3.18.1 \(\int \frac {(2+x-x^3-x^4)^{2/3} (6+2 x+x^4) (-2-x+x^3+x^4)}{x^6 (-2-x+2 x^3+x^4)} \, dx\)
  3.18.2 \(\int \frac {(-3+x^4) (1+x^4)^{2/3} (2+x^3+2 x^4)}{x^6 (4-x^3+4 x^4)} \, dx\)
  3.18.3 \(\int \frac {(-1-x^4+2 x^6) \sqrt [3]{x-x^5+x^7}}{(1+x^2-x^4+x^6)^2} \, dx\)
  3.18.4 \(\int \frac {x^4 (-4 b+a x^3)}{\sqrt [4]{-b+a x^3} (-b^2+2 a b x^3-a^2 x^6+x^8)} \, dx\)
  3.18.5 \(\int \frac {\sqrt {-1+x^2} \sqrt {x^2+x \sqrt {-1+x^2}}}{1+x^2} \, dx\)
  3.18.6 \(\int \frac {x}{(x^2 (-a+x))^{2/3} (a+(-1+d) x)} \, dx\)
  3.18.7 \(\int \frac {b-c x+a x^2}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
  3.18.8 \(\int \frac {b+c x+a x^2}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
  3.18.9 \(\int \frac {\sqrt [3]{b-a x^6} (b+a x^6)}{x^2 (-b+c x^3+a x^6)} \, dx\)
  3.18.10 \(\int \frac {x^2 (4+7 x^3)}{\sqrt [3]{x+x^4} (-1+x^4+x^7)} \, dx\)
  3.18.11 \(\int \frac {\sqrt {x-\sqrt {-1+x^2}}}{x^2} \, dx\)
  3.18.12 \(\int \frac {(a x+\sqrt {-b x+a^2 x^2})^{3/4}}{\sqrt {-b x+a^2 x^2}} \, dx\)
  3.18.13 \(\int \frac {\sqrt [4]{-b x^3+a x^4} (-d+c x^4)}{x^4} \, dx\)
  3.18.14 \(\int \frac {(1+x^3)^{2/3} (2+x^3)}{x^6 (4+x^3)} \, dx\)
  3.18.15 \(\int \frac {(-1+x^3) (1+3 x^3)^{2/3}}{x^6 (1+x^3)} \, dx\)
  3.18.16 \(\int \frac {3-8 x+8 x^2-12 x^4}{x \sqrt [3]{\frac {1-2 x^2}{1+2 x^2}} (1+2 x^2) (3-7 x+7 x^2-6 x^3+2 x^4)} \, dx\)
  3.18.17 \(\int \frac {x^2}{\sqrt {b x+a x^3} (-b^2+a^2 x^4)} \, dx\)
  3.18.18 \(\int \frac {b+a x^6}{x^6 (-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.18.19 \(\int \frac {\sqrt [3]{-1+2 x^3+x^8} (3+5 x^8)}{x^2 (-1+x^8)} \, dx\)
  3.18.20 \(\int \frac {\sqrt {b^2+a x^2}}{\sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.18.21 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{(b^2+a x^2)^3} \, dx\)
  3.18.22 \(\int \frac {(-b+a x^2)^{3/4}}{x^3} \, dx\)
  3.18.23 \(\int \frac {(1+x^3) (-1+2 x^3)^{2/3}}{x^6 (1+2 x^3)} \, dx\)
  3.18.24 \(\int \frac {(1-x^3)^{2/3} (-1+4 x^3)}{x^6 (-2+3 x^3)} \, dx\)
  3.18.25 \(\int \frac {\sqrt [4]{-b+a x^3}}{x^4} \, dx\)
  3.18.26 \(\int \frac {(-b+a x^3)^{3/4}}{x^4} \, dx\)
  3.18.27 \(\int \frac {(-a+x) (-3 a b+(a+2 b) x) (-b^3+3 b^2 x-3 b x^2+x^3)}{x (x (-a+x) (-b+x)^2)^{3/4} (a b^2-b (2 a+b) x+(a+2 b) x^2+(-1+d) x^3)} \, dx\)
  3.18.28 \(\int \frac {(-b+a x^5)^{3/4}}{x^6} \, dx\)
  3.18.29 \(\int \frac {(-b+a x^6)^{3/4}}{x^7} \, dx\)
  3.18.30 \(\int \frac {(-4+5 x^7) \sqrt [3]{-2 x+2 x^3-x^8}}{(2+x^7) (2-2 x^2+x^7)} \, dx\)
  3.18.31 \(\int \frac {\sqrt {-b^4+a^4 x^4} (b^4+a^4 x^4)}{b^8+a^8 x^8} \, dx\)
  3.18.32 \(\int \frac {-b^8+a^8 x^8}{\sqrt {-b^4+a^4 x^4} (b^8+a^8 x^8)} \, dx\)
  3.18.33 \(\int \frac {x^3 \sqrt {x+x^2}}{\sqrt {x^2+x \sqrt {x+x^2}}} \, dx\)
  3.18.34 \(\int \frac {(-b+a x^2)^{3/4} (3 b+2 a x^2)}{x} \, dx\)
  3.18.35 \(\int \frac {(-6+x^2) (2-x^2+x^3)^{2/3}}{x^3 (-2+x^2+x^3)} \, dx\)
