3.18.1 \(\int \frac {x^2 \sqrt [4]{x^3+x^4}}{-1+x} \, dx\)
  3.18.2 \(\int \frac {(-b+a x^3) (-b+2 a x^3)}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.18.3 \(\int \frac {-b+a x^4+x^8}{x^8 (-b+a x^4) \sqrt [4]{b+a x^4}} \, dx\)
  3.18.4 \(\int \frac {1+x^4}{x^4 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.18.5 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^2 \sqrt {b^2+a x^2}} \, dx\)
  3.18.6 \(\int \frac {2+x^2}{x (2-2 x+x^2) \sqrt [3]{1-x+x^2}} \, dx\)
  3.18.7 \(\int \frac {-1+x}{x^{10} \sqrt [3]{1+x^3}} \, dx\)
  3.18.8 \(\int \frac {1}{x \sqrt [3]{b+a x^3}} \, dx\)
  3.18.9 \(\int \frac {(-1-2 (-1+k) x+k x^2) (-1+3 k x-3 k^2 x^2+k^3 x^3)}{(-1+x) x \sqrt [4]{(1-x) x (1-k x)} (-1+(d+3 k) x-(d+3 k^2) x^2+k^3 x^3)} \, dx\)
  3.18.10 \(\int \frac {(3+x^4) (-1-x^3+x^4)^{2/3}}{x^3 (-1+x^4)} \, dx\)
  3.18.11 \(\int \frac {(1+2 x^2) \sqrt [3]{x+2 x^3}}{x^4 (1+2 x^4)} \, dx\)
  3.18.12 \(\int \frac {1}{x-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.18.13 \(\int \frac {1}{x-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.18.14 \(\int \frac {2-x+x^2}{\sqrt [3]{-1+x^2} (3+4 x+x^2)} \, dx\)
  3.18.15 \(\int \frac {x (-1+k x) (-1+2 (-1+k) x+k x^2)}{(-1+x) ((1-x) x (1-k x))^{3/4} (-d+(1+3 d) x-(3 d+k) x^2+d x^3)} \, dx\)
  3.18.16 \(\int \frac {(-1+x) x (-1-2 (-1+k) x+k x^2)}{((1-x) x (1-k x))^{3/4} (-1+k x) (-d+(1+3 d k) x-(1+3 d k^2) x^2+d k^3 x^3)} \, dx\)
  3.18.17 \(\int \frac {(4+x^2) \sqrt [3]{-2 x+x^3}}{x^4 (-4-4 x^2+x^4)} \, dx\)
  3.18.18 \(\int \frac {(4+x^2) \sqrt [3]{-2 x+x^3}}{x^4 (-4-4 x^2+x^4)} \, dx\)
  3.18.19 \(\int \frac {2 b+a x^3}{(-b+x^2+a x^3) \sqrt [4]{-b x^2+a x^5}} \, dx\)
  3.18.20 \(\int \frac {b+a x^2}{(-b+x+a x^2) \sqrt [4]{-b x^3+a x^5}} \, dx\)
  3.18.21 \(\int \frac {b+a x^4}{(-b+x^2+a x^4) \sqrt [4]{-b x^2+a x^6}} \, dx\)
  3.18.22 \(\int \frac {b+2 a x^3}{(-b+x+a x^3) \sqrt [4]{-b x^3+a x^6}} \, dx\)
  3.18.23 \(\int \frac {1}{\sqrt [4]{-b+a x^4} (-b-x^4+a x^8)} \, dx\)
  3.18.24 \(\int \frac {1}{\sqrt [4]{-b+a x^4} (-b-x^4+a x^8)} \, dx\)
  3.18.25 \(\int \frac {b+a x^4}{\sqrt [4]{-b+a x^4} (b+c x^4+a x^8)} \, dx\)
  3.18.26 \(\int \frac {b+a x^4}{\sqrt [4]{-b+a x^4} (b+c x^4+a x^8)} \, dx\)
  3.18.27 \(\int \frac {(1+x^5) \sqrt [3]{1+x^3+x^5} (-3+2 x^5)}{x^2 (2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10})} \, dx\)
  3.18.28 \(\int \frac {(1+x^5) \sqrt [3]{1+x^3+x^5} (-3+2 x^5)}{x^2 (2-2 x^3+4 x^5-x^6-2 x^8+2 x^{10})} \, dx\)
  3.18.29 \(\int x^4 \sqrt [3]{-x+x^3} \, dx\)
  3.18.30 \(\int \frac {x}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
  3.18.31 \(\int \frac {\sqrt {b x+a x^3}}{-b^2+a^2 x^4} \, dx\)
  3.18.32 \(\int \frac {x^{19}}{\sqrt [3]{-1+x^6}} \, dx\)
