3.29.1 \(\int \frac {1+x^8}{\sqrt [4]{-x^2+x^4} (-1+x^8)} \, dx\)
  3.29.2 \(\int \frac {1+x^8}{\sqrt [4]{-x^2+x^4} (-1+x^8)} \, dx\)
  3.29.3 \(\int \frac {a b-(a+b) x+x^2}{((-a+x) (-b+x)^2)^{2/3} (a^2-b^2 d-2 (a-b d) x+(1-d) x^2)} \, dx\)
  3.29.4 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{(-1+x^4) \sqrt {1+x^4}} \, dx\)
  3.29.5 \(\int \frac {-1+x^6}{\sqrt [3]{-x^2+x^4} (1+x^6)} \, dx\)
  3.29.6 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{1+x} \, dx\)
  3.29.7 \(\int \frac {b+a x^2}{(b-a x^2) \sqrt [4]{b x^3+a x^5}} \, dx\)
  3.29.8 \(\int \frac {(4+x^3) (1+x^3+x^4)}{\sqrt [4]{1+x^3} (1+2 x^3+x^6+x^8)} \, dx\)
  3.29.9 \(\int \frac {x^2 \sqrt {1+x}}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.29.10 \(\int \frac {x^2 \sqrt {1+x}}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.29.11 \(\int \frac {(-b-a x+x^4) \sqrt [4]{b x^3+a x^4}}{-b+a x} \, dx\)
  3.29.12 \(\int \frac {(-4 a+b+3 x) (-b^3+3 b^2 x-3 b x^2+x^3)}{((-a+x) (-b+x)^2)^{2/3} (a+b^4 d-(1+4 b^3 d) x+6 b^2 d x^2-4 b d x^3+d x^4)} \, dx\)
  3.29.13 \(\int \frac {x^2 (-2+(1+k) x)}{\sqrt [3]{(1-x) x (1-k x)} (1-(2+2 k) x+(1+4 k+k^2) x^2-(2 k+2 k^2) x^3+(-b+k^2) x^4)} \, dx\)
  3.29.14 \(\int \frac {1}{c+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.29.15 \(\int \frac {(-7+x) \sqrt [3]{1+x-5 x^2+3 x^3}}{(-5+x) (-1+x)^3} \, dx\)
  3.29.16 \(\int \frac {b^2+a^2 x^2}{(-b^2+a^2 x^2)^3 \sqrt [3]{-b x^2+a x^3}} \, dx\)
  3.29.17 \(\int \frac {d+c x}{(-d+c x) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.29.18 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{-d-2 c x+x^2} \, dx\)
  3.29.19 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{-d-2 c x+x^2} \, dx\)
  3.29.20 \(\int \frac {x (-1+k x) (-1+(-1+2 k) x)}{\sqrt [3]{(1-x) x (1-k x)} (-1+4 x+(-6+b) x^2+(4-2 b k) x^3+(-1+b k^2) x^4)} \, dx\)
  3.29.21 \(\int \frac {1+(-2+3 k) x-(k+4 k^2) x^2+3 k^2 x^3}{\sqrt [3]{(1-x) x (1-k x)} (-b+(1+5 b k) x-(1+10 b k^2) x^2+10 b k^3 x^3-5 b k^4 x^4+b k^5 x^5)} \, dx\)
  3.29.22 \(\int \frac {(d+c x)^2}{\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.29.23 \(\int \frac {1-\sqrt [3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}}}{x^2+\sqrt [3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}}} \, dx\)
  3.29.24 \(\int \frac {1-k x}{(1+(-2+k) x) ((1-x) x (1-k x))^{2/3}} \, dx\)
  3.29.25 \(\int \frac {1+x^2+x^3}{(-1+x^2+x^3) \sqrt [3]{x^2+x^3}} \, dx\)
