3.13.1 \(\int \frac {x (-b+x) (a b-2 a x+x^2)}{\sqrt {x (-a+x) (-b+x)} (-a^2+2 a x+(-1+b^2 d) x^2-2 b d x^3+d x^4)} \, dx\)
  3.13.2 \(\int \frac {1+x^4}{(-1-x^2+x^4) \sqrt [3]{-x+x^5}} \, dx\)
  3.13.3 \(\int \frac {x^3}{(-1+x^6)^{2/3}} \, dx\)
  3.13.4 \(\int \frac {x}{\sqrt [3]{-1+x^6}} \, dx\)
  3.13.5 \(\int \frac {x^3}{(1+x^6)^{2/3}} \, dx\)
  3.13.6 \(\int \frac {x}{\sqrt [3]{1+x^6}} \, dx\)
  3.13.7 \(\int \frac {-b+a x^8}{x^2 (-b+a x^4)^{3/4}} \, dx\)
  3.13.8 \(\int \frac {-3 b+2 a x^8}{x^8 \sqrt [4]{-b+a x^4}} \, dx\)
  3.13.9 \(\int \frac {-b^2+a^2 x^8}{x^2 (b+a x^4)^{3/4} (b^2+a^2 x^8)} \, dx\)
  3.13.10 \(\int \frac {\sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}}{x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}} \, dx\)
  3.13.11 \(\int \frac {(-1+x^2)^{2/3}}{x} \, dx\)
  3.13.12 \(\int \frac {-3+x}{\sqrt [3]{-1+x^2} (2+x+x^2)} \, dx\)
  3.13.13 \(\int \frac {2+x^2}{(-2-2 x+x^2) \sqrt {-1+x^3}} \, dx\)
  3.13.14 \(\int \frac {(-1+x^3) \sqrt [3]{1+x^3}}{x} \, dx\)
  3.13.15 \(\int \frac {-a b+2 (a-b) x+x^2}{\sqrt [4]{x (-a+x) (-b+x)} (-a^3+(3 a^2+b d) x-(3 a+d) x^2+x^3)} \, dx\)
  3.13.16 \(\int \frac {(1-2 x+x^2) (-1+2 (-1+k) x+k x^2)}{((1-x) x (1-k x))^{3/4} (-d+(1+3 d) x-(3 d+k) x^2+d x^3)} \, dx\)
  3.13.17 \(\int \frac {x^2}{\sqrt {x+x^2+x^3} (-1+x^4)} \, dx\)
  3.13.18 \(\int \frac {\sqrt {x+x^2+x^3}}{-1+x^4} \, dx\)
  3.13.19 \(\int \frac {(-1+x^4)^{2/3}}{x} \, dx\)
  3.13.20 \(\int \frac {1-x^2+x^4}{\sqrt {x+x^2+x^3} (-1+x^4)} \, dx\)
  3.13.21 \(\int \frac {1-x+x^2}{(-1+x^2) \sqrt {1-x+x^2-x^3+x^4}} \, dx\)
  3.13.22 \(\int \frac {(-1+x)^2 (x-2 x^2+2 x^3)}{(-1+2 x) \sqrt {\frac {1-2 x}{1+2 x^2}} (-2+4 x+3 x^2-4 x^3+2 x^4)} \, dx\)
  3.13.23 \(\int \frac {(-1+x^5)^{2/3}}{x} \, dx\)
  3.13.24 \(\int \frac {(-1+x^6)^{2/3}}{x} \, dx\)
  3.13.25 \(\int \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\)
  3.13.26 \(\int \frac {(-1+x^2)^{2/3}}{x^3} \, dx\)
  3.13.27 \(\int \frac {-2+x+x^2}{x^2 (-1+x^2)^{3/4}} \, dx\)
  3.13.28 \(\int \frac {\sqrt [3]{1+x^3}}{x^4} \, dx\)
  3.13.29 \(\int \frac {(1+x^3)^{2/3}}{x^4} \, dx\)
  3.13.30 \(\int \frac {-2 k-(-1+k) (1+k) x+2 k x^2}{\sqrt [4]{(1-x^2) (1-k^2 x^2)} (-1+d+(3+d) k x-(d+3 k^2) x^2+k (-d+k^2) x^3)} \, dx\)
  3.13.31 \(\int \frac {-2 k+(-1+k) (1+k) x+2 k x^2}{\sqrt [4]{(1-x^2) (1-k^2 x^2)} (1-d+(3+d) k x+(d+3 k^2) x^2+k (-d+k^2) x^3)} \, dx\)
  3.13.32 \(\int \frac {(1+x^2) \sqrt {1-2 x^4}}{x^5} \, dx\)
