3.13.1 \(\int \frac {(-3+x^4) \sqrt [3]{1+x^4}}{x^9} \, dx\)
  3.13.2 \(\int \frac {-b+a x^3}{x^3 \sqrt [4]{b x+a x^4}} \, dx\)
  3.13.3 \(\int \frac {b+a x^3}{x^3 \sqrt [4]{b x+a x^4}} \, dx\)
  3.13.4 \(\int \frac {1}{x^{13} \sqrt [3]{1+x^6}} \, dx\)
  3.13.5 \(\int \frac {-3+5 x^8}{(1+x^8) \sqrt [3]{1-x^3+x^8}} \, dx\)
  3.13.6 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{1+\sqrt {1+x}} \, dx\)
  3.13.7 \(\int \frac {x+\sqrt {1+x^2}}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.13.8 \(\int \frac {x^2}{(-2 b+a x^2) (-b+a x^2)^{3/4}} \, dx\)
  3.13.9 \(\int \frac {(-2 k-(-1+k) (1+k) x+2 k x^2) (1-2 k x+k^2 x^2)}{((1-x^2) (1-k^2 x^2))^{3/4} (1-d+(1+3 d) k x-(1+3 d k^2) x^2+k (-1+d k^2) x^3)} \, dx\)
  3.13.10 \(\int \frac {(-1+x^2) (1+x^2) \sqrt {1+3 x^2+x^4}}{x^2 (1+x+x^2)^2} \, dx\)
  3.13.11 \(\int \frac {(2+x^2) (-4+x+2 x^2) \sqrt {8-7 x^2+2 x^4}}{x^4} \, dx\)
  3.13.12 \(\int x^4 (-b+a x^4)^{3/4} \, dx\)
  3.13.13 \(\int \frac {(-2 b+a x^2) \sqrt [4]{b x^2+a x^4}}{x^2} \, dx\)
  3.13.14 \(\int \frac {(2 b+a x^2) \sqrt [4]{b x^2+a x^4}}{x^2} \, dx\)
  3.13.15 \(\int \frac {(1-3 k^2) x+2 k^2 x^3}{\sqrt [4]{(1-x^2) (1-k^2 x^2)} (-1+d+(-d+3 k^2) x^2-3 k^4 x^4+k^6 x^6)} \, dx\)
  3.13.16 \(\int \frac {1}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\)
  3.13.17 \(\int \frac {(-3 b+2 a x^2) (b^2+a^2 x^2)^{3/4}}{x} \, dx\)
  3.13.18 \(\int \frac {-1+x}{(-2-2 x+x^2) \sqrt {-1+x^3}} \, dx\)
  3.13.19 \(\int \frac {3-x+x^2}{(-2-2 x+x^2) \sqrt {-1+x^3}} \, dx\)
  3.13.20 \(\int \frac {2 x+x^2}{(-2-2 x+x^2) \sqrt {-1+x^3}} \, dx\)
  3.13.21 \(\int \frac {\sqrt [3]{-1+x^3} (1+x^3)}{x^7} \, dx\)
  3.13.22 \(\int \frac {\sqrt [3]{-1+x^3} (-1+2 x^3)}{x^7} \, dx\)
  3.13.23 \(\int \frac {(a^2-2 a x+x^2) (-2 a b x+(3 a-b) x^2)}{(x^2 (-a+x) (-b+x))^{3/4} (a^3 d-3 a^2 d x+(-b+3 a d) x^2+(1-d) x^3)} \, dx\)
  3.13.24 \(\int \frac {1+x^2}{\sqrt {\frac {-2-x+2 x^2}{-1+x+x^2}} (1-x^2+x^4)} \, dx\)
  3.13.25 \(\int \sqrt [4]{b x^3+a x^4} \, dx\)
  3.13.26 \(\int \frac {1}{x^{13} \sqrt [3]{-1+x^6}} \, dx\)
  3.13.27 \(\int \frac {(-1+2 x^2) (-1+4 x-4 x^2+4 x^4)}{\sqrt {\frac {1-2 x^2}{1+2 x^2}} (1+2 x^2) (-1-8 x+32 x^2-40 x^3+46 x^4-64 x^5+56 x^6-32 x^7+8 x^8)} \, dx\)
  3.13.28 \(\int \frac {1+k x^2}{(-1+c k x+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.13.29 \(\int \frac {-1+k x^2}{(1+c k x+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.13.30 \(\int x^2 \sqrt [3]{x+x^3} \, dx\)