  3.18.36 \(\int \frac {x^3 (-4 a+3 x)}{(x^2 (-a+x))^{2/3} (a d-d x+x^4)} \, dx\)
  3.18.37 \(\int \frac {-1+k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (1+k^4 x^4)} \, dx\)
  3.18.38 \(\int \frac {1-x^4}{(1+x^4) \sqrt [4]{x^3+x^5}} \, dx\)
  3.18.39 \(\int \frac {(1+x^3)^{2/3} (2+x^6)}{x^6 (-1+x^3)^2} \, dx\)
  3.18.40 \(\int \frac {(-1+x^3)^{2/3} (-2+2 x^3+x^6)}{x^6 (1+x^3)^2} \, dx\)
  3.18.41 \(\int \frac {(2 b+a x^6) (-b-c x^4+a x^6)}{x^2 (-b+a x^6)^{3/4} (-b+c x^4+a x^6)} \, dx\)
  3.18.42 \(\int \frac {\sqrt {c+d \sqrt {b+a x^2}}}{x} \, dx\)
  3.18.43 \(\int \frac {(-b+a^2 x^4) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{\sqrt {b+a^2 x^4}} \, dx\)
  3.18.44 \(\int \sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\)
  3.18.45 \(\int \frac {1}{(2 b+a x) \sqrt [4]{b x^2+a x^3}} \, dx\)
  3.18.46 \(\int \frac {x (-4 a+3 x)}{\sqrt [3]{x^2 (-a+x)} (a d-d x+x^4)} \, dx\)
  3.18.47 \(\int \frac {(-b+a x^5)^{3/4} (4 b+a x^5)}{x^4 (-b+c x^4+a x^5)} \, dx\)
  3.18.48 \(\int \frac {(1+x^8)^{3/4}}{-1+x^8} \, dx\)
  3.18.49 \(\int \frac {x^4}{\sqrt [4]{-1+x^4} (-1+2 x^4+x^8)} \, dx\)
  3.18.50 \(\int \frac {(-1+x^4)^{3/4}}{-1+2 x^4+x^8} \, dx\)
  3.18.51 \(\int \frac {1+x^4}{(-1+x^4) \sqrt {1+\sqrt {1+x^2}}} \, dx\)
  3.18.52 \(\int \frac {1}{x^3 (-b+a x^2)^{3/4}} \, dx\)
  3.18.53 \(\int \frac {a b-2 b x+x^2}{\sqrt [4]{x (-a+x) (-b+x)^3} (b-(1+a d) x+d x^2)} \, dx\)
  3.18.54 \(\int \frac {1}{x^4 (-b+a x^3)^{3/4}} \, dx\)
  3.18.55 \(\int \frac {1}{x^4 \sqrt [4]{-b+a x^3}} \, dx\)
  3.18.56 \(\int \frac {1}{x^5 (-b+a x^4)^{3/4}} \, dx\)
  3.18.57 \(\int \frac {a b^3-2 (3 a-b) b^2 x+3 (3 a-b) b x^2-4 a x^3+x^4}{\sqrt [4]{x (-a+x) (-b+x)^3} (a^3-(3 a^2+b^3 d) x+3 (a+b^2 d) x^2-(1+3 b d) x^3+d x^4)} \, dx\)
  3.18.58 \(\int \frac {1}{x^6 (-b+a x^5)^{3/4}} \, dx\)
  3.18.59 \(\int \frac {1}{x^7 (-b+a x^6)^{3/4}} \, dx\)
  3.18.60 \(\int \frac {b^6+a^6 x^6}{\sqrt {b^4+a^4 x^4} (-b^6+a^6 x^6)} \, dx\)
  3.18.61 \(\int \frac {\sqrt {-1+x^2} \sqrt {x^2+x \sqrt {-1+x^2}}}{1+x} \, dx\)
  3.18.62 \(\int \frac {(1+x^4) \sqrt {1+\sqrt {1+x^2}}}{-1+x^4} \, dx\)
  3.18.63 \(\int \frac {-b^2+a x^2}{(b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.18.64 \(\int \frac {x}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.18.65 \(\int \frac {-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} (b-b (1+k) x+(-1+b k) x^2)} \, dx\)
  3.18.66 \(\int \frac {(-b+a x^2) \sqrt {-b x+a x^3}}{x^2 (b+a x^2)} \, dx\)
  3.18.67 \(\int \frac {(-3+x^4) (1-x^3+x^4)^{2/3}}{x^3 (1+x^3+x^4)} \, dx\)
  3.18.68 \(\int \frac {(-4 b+a x^5) (b+a x^5)^{3/4}}{x^4 (2 b+c x^4+2 a x^5)} \, dx\)
  3.18.69 \(\int \frac {-1+x^6}{\sqrt [3]{x^2+x^4} (1+x^6)} \, dx\)
  3.18.70 \(\int \frac {\sqrt [4]{2+3 x^4} (4+6 x^4+x^8)}{x^6 (1+x^4) (1+2 x^4)} \, dx\)