  3.29.26 \(\int \frac {1+x^2+x^3}{(-1+x^2+x^3) \sqrt [3]{x^2+x^3}} \, dx\)
  3.29.27 \(\int \frac {\sqrt {a x+\sqrt {-b+a x}}}{x \sqrt {-b+a x}} \, dx\)
  3.29.28 \(\int \sqrt {a x+\sqrt {b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.29.29 \(\int x^4 \sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\)
  3.29.30 \(\int \frac {\sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}}}{(b+a^2 x^2)^{3/2} \sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.29.31 \(\int \frac {\sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}}}{(b+a^2 x^2)^{3/2} \sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.29.32 \(\int \frac {x^2}{(b+a x^2) \sqrt [3]{x+x^3}} \, dx\)
  3.29.33 \(\int \frac {1+x^6}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\)
  3.29.34 \(\int \frac {\sqrt {-2+3 x^4} (-1+3 x^4)}{x^3 (1-3 x^4+3 x^8)} \, dx\)
  3.29.35 \(\int \frac {1}{(-b x+a^2 x^2)^{5/2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.29.36 \(\int \frac {(a-2 b+x) (-b+x)}{\sqrt [3]{(-a+x) (-b+x)} (a^4-b^2 d-2 (2 a^3-b d) x+(6 a^2-d) x^2-4 a x^3+x^4)} \, dx\)
  3.29.37 \(\int \frac {(-1+x) x (1+(-2+k) x)}{\sqrt [3]{(1-x) x (1-k x)} (1-4 k x+(-b+6 k^2) x^2+(2 b-4 k^3) x^3+(-b+k^4) x^4)} \, dx\)
  3.29.38 \(\int \frac {(-1+x^3)^{2/3} (4+x^6)}{x^6 (-4+x^6)} \, dx\)
  3.29.39 \(\int \frac {\sqrt [6]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}}{\sqrt {-b+a^2 x^2}} \, dx\)
  3.29.40 \(\int \frac {(-b+x) (a b-2 b x+x^2)}{(x (-a+x) (-b+x)^2)^{2/3} (b d-(a+d) x+x^2)} \, dx\)
  3.29.41 \(\int \frac {-d+c x^4}{x \sqrt [3]{-b+a x^3}} \, dx\)
  3.29.42 \(\int \frac {a b-2 b x+x^2}{\sqrt [3]{x (-a+x) (-b+x)^2} (b-(1+a d) x+d x^2)} \, dx\)
  3.29.43 \(\int \frac {-a b^2+(4 a-b) b x-3 a x^2+x^3}{\sqrt [3]{x (-a+x) (-b+x)^2} (-a^2+(2 a+b^2 d) x-(1+2 b d) x^2+d x^3)} \, dx\)
  3.29.44 \(\int \frac {(-4 a+b+3 x) (-b^3+3 b^2 x-3 b x^2+x^3)}{((-a+x) (-b+x)^2)^{2/3} (b^4+a d-(4 b^3+d) x+6 b^2 x^2-4 b x^3+x^4)} \, dx\)
  3.29.45 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{x (-d+c x)} \, dx\)
  3.29.46 \(\int \frac {(-a+x) (-b+x) (-2 a b x+(a+b) x^2)}{(x (-a+x) (-b+x))^{2/3} (a^2 b^2 d-2 a b (a+b) d x+(a^2+4 a b+b^2) d x^2-2 (a+b) d x^3+(-1+d) x^4)} \, dx\)
  3.29.47 \(\int \frac {1+x^3+x^6}{\sqrt [4]{x^3+x^5} (1-x^6)} \, dx\)
  3.29.48 \(\int \frac {-a-b x+(b+a k^2) x^2}{\sqrt {(1-x) x (1-k^2 x)} (1-2 x+k^2 x^2)} \, dx\)
  3.29.49 \(\int \frac {1-2 x^4+x^8}{\sqrt [4]{-1+x^4} (1-2 x^4+2 x^8)} \, dx\)