  3.13.31 \(\int \frac {6+2 x+x^2}{\sqrt [3]{2+x^2} (1+3 x-2 x^2+x^3)} \, dx\)
  3.13.32 \(\int \frac {\sqrt [3]{x^2+x^3}}{x^2} \, dx\)
  3.13.33 \(\int \frac {\sqrt [3]{1+x^4} (3+x^4)}{x^{13}} \, dx\)
  3.13.34 \(\int \frac {(-1+x^4)^{2/3} (3+x^4) (-1+x^3+x^4)}{x^6 (-1-x^3+x^4)} \, dx\)
  3.13.35 \(\int \frac {(-3+x^4) (1+x^4)^{2/3} (1+x^3+x^4)}{x^6 (1-x^3+x^4)} \, dx\)
  3.13.36 \(\int \frac {\sqrt [3]{1+2 x^7} (-3+8 x^7)}{x^2 (1+x^3+2 x^7)} \, dx\)
  3.13.37 \(\int \frac {(-1+3 x^4) \sqrt {1+x+2 x^4+x^5+x^8}}{x^2 (4+x+4 x^4)} \, dx\)
  3.13.38 \(\int \frac {-b+c x^4+a x^8}{x^2 (-b+a x^4)^{3/4}} \, dx\)
  3.13.39 \(\int \frac {1}{(1+x) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.13.40 \(\int \frac {1}{x \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.13.41 \(\int \frac {(-3+x)^6 (-1-x+x^2)^{3/2}}{-1+x} \, dx\)
  3.13.42 \(\int \frac {(-1+x^3) \sqrt [3]{1+x^3}}{x^5} \, dx\)
  3.13.43 \(\int \frac {(-1+x^3) \sqrt [3]{1+x^3}}{x^2} \, dx\)
  3.13.44 \(\int \frac {\sqrt [3]{-1+x^3} (1+x^3)}{x^5} \, dx\)
  3.13.45 \(\int \frac {x}{(1+x^2) \sqrt {-x-x^2+x^3}} \, dx\)
  3.13.46 \(\int \frac {-1+x+x^2}{(1+x^2) \sqrt {-x-x^2+x^3}} \, dx\)
  3.13.47 \(\int \frac {x}{\sqrt [3]{x^2+x^3}} \, dx\)
  3.13.48 \(\int \frac {\sqrt [3]{-1+x^3} (-1+2 x^3)}{x^5} \, dx\)
  3.13.49 \(\int \frac {(-1+x^3)^{2/3} (-1+3 x^3)}{x^6 (-1+2 x^3)} \, dx\)
  3.13.50 \(\int \frac {x^4}{(-1+x^4)^2 \sqrt [4]{x^2+x^4}} \, dx\)
  3.13.51 \(\int \frac {(1+x^2) \sqrt [4]{x^3+x^4}}{x^2 (-1+x^2)} \, dx\)
  3.13.52 \(\int \frac {(4+x^3) (-1-x^3+x^4)}{x^2 (1+x^3)^{3/4} (1+x^3+x^4)} \, dx\)
  3.13.53 \(\int \frac {1+x^2+2 x^4}{\sqrt [4]{1+x^2} (2+3 x^2+x^4)} \, dx\)
  3.13.54 \(\int \frac {(-b+a x^2) \sqrt [4]{-b x^2+a x^4}}{x^2} \, dx\)
  3.13.55 \(\int \frac {1-x^4}{x^2 \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.13.56 \(\int \frac {-1+x^2}{(1+x^2) \sqrt [4]{x^2+x^6}} \, dx\)
  3.13.57 \(\int \frac {-1+x^2}{(1+x^2) \sqrt [4]{x^2+x^6}} \, dx\)
  3.13.58 \(\int \frac {\sqrt [4]{-x^3+x^4} (-1+x^8)}{x^4} \, dx\)
  3.13.59 \(\int \frac {\sqrt {1+2 x^6} (-1+4 x^6)}{2+x^4+8 x^6+8 x^{12}} \, dx\)
  3.13.60 \(\int x^2 \sqrt {x^2+\sqrt {1+x^4}} \, dx\)
  3.13.61 \(\int \frac {(-1+x^4) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4}} \, dx\)
  3.13.62 \(\int \sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}} \, dx\)
  3.13.63 \(\int x^3 (-1+x^3)^{2/3} \, dx\)
  3.13.64 \(\int x^4 \sqrt [3]{1+x^3} \, dx\)
