3.20.13 \(\int \frac {-b+a x^3}{x^3 (b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\)
  3.20.14 \(\int \frac {-b+a x^4}{\sqrt [4]{b+a x^4} (-b+3 a x^4)} \, dx\)
  3.20.15 \(\int \frac {-2 b+a x^2}{\sqrt [4]{-b+a x^2} (-b+a x^2+c x^4)} \, dx\)
  3.20.16 \(\int \frac {(-q+p x^2) \sqrt {q^2+p^2 x^4}}{x^2 (a q+b x+a p x^2)} \, dx\)
  3.20.17 \(\int \frac {\sqrt [3]{1+x^5} (-3+2 x^5)}{x^2 (2-x^3+2 x^5)} \, dx\)
  3.20.18 \(\int \frac {x^2 (4 b+a x^5)}{(-b+a x^5)^{3/4} (-b+c x^4+a x^5)} \, dx\)
  3.20.19 \(\int \frac {(-1+x^6) (1+x^6)^{2/3}}{x^3 (2-x^3+2 x^6)} \, dx\)
  3.20.20 \(\int \frac {x^2 (2 b+a x^6)}{(-b+a x^6)^{3/4} (-b+c x^4+a x^6)} \, dx\)
  3.20.21 \(\int x^2 \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}} \, dx\)
  3.20.22 \(\int \sqrt {1+\sqrt {1+\sqrt {1+x}}} \, dx\)
  3.20.23 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.20.24 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.20.25 \(\int \frac {(-2+x^3) (1+x^3)^{2/3}}{x^6 (-1+2 x^3)} \, dx\)
  3.20.26 \(\int \frac {1}{x^3 (b+a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.20.27 \(\int \frac {1}{x^3 (b+a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.20.28 \(\int \frac {(-1+x+x^4) \sqrt [4]{-x^3+x^4}}{1+x} \, dx\)
  3.20.29 \(\int \frac {(-3+x^4) (1+x^4)^{2/3}}{x^3 (2+x^3+2 x^4)} \, dx\)
  3.20.30 \(\int \frac {(-4 b+a x^4) (b+a x^4)^{3/4}}{x^8 (4 b+a x^4)} \, dx\)
  3.20.31 \(\int \frac {(b+a x^4)^{3/4} (2 b+a x^4)}{x^8 (4 b+a x^4)} \, dx\)
  3.20.32 \(\int \frac {x^4 \sqrt [4]{b x^3+a x^4}}{b+a x} \, dx\)
  3.20.33 \(\int \frac {b+a x^2}{(-b+a x^2) \sqrt {b^2+a^2 x^4}} \, dx\)
  3.20.34 \(\int \frac {(1+x^2) \sqrt {1+\sqrt {1+x^2}}}{-1+x^2} \, dx\)
  3.20.35 \(\int \frac {1}{\sqrt [3]{-b+a x^3}} \, dx\)
  3.20.36 \(\int \frac {(a^2-2 a x+x^2) (-a b-a c+3 b c+2 (a-b-c) x+x^2)}{((-a+x) (-b+x) (-c+x))^{3/4} (-b c-a^3 d+(b+c+3 a^2 d) x-(1+3 a d) x^2+d x^3)} \, dx\)
  3.20.37 \(\int \frac {(-4+x^5) \sqrt [4]{1-2 x^4+x^5}}{x^2 (1+x^5)} \, dx\)
  3.20.38 \(\int \frac {b+a x^6}{x^6 \sqrt [3]{x+x^3}} \, dx\)
  3.20.39 \(\int \frac {b^2+a^2 x^2}{\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.20.40 \(\int \frac {x^2}{(b+a x^2)^{3/4} (2 b+a x^2)} \, dx\)
  3.20.41 \(\int \frac {x}{(-b+a x^3)^{2/3}} \, dx\)
  3.20.42 \(\int \frac {x \sqrt [3]{x^2+x^4}}{1+2 x^2} \, dx\)
  3.20.43 \(\int \frac {b+a x^3}{x^6 (-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.20.44 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^4+x^8} \, dx\)
  3.20.45 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1+x^4+x^8} \, dx\)
  3.20.46 \(\int \frac {x \sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x}} \, dx\)
  3.20.47 \(\int \frac {(-1+a x) \sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x}} \, dx\)
  3.20.48 \(\int \frac {-1+x^4}{(1+x^4) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.20.49 \(\int \frac {-1+x^4}{(1+x^4) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.20.50 \(\int \frac {1}{\sqrt [4]{-x^2+x^4} (-1+x^8)} \, dx\)
  3.20.51 \(\int \frac {1}{\sqrt [4]{-x^2+x^4} (-1+x^8)} \, dx\)
  3.20.52 \(\int \frac {-2+x^4}{\sqrt [4]{1+x^4} (-1-x^4+2 x^8)} \, dx\)
  3.20.53 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{(b^2+a x^2)^{5/2}} \, dx\)
  3.20.54 \(\int \frac {\sqrt [4]{-b+a x^2}}{x} \, dx\)
  3.20.55 \(\int \frac {(b+a x^2) \sqrt [3]{-x+x^3}}{x^2} \, dx\)
  3.20.56 \(\int \frac {-b+a x}{x \sqrt [3]{b^3+a^3 x^3}} \, dx\)
  3.20.57 \(\int \frac {x^2 \sqrt [4]{-x^3+x^4}}{2+x} \, dx\)