  3.13.33 \(\int \frac {(1+x^4)^{2/3}}{x^5} \, dx\)
  3.13.34 \(\int \frac {(-3+x^4) (1+x^4)^{2/3}}{x^3 (1-x^3+x^4)} \, dx\)
  3.13.35 \(\int \frac {\sqrt [3]{-1+x^4} (3+x^4)}{x^2 (-1+x^3+x^4)} \, dx\)
  3.13.36 \(\int \frac {(-1+x^4)^{2/3} (3+x^4)}{x^3 (-1+x^3+x^4)} \, dx\)
  3.13.37 \(\int \frac {(-3+x^4) \sqrt [3]{1+x^4}}{x^2 (1+x^3+x^4)} \, dx\)
  3.13.38 \(\int \frac {(4+3 x) (-1-x+x^4) \sqrt [4]{-1-x+2 x^4}}{x^6 (1+x+x^4)} \, dx\)
  3.13.39 \(\int \frac {\sqrt {1+3 x^4}}{-1+3 x^4} \, dx\)
  3.13.40 \(\int \frac {(b+a x^2) \sqrt [4]{-b x^2+a x^4}}{-b+a x^2} \, dx\)
  3.13.41 \(\int \frac {-b+2 a x^2}{(b+a x^2) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.13.42 \(\int \frac {(1+x^5)^{2/3}}{x^6} \, dx\)
  3.13.43 \(\int \frac {(1+x^5)^{2/3} (-3+2 x^5)}{x^3 (1-x^3+x^5)} \, dx\)
  3.13.44 \(\int \frac {(-1+x^5)^{2/3} (3+2 x^5)}{x^3 (-1-x^3+x^5)} \, dx\)
  3.13.45 \(\int \frac {\sqrt [4]{-1+x^6}}{x} \, dx\)
  3.13.46 \(\int \frac {1}{x^7 \sqrt [3]{1+x^6}} \, dx\)
  3.13.47 \(\int \frac {(1+x^6)^{2/3}}{x^7} \, dx\)
  3.13.48 \(\int \frac {(-3+k^2) x+2 k^2 x^3}{\sqrt [4]{(1-x^2) (1-k^2 x^2)} (-1+d+(3-d k^2) x^2-3 x^4+x^6)} \, dx\)
  3.13.49 \(\int \frac {(-1+x^7)^{2/3} (3+4 x^7)}{x^3 (-1+x^3+x^7)} \, dx\)
  3.13.50 \(\int \frac {x}{\sqrt {-b x+a^2 x^2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.13.51 \(\int \frac {-\sqrt {a b}+x}{\sqrt {x (a+x) (b+x)} (\sqrt {a b}+x)} \, dx\)
  3.13.52 \(\int \frac {1}{\sqrt [3]{-x^2+x^3}} \, dx\)
  3.13.53 \(\int \frac {3-x^2}{(1-x^2) \sqrt [4]{1-6 x^2+x^4}} \, dx\)
  3.13.54 \(\int \frac {-3+x^4}{(1+x^4) \sqrt [4]{-3 x+4 x^4-3 x^5}} \, dx\)
  3.13.55 \(\int \frac {\sqrt [3]{-1+x^6} (1+x^6)}{x^2 (-1+x^3+x^6)} \, dx\)
  3.13.56 \(\int \frac {(-1+x^4) \sqrt {1+x^4}}{1+x^2+3 x^4+x^6+x^8} \, dx\)
  3.13.57 \(\int \frac {-1+2 x^8}{\sqrt [4]{1+x^4} (-1+x^8)} \, dx\)
  3.13.58 \(\int \sqrt [4]{b x^5+a x^8} \, dx\)
  3.13.59 \(\int \frac {\sqrt {x-\sqrt {1+x^2}}}{1-\sqrt {1+x^2}} \, dx\)
  3.13.60 \(\int \frac {(-1+x) (3+x)}{(-1+x^2)^{2/3} (2-x+x^2)} \, dx\)
  3.13.61 \(\int \frac {\sqrt [3]{-1+x^3}}{x^4} \, dx\)
  3.13.62 \(\int \frac {(-1+x^3)^{2/3}}{x^4} \, dx\)
  3.13.63 \(\int \frac {\sqrt [3]{1+x^3}}{x^2} \, dx\)
  3.13.64 \(\int \frac {-1+x}{(1+x) \sqrt [3]{2+x^3}} \, dx\)
  3.13.65 \(\int \frac {1}{x^7 (b+a x^3)^{3/4}} \, dx\)
  3.13.66 \(\int \frac {(1+2 x+x^2) (-2-(-1+k) (1+k) x+2 k^2 x^2)}{((1-x^2) (1-k^2 x^2))^{3/4} (1-d-(1+3 d) x-(3 d+k^2) x^2+(-d+k^2) x^3)} \, dx\)
