3.15.1 \(\int \frac {-b+2 a x^4}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\)
  3.15.2 \(\int \frac {(-1+3 x^4) \sqrt {1+x+2 x^4+x^5+x^8}}{x^2 (4+x+4 x^4)} \, dx\)
  3.15.3 \(\int \frac {-b+c x^4+a x^8}{x^2 (-b+a x^4)^{3/4}} \, dx\)
  3.15.4 \(\int \frac {1}{(1+x) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.15.5 \(\int \frac {1}{x \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.15.6 \(\int \frac {(-3+x)^6 (-1-x+x^2)^{3/2}}{-1+x} \, dx\)
  3.15.7 \(\int \frac {(-1+x^3) \sqrt [3]{1+x^3}}{x^5} \, dx\)
  3.15.8 \(\int \frac {(-1+x^3) \sqrt [3]{1+x^3}}{x^2} \, dx\)
  3.15.9 \(\int \frac {\sqrt [3]{-1+x^3} (1+x^3)}{x^5} \, dx\)
  3.15.10 \(\int \frac {x}{(1+x^2) \sqrt {-x-x^2+x^3}} \, dx\)
  3.15.11 \(\int \frac {-1+x+x^2}{(1+x^2) \sqrt {-x-x^2+x^3}} \, dx\)
  3.15.12 \(\int \frac {x}{\sqrt [3]{x^2+x^3}} \, dx\)
  3.15.13 \(\int \frac {1}{x^6 (1+x^3) \sqrt [3]{x^2+x^3}} \, dx\)
  3.15.14 \(\int \frac {1}{x^6 (1+x^3) \sqrt [3]{x^2+x^3}} \, dx\)
  3.15.15 \(\int \frac {\sqrt [3]{-1+x^3} (-1+2 x^3)}{x^5} \, dx\)
  3.15.16 \(\int \frac {(-1+x^3)^{2/3} (-1+3 x^3)}{x^6 (-1+2 x^3)} \, dx\)
  3.15.17 \(\int \frac {x^4}{(-1+x^4)^2 \sqrt [4]{x^2+x^4}} \, dx\)
  3.15.18 \(\int \frac {(1+x^2) \sqrt [4]{x^3+x^4}}{x^2 (-1+x^2)} \, dx\)
  3.15.19 \(\int \frac {(4+x^3) (-1-x^3+x^4)}{x^2 (1+x^3)^{3/4} (1+x^3+x^4)} \, dx\)
  3.15.20 \(\int \frac {1+x^2+2 x^4}{\sqrt [4]{1+x^2} (2+3 x^2+x^4)} \, dx\)
  3.15.21 \(\int \frac {(-b+a x^2) \sqrt [4]{-b x^2+a x^4}}{x^2} \, dx\)
  3.15.22 \(\int \frac {b+a x^4}{x^4 (2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.15.23 \(\int \frac {b+a x^4}{x^4 (2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.15.24 \(\int \frac {1-x^4}{x^2 \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.15.25 \(\int \frac {-1+x^2}{(1+x^2) \sqrt [4]{x^2+x^6}} \, dx\)
  3.15.26 \(\int \frac {-1+x^2}{(1+x^2) \sqrt [4]{x^2+x^6}} \, dx\)
  3.15.27 \(\int \frac {\sqrt [4]{-x^3+x^4} (-1+x^8)}{x^4} \, dx\)
  3.15.28 \(\int \frac {\sqrt [4]{1+x^4} (2+x^4)}{x^2 (-1+2 x^4+x^8)} \, dx\)
  3.15.29 \(\int \frac {\sqrt [4]{1+x^4} (2+x^4)}{x^2 (-1+2 x^4+x^8)} \, dx\)
  3.15.30 \(\int \frac {-b+2 a x^4}{\sqrt [4]{-b+a x^4} (-b+a x^8)} \, dx\)
  3.15.31 \(\int \frac {\sqrt {1+2 x^6} (-1+4 x^6)}{2+x^4+8 x^6+8 x^{12}} \, dx\)
  3.15.32 \(\int \frac {(-1+x^2) \sqrt {1+\sqrt {1+x}}}{1+x^2} \, dx\)
  3.15.33 \(\int \frac {(-1+x^2) \sqrt {1+\sqrt {1+x}}}{1+x^2} \, dx\)