  3.29.50 \(\int \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.29.51 \(\int \frac {x^3}{\sqrt [3]{x^2 (-a+x)} (-a^4+4 a^3 x-6 a^2 x^2+4 a x^3+(-1+d) x^4)} \, dx\)
  3.29.52 \(\int \frac {\sqrt {c+\sqrt {a x^2+x \sqrt {-b+a^2 x^2}}}}{\sqrt {-b+a^2 x^2}} \, dx\)
  3.29.53 \(\int \frac {-a (a b+a c-2 b c)+2 (a^2-b c) x+(-2 a+b+c) x^2}{((-a+x) (-b+x) (-c+x))^{2/3} (-b c+a^2 d+(b+c-2 a d) x+(-1+d) x^2)} \, dx\)
  3.29.54 \(\int \frac {x^2 (-2 a b+(a+b) x)}{\sqrt [3]{x (-a+x) (-b+x)} (-a^2 b^2+2 a b (a+b) x-(a^2+4 a b+b^2) x^2+2 (a+b) x^3+(-1+d) x^4)} \, dx\)
  3.29.55 \(\int \frac {1+x^6}{\sqrt [4]{x^3+x^5} (1-x^6)} \, dx\)
  3.29.56 \(\int \frac {b^{16}+a^{16} x^{16}}{\sqrt {-b^4+a^4 x^4} (-b^{16}+a^{16} x^{16})} \, dx\)
  3.29.57 \(\int \frac {\sqrt [3]{-b^2 x^2+a^3 x^3}}{b+a x^2} \, dx\)
  3.29.58 \(\int \frac {\sqrt [3]{-b^2 x^2+a^3 x^3}}{b+a x^2} \, dx\)
  3.29.59 \(\int \frac {b^8+x^4+a^8 x^8}{\sqrt {-b^4+a^4 x^4} (-b^8+a^8 x^8)} \, dx\)
  3.29.60 \(\int \frac {\sqrt [3]{-b^2 x^2+a^3 x^3}}{-b+a x^2} \, dx\)
  3.29.61 \(\int \frac {\sqrt [3]{-b^2 x^2+a^3 x^3}}{-b+a x^2} \, dx\)
  3.29.62 \(\int \frac {-b+x}{((-a+x) (-b+x)^2)^{2/3} (a-b d+(-1+d) x)} \, dx\)
  3.29.63 \(\int \frac {\sqrt {-b+x^2} (c+x^4) \sqrt {x+\sqrt {-b+x^2}}}{x} \, dx\)
  3.29.64 \(\int \frac {x^8}{\sqrt {-b^4+a^4 x^4} (-b^{16}+a^{16} x^{16})} \, dx\)
  3.29.65 \(\int \frac {x^2}{(-b+a x^2) \sqrt [3]{-x+x^3}} \, dx\)
  3.29.66 \(\int \frac {(1+x^4) \sqrt {x+\sqrt {1+x^2}}}{-1+x^4} \, dx\)
  3.29.67 \(\int \frac {(-a+x) (-b+x)}{((-a+x) (-b+x)^2)^{2/3} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.29.68 \(\int \frac {a b-(a+b) x+x^2}{((-a+x) (-b+x)^2)^{2/3} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.29.69 \(\int \frac {x}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.29.70 \(\int \frac {x}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.29.71 \(\int \frac {a b-2 b x+x^2}{\sqrt [3]{x (-a+x) (-b+x)^2} (b d-(a+d) x+x^2)} \, dx\)
  3.29.72 \(\int \frac {-a b^2+(4 a-b) b x-3 a x^2+x^3}{\sqrt [3]{x (-a+x) (-b+x)^2} (-a^2 d+(b^2+2 a d) x-(2 b+d) x^2+x^3)} \, dx\)
  3.29.73 \(\int \frac {-d+c x^7}{x \sqrt [3]{-b+a x^3}} \, dx\)
  3.29.74 \(\int \frac {\sqrt {c+\sqrt {b+a x}}}{x-\sqrt {b+a x}} \, dx\)
  3.29.75 \(\int \frac {1+x}{(1+2 x) \sqrt [3]{27+27 x+36 x^2+28 x^3+9 x^4+x^5}} \, dx\)
