3.9.1 \(\int \frac {(-3+x^2) (1-x^2+x^3)^{2/3}}{1-2 x^2-x^3+x^4+x^5+x^6} \, dx\)
  3.9.2 \(\int \frac {(-3+x^2) (1-x^2+x^3)^{2/3}}{1-2 x^2-x^3+x^4+x^5+x^6} \, dx\)
  3.9.3 \(\int \frac {\sqrt {-1+x^6} (-1+2 x^6)^2}{x (-1+4 x^6)} \, dx\)
  3.9.4 \(\int \frac {1}{\sqrt [3]{x+x^3} (b+a x^6)} \, dx\)
  3.9.5 \(\int \frac {1}{\sqrt [3]{x+x^3} (b+a x^6)} \, dx\)
  3.9.6 \(\int \frac {-b+a x^4}{(b-2 x^2+a x^4) \sqrt [4]{b x^2+a x^6}} \, dx\)
  3.9.7 \(\int \frac {(4+x^5) \sqrt {1-2 x^5+x^8+x^{10}}}{x^9} \, dx\)
  3.9.8 \(\int \frac {(1+x^6) (-1+x^3+x^6)^{2/3}}{1-x^6+x^{12}} \, dx\)
  3.9.9 \(\int \frac {(1+x^6) (-1+x^3+x^6)^{2/3}}{1-x^6+x^{12}} \, dx\)
  3.9.10 \(\int \frac {(-2+5 x^7) \sqrt [3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx\)
  3.9.11 \(\int \frac {(-2+5 x^7) \sqrt [3]{2 x+x^3+2 x^8}}{4+x^4+8 x^7+4 x^{14}} \, dx\)
  3.9.12 \(\int \frac {1}{\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.9.13 \(\int x^{10} \sqrt [4]{-1+x^4} \, dx\)
  3.9.14 \(\int x^{10} \sqrt [4]{1+x^4} \, dx\)
  3.9.15 \(\int \frac {1+x^2}{(1-x^2+x^4) \sqrt [4]{x^2+x^4}} \, dx\)
  3.9.16 \(\int \frac {1}{(-b+a x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.9.17 \(\int \frac {1}{(-b+a x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.9.18 \(\int \frac {1-x^2}{x \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.9.19 \(\int \frac {x^2 (-1+3 x^4)}{(1+x^4)^2 (a-x+a x^4) \sqrt {x+x^5}} \, dx\)
  3.9.20 \(\int \frac {(-3+x^4) (1-x^3+2 x^4-x^6-x^7+x^8)}{x^6 (1-x^3+x^4) \sqrt [4]{x+x^5}} \, dx\)
  3.9.21 \(\int \frac {1+x^2}{\sqrt {1+\sqrt {1+x}}} \, dx\)
  3.9.22 \(\int \frac {-1+2 x}{(1+x) \sqrt {-a^2 x^2+(1+x)^6}} \, dx\)
  3.9.23 \(\int \frac {x}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.9.24 \(\int \sqrt {a x+\sqrt {b^2+a^2 x^2}} \, dx\)
  3.9.25 \(\int \frac {1}{(1+\sqrt {x}) \sqrt {-\sqrt {x}+x}} \, dx\)
  3.9.26 \(\int \frac {x}{(-1+x^2) \sqrt {x+x^2+x^3}} \, dx\)
  3.9.27 \(\int \frac {-a b c+2 a (b+c) x-(3 a+b+c) x^2+2 x^3}{\sqrt {x (-a+x) (-b+x) (-c+x)} (a d+(b c-d) x-(b+c) x^2+x^3)} \, dx\)
  3.9.28 \(\int \frac {3 b+a x^3}{x (-b+a x^3) \sqrt {b+a x^3}} \, dx\)
  3.9.29 \(\int \frac {(2 c-a x^3) \sqrt {c+b x^2+a x^3}}{(c+(-3+b) x^2+a x^3) (c+(-2+b) x^2+a x^3)} \, dx\)
  3.9.30 \(\int \frac {-a b c+2 a (b+c) x-(3 a+b+c) x^2+2 x^3}{\sqrt {x (-a+x) (-b+x) (-c+x)} (a+(-1+b c d) x-(b+c) d x^2+d x^3)} \, dx\)
  3.9.31 \(\int \frac {-1+x^3}{(1+x^3) \sqrt {1+x^4}} \, dx\)
  3.9.32 \(\int x^4 \sqrt [4]{-x+x^4} \, dx\)
  3.9.33 \(\int \sqrt [4]{-x^3+x^4} \, dx\)