  3.15.34 \(\int x^2 \sqrt {x^2+\sqrt {1+x^4}} \, dx\)
  3.15.35 \(\int \frac {(-1+x^4) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4}} \, dx\)
  3.15.36 \(\int \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}} \, dx\)
  3.15.37 \(\int x^3 (-1+x^3)^{2/3} \, dx\)
  3.15.38 \(\int x^4 \sqrt [3]{1+x^3} \, dx\)
  3.15.39 \(\int x^3 (1+x^3)^{2/3} \, dx\)
  3.15.40 \(\int \frac {(-2+x^3)^{2/3} (4+x^3)}{x^6 (-1+x^3)} \, dx\)
  3.15.41 \(\int \frac {3 b+a x^2}{(b+a x^2+x^3) \sqrt [4]{b x+a x^3}} \, dx\)
  3.15.42 \(\int \frac {(-3+x^4) \sqrt [3]{1+x^4}}{x^{13}} \, dx\)
  3.15.43 \(\int \frac {-2 b+a x^2}{\sqrt [4]{-b+a x^2} (-b+a x^2+x^4)} \, dx\)
  3.15.44 \(\int \frac {-4 b+a x^3}{\sqrt [4]{-b+a x^3} (-b+a x^3+x^4)} \, dx\)
  3.15.45 \(\int \frac {b+a x^2}{(b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.15.46 \(\int \frac {b+a x^2}{(b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.15.47 \(\int \frac {b+a x^4}{x^4 (-2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.15.48 \(\int \frac {b+a x^4}{x^4 (-2 b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.15.49 \(\int \frac {(-1+x^3) (1+x^3)^3 (1+x^6)^{2/3}}{x^6 (1-x^3+x^6)} \, dx\)
  3.15.50 \(\int \frac {(-1+x^6)^{2/3} (1+x^6) (-2+x^3+2 x^6)}{x^6 (-1-x^3+x^6)} \, dx\)
  3.15.51 \(\int \frac {1}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\)
  3.15.52 \(\int \frac {1}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\)
  3.15.53 \(\int \frac {-b+a x^4}{\sqrt [4]{-b x^2+a x^4} (-b+2 a x^4+2 x^8)} \, dx\)
  3.15.54 \(\int \frac {-b+a x^4}{\sqrt [4]{-b x^2+a x^4} (-b+2 a x^4+2 x^8)} \, dx\)
  3.15.55 \(\int \frac {\sqrt {c x^2-x \sqrt {-b x+a x^2}}}{x^3} \, dx\)
  3.15.56 \(\int \frac {x}{x+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.15.57 \(\int \frac {x}{x+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.15.58 \(\int \frac {1+x}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.15.59 \(\int \frac {3+x+x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.15.60 \(\int \frac {3-x+2 x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.15.61 \(\int \frac {(-1+x^3)^{2/3} (1+x^3)}{x^3} \, dx\)
  3.15.62 \(\int x^8 (b+a x^4)^{3/4} \, dx\)
  3.15.63 \(\int \frac {1}{(-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.15.64 \(\int \frac {(-2+x^3) (1+x^3)^{2/3}}{x^3 (-2+x^3+2 x^6)} \, dx\)
  3.15.65 \(\int \frac {(-2+x^3) (1+x^3)^{2/3}}{x^3 (-2+x^3+2 x^6)} \, dx\)