  3.13.67 \(\int \frac {1}{x^5 \sqrt [3]{-1+x^4}} \, dx\)
  3.13.68 \(\int \frac {x (-b+x) (a b-2 a x+x^2)}{\sqrt {x (-a+x) (-b+x)} (-a^2 d+2 a d x+(b^2-d) x^2-2 b x^3+x^4)} \, dx\)
  3.13.69 \(\int \frac {1}{x^9 (b+a x^4)^{3/4}} \, dx\)
  3.13.70 \(\int x^4 (b+a x^4)^{3/4} \, dx\)
  3.13.71 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{x (d+c x+x^2)} \, dx\)
  3.13.72 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{x (d+c x+x^2)} \, dx\)
  3.13.73 \(\int \frac {(-1+x^5)^{2/3}}{x^6} \, dx\)
  3.13.74 \(\int \frac {1}{x^{11} (b+a x^5)^{3/4}} \, dx\)
  3.13.75 \(\int \frac {1}{x^7 \sqrt [3]{-1+x^6}} \, dx\)
  3.13.76 \(\int \frac {(-1+x^6)^{2/3}}{x^7} \, dx\)
  3.13.77 \(\int \frac {(-1+x^4+2 x^6) \sqrt [3]{x+x^5+x^7}}{(1+x^4+x^6) (1-x^2+x^4+x^6)} \, dx\)
  3.13.78 \(\int \frac {\sqrt {1+\sqrt {1+x}}}{x-\sqrt {1+x}} \, dx\)
  3.13.79 \(\int \frac {1}{x^3 (-1+x^2)^{3/4}} \, dx\)
  3.13.80 \(\int \frac {(-1+x^3)^{2/3}}{x^3} \, dx\)
  3.13.81 \(\int \frac {2+x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.13.82 \(\int \frac {(1+x^3)^{2/3}}{x^3} \, dx\)
  3.13.83 \(\int \frac {2 a b x+(-3 a+b) x^2}{\sqrt [4]{x^2 (-a+x) (-b+x)} (a^3-3 a^2 x+(3 a-b d) x^2+(-1+d) x^3)} \, dx\)
  3.13.84 \(\int \frac {\sqrt [4]{-1+x^4}}{x^5} \, dx\)
  3.13.85 \(\int \frac {1+x^2}{(-1+x+x^2) \sqrt [3]{-x^2+x^4}} \, dx\)
  3.13.86 \(\int \frac {(-1+2 x) (2-x+x^2) \sqrt {-2+x^2-2 x^3+x^4}}{3-2 x+2 x^2} \, dx\)
  3.13.87 \(\int \frac {\sqrt [4]{-x^3+x^4}}{x (1+x)} \, dx\)
  3.13.88 \(\int \frac {1+2 x^3}{(-1+x+x^3) \sqrt [3]{-x^2+x^5}} \, dx\)
  3.13.89 \(\int \frac {\sqrt [4]{-1+x^6}}{x^7} \, dx\)
  3.13.90 \(\int \frac {1+3 x^4}{(-1+x+x^4) \sqrt [3]{-x^2+x^6}} \, dx\)
  3.13.91 \(\int \frac {(2+x^3) \sqrt {-1-x^2+x^3}}{1-x^2-2 x^3-x^4+x^5+x^6} \, dx\)
  3.13.92 \(\int \frac {(1+x^4) \sqrt {-1-x^2+x^4}}{1-x^2-3 x^4+x^6+x^8} \, dx\)
  3.13.93 \(\int \frac {x^2 \sqrt {x+\sqrt {1+x}}}{\sqrt {1+x}} \, dx\)
  3.13.94 \(\int (-1+x^3)^{2/3} \, dx\)
  3.13.95 \(\int (1+x^3)^{2/3} \, dx\)
  3.13.96 \(\int \frac {-1+x^3}{\sqrt [3]{2+x^3}} \, dx\)
  3.13.97 \(\int \sqrt [3]{x+x^3} \, dx\)
  3.13.98 \(\int \frac {(-2 k+(-1+k) (1+k) x+2 k x^2) (1+2 k x+k^2 x^2)}{((1-x^2) (1-k^2 x^2))^{3/4} (-1+d+(1+3 d) k x+(1+3 d k^2) x^2+k (-1+d k^2) x^3)} \, dx\)
  3.13.99 \(\int \frac {(-1+x^4)^{3/4} (4+x^4)}{x^8 (-4+x^4)} \, dx\)
  3.13.100 \(\int \frac {4 b+a x^3}{\sqrt [4]{b+a x^3} (b+a x^3+x^4)} \, dx\)