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