  3.9.34 \(\int \frac {\sqrt {2-x^3-x^4} (4+x^3+2 x^4)}{(-2-3 x^2+x^3+x^4) (-2-x^2+x^3+x^4)} \, dx\)
  3.9.35 \(\int \frac {\sqrt [4]{b x^3+a x^4}}{x (b+a x+x^2)} \, dx\)
  3.9.36 \(\int \frac {\sqrt [4]{b x^3+a x^4}}{x (b+a x+x^2)} \, dx\)
  3.9.37 \(\int \frac {x^2 (-4+x^6)}{\sqrt {-1+x^6} (2+x^6)} \, dx\)
  3.9.38 \(\int \frac {(-1+x^5) (-1+x^3+x^5) (3+2 x^5)}{x^6 (-1-x^3+x^5) \sqrt [4]{-x+x^6}} \, dx\)
  3.9.39 \(\int \frac {\sqrt {1+x^3} (2+2 x^3+x^6)}{x^7 (-1+x^6)} \, dx\)
  3.9.40 \(\int \frac {\sqrt {-1+x^2+x^5} (2+3 x^5)}{1+x^4-2 x^5+x^{10}} \, dx\)
  3.9.41 \(\int \frac {1}{x \sqrt {x+x^2} \sqrt {x^2+x \sqrt {x+x^2}}} \, dx\)
  3.9.42 \(\int \sqrt {b+\sqrt {b^2+a x^2}} \, dx\)
  3.9.43 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\sqrt {1+x^2} \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.9.44 \(\int \frac {-b+a x}{(b+a x) \sqrt {b^2 x+a^2 x^3}} \, dx\)
  3.9.45 \(\int \frac {b+a x}{(-b+a x) \sqrt {b^2 x+a^2 x^3}} \, dx\)
  3.9.46 \(\int \frac {-b x^2+a x^3}{(b x^2+a x^3) \sqrt {b^2 x+a^2 x^3}} \, dx\)
  3.9.47 \(\int \frac {2+5 x}{\sqrt {-12+20 x+5 x^2+2 x^3+x^4}} \, dx\)
  3.9.48 \(\int \frac {(-1+x^3) \sqrt {-1+x^6}}{x^7} \, dx\)
  3.9.49 \(\int \frac {\sqrt {-1+x^6} (-1+2 x^6)^2}{x^7 (-1+4 x^6)} \, dx\)
  3.9.50 \(\int \frac {-2+x^4}{\sqrt [4]{1+x^4} (-1+x^4+2 x^8)} \, dx\)
  3.9.51 \(\int \frac {-x^2+10 x^8}{\sqrt {-1+x^6} (-1+4 x^6)} \, dx\)
  3.9.52 \(\int \frac {1+x^2}{(-1+x^2) (1+2 x^2)^{3/2}} \, dx\)
  3.9.53 \(\int \frac {(b+a x^2)^{3/4}}{x} \, dx\)
  3.9.54 \(\int \frac {1-x+x^2}{(-1+x^2) \sqrt {x+x^3}} \, dx\)
  3.9.55 \(\int \frac {-1+2 x^2}{(1+x^2) \sqrt {-1-x^2+x^4}} \, dx\)
  3.9.56 \(\int \frac {1}{(-2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.9.57 \(\int \frac {1}{(-2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.9.58 \(\int \frac {-2 b+c x^2}{(-b+c x^2) \sqrt [4]{-b+c x^2+a x^4}} \, dx\)
  3.9.59 \(\int \frac {-4 b+a x^3}{(-b+a x^3) \sqrt [4]{b-a x^3+c x^4}} \, dx\)
  3.9.60 \(\int \frac {-b+a x^6}{(b+a x^6) \sqrt [3]{-b+a^3 x^3+a x^6}} \, dx\)
  3.9.61 \(\int \frac {-b+a x^6}{(b+a x^6) \sqrt [3]{-b+a^3 x^3+a x^6}} \, dx\)
  3.9.62 \(\int \frac {\sqrt {1-x^4} (1+x^4)}{4-7 x^4+4 x^8} \, dx\)
  3.9.63 \(\int \frac {x^4}{\sqrt [4]{-b+a x^4} (-b+a x^8)} \, dx\)
  3.9.64 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1+x^2} \, dx\)
  3.9.65 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1+x^2} \, dx\)
  3.9.66 \(\int \frac {\sqrt {-b+a x^3}}{x (2 b+a x^3)} \, dx\)