  3.18.33 \(\int x^{15} \sqrt [3]{-1+x^6} \, dx\)
  3.18.34 \(\int \frac {x^{19}}{\sqrt [3]{1+x^6}} \, dx\)
  3.18.35 \(\int x^{15} \sqrt [3]{1+x^6} \, dx\)
  3.18.36 \(\int \frac {-b-a x^3+x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.18.37 \(\int \frac {-3-x^4+3 x^6}{(1-x^4+x^6) \sqrt [3]{1-x^3-x^4+x^6}} \, dx\)
  3.18.38 \(\int \frac {-b+a x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.18.39 \(\int \frac {b+a x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.18.40 \(\int \frac {\sqrt [4]{x^2+x^4} (-1-x^4+x^8)}{-1+x^4} \, dx\)
  3.18.41 \(\int \frac {-b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b-a x^4+x^8)} \, dx\)
  3.18.42 \(\int \frac {-b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b-a x^4+x^8)} \, dx\)
  3.18.43 \(\int \frac {\sqrt {c x^2-x \sqrt {-b x+a x^2}}}{x^3 \sqrt {-b x+a x^2}} \, dx\)
  3.18.44 \(\int \frac {b+x^3}{\sqrt [3]{a+x^3}} \, dx\)
  3.18.45 \(\int \frac {b+a x^2}{\sqrt [3]{x+x^3}} \, dx\)
  3.18.46 \(\int \sqrt [3]{-x^2+x^3} \, dx\)
  3.18.47 \(\int x^2 \sqrt [3]{x^2+x^3} \, dx\)
  3.18.48 \(\int \frac {x^4}{(1+x^4)^2 \sqrt [4]{x^2+x^4}} \, dx\)
  3.18.49 \(\int \frac {x^4}{(1+x^4)^2 \sqrt [4]{x^2+x^4}} \, dx\)
  3.18.50 \(\int \frac {(-3+x^4) (1-x^3+x^4) (1+x^3+x^4)^{2/3}}{x^6 (1+x^4)} \, dx\)
  3.18.51 \(\int \frac {-b+2 a x^4}{(b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.18.52 \(\int \frac {-b+2 a x^4}{(b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.18.53 \(\int \frac {1+x^2}{(-1+x^2) \sqrt [3]{x+x^5}} \, dx\)
  3.18.54 \(\int \frac {(-1+x^2) \sqrt [4]{x^2+x^6}}{x^2 (1+x^2)} \, dx\)
  3.18.55 \(\int \frac {(-1+x^2) \sqrt [4]{x^2+x^6}}{x^2 (1+x^2)} \, dx\)
  3.18.56 \(\int \frac {(-1+x^3)^{2/3} (1-5 x^3+4 x^6)}{x^6 (-1+2 x^3)^2} \, dx\)
  3.18.57 \(\int \frac {\sqrt {1+x} \sqrt {1+\sqrt {1+x}}}{x-\sqrt {1+x}} \, dx\)
  3.18.58 \(\int \frac {\sqrt {b+a x}}{\sqrt {a b x+\sqrt {b+a x}}} \, dx\)
  3.18.59 \(\int \frac {\sqrt {b+a^2 x^4}}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\)
  3.18.60 \(\int \frac {1}{(f+e x) \sqrt {d+\sqrt {c+\sqrt {b+a x}}}} \, dx\)
  3.18.61 \(\int \frac {-a b+(-a+2 b) x}{\sqrt [4]{x (-a+x) (-b+x)^2} (-b^2+(2 b-a d) x+(-1+d) x^2)} \, dx\)
  3.18.62 \(\int x^{13} \sqrt [3]{-1+x^3} \, dx\)
  3.18.63 \(\int \frac {a b^2-2 (2 a-b) b x+(3 a-2 b) x^2}{\sqrt [4]{x (-a+x) (-b+x)^2} (a^3+(-3 a^2+b^2 d) x+(3 a-2 b d) x^2+(-1+d) x^3)} \, dx\)
  3.18.64 \(\int \frac {\sqrt [3]{x+2 x^3} (-1+x^4)}{x^4 (2-x^2+x^4)} \, dx\)
  3.18.65 \(\int \frac {b+2 a x^4}{(-b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.18.66 \(\int \frac {b+2 a x^4}{(-b+a x^4) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.18.67 \(\int \frac {(1+x^6) (-1-x^3+x^6)^{2/3}}{x^3 (-1+x^6)} \, dx\)