  3.13.65 \(\int x^3 (1+x^3)^{2/3} \, dx\)
  3.13.66 \(\int \frac {(-2+x^3)^{2/3} (4+x^3)}{x^6 (-1+x^3)} \, dx\)
  3.13.67 \(\int \frac {3 b+a x^2}{(b+a x^2+x^3) \sqrt [4]{b x+a x^3}} \, dx\)
  3.13.68 \(\int \frac {(-3+x^4) \sqrt [3]{1+x^4}}{x^{13}} \, dx\)
  3.13.69 \(\int \frac {-2 b+a x^2}{\sqrt [4]{-b+a x^2} (-b+a x^2+x^4)} \, dx\)
  3.13.70 \(\int \frac {-4 b+a x^3}{\sqrt [4]{-b+a x^3} (-b+a x^3+x^4)} \, dx\)
  3.13.71 \(\int \frac {(-1+x^3) (1+x^3)^3 (1+x^6)^{2/3}}{x^6 (1-x^3+x^6)} \, dx\)
  3.13.72 \(\int \frac {(-1+x^6)^{2/3} (1+x^6) (-2+x^3+2 x^6)}{x^6 (-1-x^3+x^6)} \, dx\)
  3.13.73 \(\int \frac {\sqrt {c x^2-x \sqrt {-b x+a x^2}}}{x^3} \, dx\)
  3.13.74 \(\int \frac {1+x}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.13.75 \(\int \frac {3+x+x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.13.76 \(\int \frac {3-x+2 x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.13.77 \(\int \frac {(-1+x^3)^{2/3} (1+x^3)}{x^3} \, dx\)
  3.13.78 \(\int x^8 (b+a x^4)^{3/4} \, dx\)
  3.13.79 \(\int \frac {1}{(-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.13.80 \(\int \frac {x^2 (-2+x^4)}{\sqrt [3]{-x+x^5} (-1+x^4+x^8)} \, dx\)
  3.13.81 \(\int \frac {1}{x^2 \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.13.82 \(\int \frac {\sqrt [3]{-1+x^3}}{x^{10}} \, dx\)
  3.13.83 \(\int x^4 \sqrt [3]{-1+x^3} \, dx\)
  3.13.84 \(\int \sqrt [3]{-x+x^3} \, dx\)
  3.13.85 \(\int \frac {\sqrt [3]{-1+x^3} (-1+2 x^3)}{x^{10}} \, dx\)
  3.13.86 \(\int \frac {1+k^3 x^3}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^3 x^3)} \, dx\)
  3.13.87 \(\int \frac {(-3+x^4) (1+x^4)^{2/3} (1+2 x^3+x^4)}{x^6 (1-x^3+x^4)} \, dx\)
  3.13.88 \(\int \frac {(b+a x^4)^{3/4}}{x^4 (2 b+a x^4)} \, dx\)
  3.13.89 \(\int \frac {-b+a x^3}{x^3 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.13.90 \(\int \frac {b+a x^3}{x^3 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.13.91 \(\int \frac {\sqrt [4]{-b x+a x^4}}{x^2} \, dx\)
  3.13.92 \(\int \frac {-b+a x^4}{x^4 \sqrt [4]{-b+2 a x^4}} \, dx\)
  3.13.93 \(\int \frac {x^4 (4 b+a x^5)}{(-b+a x^5)^2 \sqrt [4]{-b+c x^4+a x^5}} \, dx\)
  3.13.94 \(\int \frac {1}{x^{19} \sqrt [3]{-1+x^6}} \, dx\)
  3.13.95 \(\int \frac {x^7}{\sqrt [3]{-1+x^6}} \, dx\)
  3.13.96 \(\int x^3 \sqrt [3]{-1+x^6} \, dx\)
  3.13.97 \(\int x (-1+x^6)^{2/3} \, dx\)
  3.13.98 \(\int \frac {x^7}{\sqrt [3]{1+x^6}} \, dx\)
  3.13.99 \(\int x^3 \sqrt [3]{1+x^6} \, dx\)
  3.13.100 \(\int x (1+x^6)^{2/3} \, dx\)