  3.29.76 \(\int \frac {-b x+a x^3}{(-b+2 a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.29.77 \(\int \frac {-b x+a x^3}{(-b+2 a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.29.78 \(\int \frac {b x+a x^3}{(b+2 a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.29.79 \(\int \frac {x (-b+x) (a b+(-2 a+b) x)}{\sqrt [3]{x (-a+x) (-b+x)} (-a^4+4 a^3 x+(-6 a^2+b^2 d) x^2+2 (2 a-b d) x^3+(-1+d) x^4)} \, dx\)
  3.29.80 \(\int \frac {-a b-a c+2 b c+(2 a-b-c) x}{\sqrt [3]{(-a+x) (-b+x) (-c+x)} (-b c+a^2 d+(b+c-2 a d) x+(-1+d) x^2)} \, dx\)
  3.29.81 \(\int \frac {x (-a b+x^2)}{\sqrt [3]{x^2 (-a+x) (-b+x)} (a^2 b^2-2 a b (a+b) x+(a^2+4 a b+b^2-d) x^2-2 (a+b) x^3+x^4)} \, dx\)
  3.29.82 \(\int \frac {-b^6+a^6 x^6}{\sqrt {-b^2 x+a^2 x^3} (b^6+a^6 x^6)} \, dx\)
  3.29.83 \(\int \frac {\sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}}}{-1+x^4} \, dx\)
  3.29.84 \(\int \frac {x^4}{1-x \sqrt {1+x^2} \sqrt {x-\sqrt {1+x^2}}} \, dx\)
  3.29.85 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{(1+x)^2 \sqrt {1+x^4}} \, dx\)
  3.29.86 \(\int \frac {(-b+x) (a b-2 b x+x^2)}{\sqrt [3]{x (-a+x) (-b+x)^2} (-b^2 d+2 b d x-(-a^2+d) x^2-2 a x^3+x^4)} \, dx\)
  3.29.87 \(\int \frac {b^8+a^8 x^8}{\sqrt {-b^4+a^4 x^4} (-b^8+a^8 x^8)} \, dx\)
  3.29.88 \(\int \frac {1}{\sqrt {-1+x^2} (\sqrt {x}+\sqrt {-1+x^2})^2} \, dx\)
  3.29.89 \(\int \frac {b+a x^2}{(d+c x^2) \sqrt [3]{x+x^3}} \, dx\)
  3.29.90 \(\int \frac {x^3 (4 a b-3 (a+b) x+2 x^2)}{(x^2 (-a+x) (-b+x))^{2/3} (-a b+(a+b) x-x^2+d x^4)} \, dx\)
  3.29.91 \(\int \frac {b x+a x^3}{(b+2 a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.29.92 \(\int \frac {1}{\sqrt {-1+2 x} (4+3 x)+(1+x) \sqrt {-3+4 x}} \, dx\)
  3.29.93 \(\int \frac {f+e x}{(h+g x) \sqrt {d+\sqrt {c+\sqrt {b+a x}}}} \, dx\)
  3.29.94 \(\int (1+x^2)^{3/2} \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.29.95 \(\int \frac {(a-5 b+4 x) (-a^3+3 a^2 x-3 a x^2+x^3)}{((-a+x) (-b+x))^{2/3} (b-a^5 d-(1-5 a^4 d) x-10 a^3 d x^2+10 a^2 d x^3-5 a d x^4+d x^5)} \, dx\)
  3.29.96 \(\int \frac {(2-2 x+2 x^2-3 x^3+3 x^4) \sqrt [3]{-x-x^3-x^4+x^6}}{(1+x) (-1+2 x-2 x^2+x^3) (-1-x^3+x^5)} \, dx\)
  3.29.97 \(\int \frac {1}{(-b+a x) \sqrt [3]{-b^2 x^2+a^3 x^3}} \, dx\)
  3.29.98 \(\int \frac {(-b+x) (-4 a+b+3 x)}{\sqrt [3]{(-a+x) (-b+x)^2} (b^4+a d-(4 b^3+d) x+6 b^2 x^2-4 b x^3+x^4)} \, dx\)
  3.29.99 \(\int \frac {x^4}{\sqrt {-b^4+a^4 x^4} (-b^8+a^8 x^8)} \, dx\)
  3.29.100 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt {a x+\sqrt {-b+a^2 x^2}} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)