  3.18.68 \(\int \frac {(4+x^6) \sqrt [4]{-2-x^4+x^6}}{x^2 (-2+x^6)} \, dx\)
  3.18.69 \(\int \sqrt [4]{b x^7+a x^8} \, dx\)
  3.18.70 \(\int \frac {-1+x^{10}}{\sqrt {1+x^4} (1+x^{10})} \, dx\)
  3.18.71 \(\int \frac {1+x^{10}}{\sqrt {1+x^4} (-1+x^{10})} \, dx\)
  3.18.72 \(\int \frac {1+x^{16}}{\sqrt {1+x^4} (-1+x^{16})} \, dx\)
  3.18.73 \(\int \frac {\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{1-\sqrt {b+a x}} \, dx\)
  3.18.74 \(\int x \sqrt {-1+x^2} \sqrt {x^2+x \sqrt {-1+x^2}} \, dx\)
  3.18.75 \(\int \frac {(-q+p x^2) \sqrt {q^2+p^2 x^4} (b x^3+a (q+p x^2)^3)}{x^6} \, dx\)
  3.18.76 \(\int \frac {(-1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4}} \, dx\)
  3.18.77 \(\int \frac {x \sqrt {1+x}}{x+\sqrt {1+\sqrt {1+x}}} \, dx\)
  3.18.78 \(\int \frac {\sqrt [3]{-x+x^3} (8-10 x^2+x^4)}{x^4 (4-2 x^2+x^4)} \, dx\)
  3.18.79 \(\int \frac {\sqrt [3]{-x+x^3} (8-10 x^2+x^4)}{x^4 (4-2 x^2+x^4)} \, dx\)
  3.18.80 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
  3.18.81 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
  3.18.82 \(\int \frac {-1+x^4}{(1+x^4) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
  3.18.83 \(\int \frac {-1+x^4}{(1+x^4) \sqrt {1-x-x^2+x^3+x^4}} \, dx\)
  3.18.84 \(\int \frac {b+a x^8}{x^6 (-b+a x^4) (b+a x^4)^{3/4}} \, dx\)
  3.18.85 \(\int \frac {-b+2 a x^4}{\sqrt [4]{-b+a x^4} (-2 b-c x^4+2 a x^8)} \, dx\)
  3.18.86 \(\int \frac {-b+2 a x^4}{\sqrt [4]{-b+a x^4} (-2 b-c x^4+2 a x^8)} \, dx\)
  3.18.87 \(\int \frac {-a b-a c+3 b c+2 (a-b-c) x+x^2}{\sqrt [4]{(-a+x) (-b+x) (-c+x)} (-a^3-b c d+(3 a^2+b d+c d) x-(3 a+d) x^2+x^3)} \, dx\)
  3.18.88 \(\int \frac {1}{(-b+a x) \sqrt [4]{b^2 x+a^2 x^3}} \, dx\)
  3.18.89 \(\int \frac {(2+x^2) (-2-2 x+x^2) \sqrt {4-3 x^2+x^4}}{x^2 (-2+x^2) (-4+x+2 x^2)} \, dx\)
  3.18.90 \(\int \frac {1+x}{(-1+x) \sqrt [3]{x^2+x^4}} \, dx\)
  3.18.91 \(\int \frac {-b^2+a^4 x^4}{\sqrt {b x+a^2 x^3} (b^2+a^4 x^4)} \, dx\)
  3.18.92 \(\int \frac {-1+x^2}{(1+x^2) \sqrt [3]{x+x^5}} \, dx\)
  3.18.93 \(\int \frac {(1+x^4) \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx\)
  3.18.94 \(\int \frac {(1+x^4) \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx\)
  3.18.95 \(\int \frac {1-2 x^4+2 x^8}{\sqrt [4]{-1+x^4} (-2-x^4+2 x^8)} \, dx\)
  3.18.96 \(\int \frac {\sqrt {-x+x^2} \sqrt {x^2-x \sqrt {-x+x^2}}}{x^3} \, dx\)
  3.18.97 \(\int \frac {b+2 a x}{\sqrt [4]{c+b x+a x^2} (5 c+4 b x+4 a x^2)} \, dx\)
  3.18.98 \(\int x^6 \sqrt [3]{-x+x^3} \, dx\)
  3.18.99 \(\int \frac {1}{\sqrt [3]{-1-x+x^2+x^3}} \, dx\)
  3.18.100 \(\int \frac {1+2 x^4}{(-1+x^4) \sqrt [4]{-x^2+x^4}} \, dx\)