  3.15.66 \(\int \frac {x^2 (-2+x^4)}{\sqrt [3]{-x+x^5} (-1+x^4+x^8)} \, dx\)
  3.15.67 \(\int \frac {-b+2 a x^4}{\sqrt [4]{-b+a x^4} (-b-a x^4+x^8)} \, dx\)
  3.15.68 \(\int \frac {-2 b+a x^4}{\sqrt [4]{b+a x^4} (-2 b+a x^4+x^8)} \, dx\)
  3.15.69 \(\int \frac {1}{x^2 \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.15.70 \(\int \frac {\sqrt [3]{-1+x^3}}{x^{10}} \, dx\)
  3.15.71 \(\int x^4 \sqrt [3]{-1+x^3} \, dx\)
  3.15.72 \(\int \sqrt [3]{-x+x^3} \, dx\)
  3.15.73 \(\int \frac {\sqrt [3]{-1+x^3} (-1+2 x^3)}{x^{10}} \, dx\)
  3.15.74 \(\int \frac {1+k^3 x^3}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^3 x^3)} \, dx\)
  3.15.75 \(\int \frac {(-3+x^4) (1+x^4)^{2/3} (1+2 x^3+x^4)}{x^6 (1-x^3+x^4)} \, dx\)
  3.15.76 \(\int \frac {(b+a x^4)^{3/4}}{x^4 (2 b+a x^4)} \, dx\)
  3.15.77 \(\int \frac {-b+a x^3}{x^3 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.15.78 \(\int \frac {b+a x^3}{x^3 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.15.79 \(\int \frac {\sqrt [4]{-b x+a x^4}}{x^2} \, dx\)
  3.15.80 \(\int \frac {1}{(b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.15.81 \(\int \frac {1}{(b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.15.82 \(\int \frac {-b+a x^4}{x^4 \sqrt [4]{-b+2 a x^4}} \, dx\)
  3.15.83 \(\int \frac {x^4 (4 b+a x^5)}{(-b+a x^5)^2 \sqrt [4]{-b+c x^4+a x^5}} \, dx\)
  3.15.84 \(\int \frac {1}{x^{19} \sqrt [3]{-1+x^6}} \, dx\)
  3.15.85 \(\int \frac {x^7}{\sqrt [3]{-1+x^6}} \, dx\)
  3.15.86 \(\int x^3 \sqrt [3]{-1+x^6} \, dx\)
  3.15.87 \(\int x (-1+x^6)^{2/3} \, dx\)
  3.15.88 \(\int \frac {x^7}{\sqrt [3]{1+x^6}} \, dx\)
  3.15.89 \(\int x^3 \sqrt [3]{1+x^6} \, dx\)
  3.15.90 \(\int x (1+x^6)^{2/3} \, dx\)
  3.15.91 \(\int \frac {(1-x^3+x^5) (-3+2 x^5)}{x^3 (1+x^3+x^5) \sqrt [4]{x+x^6}} \, dx\)
  3.15.92 \(\int \frac {x}{\sqrt [3]{-x^2+x^6}} \, dx\)
  3.15.93 \(\int \frac {(-1+x^3)^{2/3} (2+x^3)}{x^3 (-4+x^3+x^6)} \, dx\)
  3.15.94 \(\int \frac {(-1+x^3)^{2/3} (2+x^3)}{x^3 (-4+x^3+x^6)} \, dx\)
  3.15.95 \(\int \frac {(-3+2 x) (1-x+x^3)^{2/3}}{1-2 x+x^2+2 x^3-2 x^4+2 x^6} \, dx\)
  3.15.96 \(\int \frac {(-2+x^6) (4+x^6) \sqrt [4]{-2+2 x^4+x^6}}{x^6 (-4-x^4+2 x^6)} \, dx\)
  3.15.97 \(\int \frac {(1+x^3)^{2/3} (-1+3 x^6)}{x^9 (1+2 x^3)} \, dx\)
  3.15.98 \(\int \frac {\sqrt {1-x^4} (1+x^4)}{1-x^4+x^8} \, dx\)
  3.15.99 \(\int \frac {x^2}{(b+a x^4)^{3/4} (-b^2+a^2 x^8)} \, dx\)
  3.15.100 \(\int \frac {\sqrt {1+\sqrt {1+x^2}}}{x+\sqrt {1+x^2}} \, dx\)