  3.9.67 \(\int \frac {-b+4 a x^3}{x \sqrt {-b+a x^3} (2 b+a x^3)} \, dx\)
  3.9.68 \(\int \frac {\sqrt {1+6 x^2+x^4}}{(-1+x) (1+x)^3} \, dx\)
  3.9.69 \(\int \frac {\sqrt [4]{b+a x^4}}{x} \, dx\)
  3.9.70 \(\int \frac {1}{(-2 b+a x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.9.71 \(\int \frac {1}{(-2 b+a x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.9.72 \(\int \frac {x^6}{(b+a x^4)^{3/4} (b^2+a^2 x^8)} \, dx\)
  3.9.73 \(\int \sqrt {x^3+x^2 \sqrt {-1+x^2}} \, dx\)
  3.9.74 \(\int \frac {(-a+x) (-b+x) (-a b+x^2)}{x \sqrt {x (-a+x) (-b+x)} (a b-(a+b+d) x+x^2)} \, dx\)
  3.9.75 \(\int \frac {1}{(b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\)
  3.9.76 \(\int \frac {1}{(b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\)
  3.9.77 \(\int \frac {\sqrt {-1+x^4}}{1+x^4} \, dx\)
  3.9.78 \(\int x^2 \sqrt [4]{-x^2+x^4} \, dx\)
  3.9.79 \(\int \frac {x}{\sqrt {1+4 x+3 x^2-2 x^3+x^4}} \, dx\)
  3.9.80 \(\int \frac {x}{\sqrt {1-4 x+3 x^2+2 x^3+x^4}} \, dx\)
  3.9.81 \(\int \frac {3-3 x^2+2 x^4}{\sqrt [4]{-1+x^2} (2-3 x^2+x^4)} \, dx\)
  3.9.82 \(\int \frac {x^2}{(-b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.9.83 \(\int \frac {x^2}{(-b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.9.84 \(\int \frac {4 b+x^3}{(b+x^3) \sqrt [4]{-b-x^3+a x^4}} \, dx\)
  3.9.85 \(\int \frac {4 b+a x^5}{(-b+a x^5) \sqrt [4]{-b+c x^4+a x^5}} \, dx\)
  3.9.86 \(\int \frac {\sqrt {1+x^2-2 x^6} (1+4 x^6)}{(-1-4 x^2+2 x^6) (-1-2 x^2+2 x^6)} \, dx\)
  3.9.87 \(\int \frac {x^4}{\sqrt [4]{-1+x^4} (-1+x^8)} \, dx\)
  3.9.88 \(\int \frac {1}{\sqrt [4]{1+x^4} (-1+x^8)} \, dx\)
  3.9.89 \(\int \frac {-1+2 x^4}{\sqrt [4]{-1+x^4} (-1+x^8)} \, dx\)
  3.9.90 \(\int \frac {1+x^8}{\sqrt {1+x^4} (-1+x^8)} \, dx\)
  3.9.91 \(\int \frac {-1+x^{12}}{\sqrt {1+x^4} (1+x^{12})} \, dx\)
  3.9.92 \(\int \frac {-1+x^2}{\sqrt {1+x^2} \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.9.93 \(\int \frac {\sqrt {1+x^2}}{\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.9.94 \(\int \frac {1}{(-b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\)
  3.9.95 \(\int \frac {1}{(-b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\)
  3.9.96 \(\int \frac {1}{(b+a x^2) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.9.97 \(\int \frac {1}{(b+a x^2) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.9.98 \(\int x^7 \sqrt [4]{-x+x^4} \, dx\)
  3.9.99 \(\int \frac {(2+x^2) \sqrt [4]{-1-x^2+x^4} (1+x^2+x^4)}{x^6 (1+x^2)} \, dx\)
  3.9.100 \(\int \frac {\sqrt [4]{x^3+x^4}}{x^2 (-1+x^2)} \, dx\)