  3.20.58 \(\int \frac {(-1+x) (-3+8 x-8 x^2+12 x^4)}{x (\frac {1-2 x^2}{1+2 x^2})^{2/3} (1+2 x^2) (3-7 x+7 x^2-6 x^3+2 x^4)} \, dx\)
  3.20.59 \(\int \frac {b-a x^5}{\sqrt {a+b x} (a b+x^5)} \, dx\)
  3.20.60 \(\int \frac {(-1+x^3)^{2/3} (1+x^3+x^6)}{x^6 (-1+x^6)} \, dx\)
  3.20.61 \(\int \frac {-1+x^2}{\sqrt {1+x} (1+x^2) \sqrt {1+\sqrt {1+x}} \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.20.62 \(\int \frac {-1+x^2}{\sqrt {1+x} (1+x^2) \sqrt {1+\sqrt {1+x}} \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.20.63 \(\int \frac {x}{(x^2 (-a+x))^{2/3} (-a d+(-1+d) x)} \, dx\)
  3.20.64 \(\int \frac {(-b+a x^2)^{3/4}}{x} \, dx\)
  3.20.65 \(\int \frac {-2 x+x^2}{(1-x+x^2) \sqrt [4]{1+x^4}} \, dx\)
  3.20.66 \(\int \frac {1+k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^4 x^4)} \, dx\)
  3.20.67 \(\int \frac {-b+a x^8}{\sqrt [4]{-b x^2+a x^4} (b+a x^8)} \, dx\)
  3.20.68 \(\int \frac {-b+a x^8}{\sqrt [4]{-b x^2+a x^4} (b+a x^8)} \, dx\)
  3.20.69 \(\int \frac {(-1+x^8) (1+x^8)}{\sqrt [4]{-1-x^4+x^8} (1-3 x^8+x^{16})} \, dx\)
  3.20.70 \(\int \frac {1}{\sqrt [3]{x^2 (-a+x)} (-a d+(-1+d) x)} \, dx\)
  3.20.71 \(\int \frac {\sqrt [3]{6+2 x+x^2}}{1+x} \, dx\)
  3.20.72 \(\int \frac {-1+x}{x \sqrt [3]{-1+x^3}} \, dx\)
  3.20.73 \(\int \frac {(-1+x^3)^{2/3} (1+x^3)}{x^6 (-2+x^3)} \, dx\)
  3.20.74 \(\int \frac {(-4+x^2) \sqrt [3]{x+x^3}}{x^4 (2+x^2)} \, dx\)
  3.20.75 \(\int \frac {2+x^2}{(1+x^2) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.20.76 \(\int \frac {x}{(b+a x^2) \sqrt {-b x+a x^3}} \, dx\)
  3.20.77 \(\int \frac {-b+a x^2}{(b+a x^2) \sqrt {-b x+a x^3}} \, dx\)
  3.20.78 \(\int \frac {\sqrt {-b x+a x^3}}{-b^2+a^2 x^4} \, dx\)
  3.20.79 \(\int \frac {(1+x^5)^{2/3} (-3+2 x^5) (2+x^3+2 x^5)}{x^6 (2-x^3+2 x^5)} \, dx\)
  3.20.80 \(\int \frac {b+a x^6}{(-b+a x^6) \sqrt [3]{-b+a^3 x^3+a x^6}} \, dx\)
  3.20.81 \(\int \frac {(1+x^2) (1+x^8) \sqrt {1+x^2+x^4+x^6+x^8}}{x^7 (-1+x^2)} \, dx\)
  3.20.82 \(\int \frac {b+a x^8}{\sqrt [4]{-b x^2+a x^4} (-b+a x^8)} \, dx\)
  3.20.83 \(\int \frac {b+a x^8}{\sqrt [4]{-b x^2+a x^4} (-b+a x^8)} \, dx\)
  3.20.84 \(\int \frac {(-1+x^4) \sqrt {x+\sqrt {1+x^2}}}{1+x^4} \, dx\)
  3.20.85 \(\int \frac {(-1+x^4) \sqrt {x+\sqrt {1+x^2}}}{1+x^4} \, dx\)
  3.20.86 \(\int \frac {x^2 \sqrt {x+x^2}}{\sqrt {x^2+x \sqrt {x+x^2}}} \, dx\)
  3.20.87 \(\int \frac {1}{(d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.20.88 \(\int \frac {1}{(d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.20.89 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2) \sqrt {1+x^2}} \, dx\)
  3.20.90 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2) \sqrt {1+x^2}} \, dx\)
  3.20.91 \(\int \frac {\sqrt {b+a^2 x^2}}{x^2-\sqrt [3]{a x-\sqrt {b+a^2 x^2}}} \, dx\)
  3.20.92 \(\int \frac {\sqrt {b+a^2 x^2}}{x^2-\sqrt {a x-\sqrt {b+a^2 x^2}}} \, dx\)
  3.20.93 \(\int \frac {\sqrt [3]{-6-2 x+x^2}}{-1+x} \, dx\)
  3.20.94 \(\int \frac {-1+x}{\sqrt [3]{1-x-x^2+x^3}} \, dx\)
  3.20.95 \(\int \frac {x}{\sqrt [3]{-1-x+x^2+x^3}} \, dx\)
  3.20.96 \(\int \frac {(3+2 x) (1+x+3 x^3)^{2/3}}{x^3 (1+x+x^3)} \, dx\)
  3.20.97 \(\int \frac {x^2 (-3 a b^3+2 b^2 (3 a+b) x-3 b (a+b) x^2+x^4)}{(x (-a+x) (-b+x)^3)^{3/4} (a b^3-b^2 (3 a+b) x+3 b (a+b) x^2-(a+3 b+d) x^3+x^4)} \, dx\)
  3.20.98 \(\int \frac {x^6}{(-b+a x^4)^{3/4} (b+a x^4)} \, dx\)
  3.20.99 \(\int \frac {-b+2 a x^2}{(-b+a x^2) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.20.100 \(\int \frac {-3 b+2 a x^4}{(-2 b+a x^4) \sqrt [4]{b+a x^4}} \, dx\)