  3.18.71 \(\int \frac {\sqrt [8]{256-256 x^2+96 x^4-16 x^6+x^8}}{-1+x^3} \, dx\)
  3.18.72 \(\int \frac {-36-6 x^2+6 x^3+x^6}{x (-6+x^3) \sqrt [6]{\frac {6+x^3}{-6+x^3}} (36-90 x+122 x^2-96 x^3+51 x^4-26 x^5+15 x^6-6 x^7+x^8)} \, dx\)
  3.18.73 \(\int \frac {-b+a x^8}{(b+a x^8) \sqrt [4]{b-c x^4+a x^8}} \, dx\)
  3.18.74 \(\int \frac {1}{x^2 \sqrt {-b x+a^2 x^2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.18.75 \(\int \frac {1+\sqrt {1+x^2}}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.18.76 \(\int \frac {-2+(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (b-b (1+k) x+(-1+b k) x^2)} \, dx\)
  3.18.77 \(\int \frac {\sqrt [4]{-b+a x^4} (-8 b+a x^8)}{x^{10} (b+a x^4)} \, dx\)
  3.18.78 \(\int \frac {(-6+x^2) (-2+x^2) (2-x^2+x^3) \sqrt [3]{-2+x^2+2 x^3}}{x^5 (-2+x^2+x^3)^2} \, dx\)
  3.18.79 \(\int \frac {(1+x) \sqrt [4]{x^3+x^5}}{x (-1+x^3)} \, dx\)
  3.18.80 \(\int \frac {(1+2 x^3)^{4/3} (1+3 x^3)}{x^8 (1+4 x^3)} \, dx\)
  3.18.81 \(\int \frac {-1+x^2}{(1+x^2) \sqrt [3]{-x^2+x^4}} \, dx\)
  3.18.82 \(\int \frac {x^3 (-4 a+3 x)}{(x^2 (-a+x))^{2/3} (a-x+d x^4)} \, dx\)
  3.18.83 \(\int \frac {b+a x^6}{x^6 (b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\)
  3.18.84 \(\int x^2 \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\)
  3.18.85 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [3]{a x+\sqrt {-b+a^2 x^2}} \sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.18.86 \(\int \frac {(2 a-3 b+x) (-a^3+3 a^2 x-3 a x^2+x^3)}{(-b+x) \sqrt [4]{(-a+x) (-b+x)^2} (-a^3-b^2 d+(3 a^2+2 b d) x-(3 a+d) x^2+x^3)} \, dx\)
  3.18.87 \(\int \frac {\sqrt {1-3 x^2-2 x^4} (1+2 x^4)}{(-1+x^2+2 x^4) (-1+2 x^2+2 x^4)} \, dx\)
  3.18.88 \(\int \frac {x (-4 a+3 x)}{\sqrt [3]{x^2 (-a+x)} (a-x+d x^4)} \, dx\)
  3.18.89 \(\int \frac {1}{(-1+x^2) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.18.90 \(\int \frac {-b^2+a^2 x^4}{\sqrt {-b x+a x^3} (b^2+c x^2+a^2 x^4)} \, dx\)
  3.18.91 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x (b x^2+a (q+p x^3)^2)} \, dx\)
  3.18.92 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x (b x^4+a (q+p x^3)^2)} \, dx\)
  3.18.93 \(\int \frac {\sqrt {1+\sqrt {1-\sqrt {1+\frac {1}{x^2}}}}}{x} \, dx\)
  3.18.94 \(\int \frac {-2 x+(1+k) x^2}{((1-x) x (1-k x))^{2/3} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.18.95 \(\int \frac {2-(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x)} \, dx\)
  3.18.96 \(\int \frac {-2+(1+k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.18.97 \(\int \frac {(3+2 x^2) (1+2 x^2+2 x^3)^{2/3}}{x^3 (-1-2 x^2+x^3)} \, dx\)
  3.18.98 \(\int \frac {-b+c x+a x^2}{(b+a x^2) \sqrt {-b x+a x^3}} \, dx\)
  3.18.99 \(\int \frac {-4-2 x+2 x^2+x^4}{x (-2+x^2) \sqrt [4]{\frac {2+x^2}{-2+x^2}} (8-10 x+4 x^2+4 x^3-4 x^4+x^5)} \, dx\)
  3.18.100 \(\int \frac {-d+c x}{x^4 \sqrt [3]{-b+a x^3}} \, dx\)