3.25.1 \(\int \frac {1}{\sqrt [4]{-1+x^4} (-1-x^4+x^8)} \, dx\)
  3.25.2 \(\int \frac {-1+2 x^4}{\sqrt [4]{-1+x^4} (-1-x^4+x^8)} \, dx\)
  3.25.3 \(\int \frac {1}{\sqrt [4]{1+x^4} (-1+x^4+x^8)} \, dx\)
  3.25.4 \(\int \frac {-2+x^4}{\sqrt [4]{1+x^4} (-1+x^4+x^8)} \, dx\)
  3.25.5 \(\int \frac {\sqrt [4]{b x^3+a x^4} (-d+c x^8)}{x^8} \, dx\)
  3.25.6 \(\int \frac {x^4 (2+x^5)}{\sqrt {1+x^5} (-1-x^5+a x^{10})} \, dx\)
  3.25.7 \(\int \frac {x^4 (-2+x^5)}{\sqrt {-1+x^5} (1-x^5+a x^{10})} \, dx\)
  3.25.8 \(\int \frac {x^4 (3+x^5)}{\sqrt {1+x^5} (-1+a-(1+2 a) x^5+a x^{10})} \, dx\)
  3.25.9 \(\int \frac {1}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.25.10 \(\int \frac {1}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.25.11 \(\int \frac {1}{\sqrt {-b+a^2 x^2} (c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}})^{2/3}} \, dx\)
  3.25.12 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.25.13 \(\int \frac {1}{\sqrt [3]{1-3 x^2} (-3+x^2)} \, dx\)
  3.25.14 \(\int \frac {-a+x}{\sqrt [3]{x^2 (-a+x)} (a^2 d-2 a d x+(-1+d) x^2)} \, dx\)
  3.25.15 \(\int \frac {b-a x^4+2 x^8}{\sqrt [4]{-b+a x^4} (b+3 a x^4)} \, dx\)
  3.25.16 \(\int \frac {d+c x^2}{\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.25.17 \(\int \frac {\sqrt [4]{b x^3+a x^4} (-c+d x^8)}{x^4} \, dx\)
  3.25.18 \(\int \frac {(b^2+a x^2)^{5/2}}{\sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.25.19 \(\int \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.25.20 \(\int \frac {(x^2 c_3-c_4) (x+3 x^2 c_3+3 c_4)}{x \sqrt {\frac {x c_0+x^2 c_3+c_4}{x c_1+x^2 c_3+c_4}} (-x^2+x^4 c_3{}^2+2 x^2 c_3 c_4+c_4{}^2)} \, dx\)
  3.25.21 \(\int \frac {1+x^6}{\sqrt [3]{x+x^5} (-1+x^6)} \, dx\)
  3.25.22 \(\int \frac {1}{x^2 \sqrt [3]{-4-8 x+11 x^2+17 x^3-20 x^4-7 x^5+16 x^6-7 x^7+x^8}} \, dx\)
  3.25.23 \(\int \frac {b^8+a^8 x^8}{\sqrt {b^4+a^4 x^4} (-b^8+a^8 x^8)} \, dx\)
  3.25.24 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{x-\sqrt {1+x}} \, dx\)
  3.25.25 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{x-\sqrt {1+x}} \, dx\)
  3.25.26 \(\int \frac {(d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}}{-d+c x^2} \, dx\)
  3.25.27 \(\int \frac {(d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}}{-d+c x^2} \, dx\)
  3.25.28 \(\int \frac {\sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}{x \sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}} \, dx\)
  3.25.29 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {1+\sqrt {1+x}} \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.25.30 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {1+\sqrt {1+x}} \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.25.31 \(\int \sqrt {1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.25.32 \(\int \frac {2+3 x}{\sqrt [3]{4+3 x^2} (-12+52 x+9 x^2)} \, dx\)
  3.25.33 \(\int (c+b x+a x^2)^{5/2} \, dx\)
  3.25.34 \(\int \frac {1-x^4+x^8}{x^2 (-1+x^4)^{3/4} (-1-x^4+x^8)} \, dx\)
  3.25.35 \(\int \frac {(-d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}}{d+c x^2} \, dx\)
  3.25.36 \(\int \frac {(-d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}}{d+c x^2} \, dx\)
  3.25.37 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.25.38 \(\int \frac {1}{x \sqrt [3]{4-6 x+3 x^2}} \, dx\)
  3.25.39 \(\int \frac {x^2 \sqrt [4]{b x^3+a x^4}}{-b+a x} \, dx\)
  3.25.40 \(\int \frac {-1+x^6}{\sqrt [3]{x+x^5} (1+x^6)} \, dx\)
  3.25.41 \(\int \frac {b-2 x^4+a x^8}{\sqrt [4]{-b+a x^4} (b-2 x^4+2 a x^8)} \, dx\)
  3.25.42 \(\int \frac {b-2 x^4+a x^8}{\sqrt [4]{-b+a x^4} (b-2 x^4+2 a x^8)} \, dx\)
  3.25.43 \(\int \frac {-b+c x^4+2 a x^8}{\sqrt [4]{-b+a x^4} (b-c x^4+a x^8)} \, dx\)
  3.25.44 \(\int \frac {-b+c x^4+2 a x^8}{\sqrt [4]{-b+a x^4} (b-c x^4+a x^8)} \, dx\)
  3.25.45 \(\int \frac {\sqrt [4]{-b x^3+a x^4} (-d+c x^8)}{x^4} \, dx\)
  3.25.46 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^6} \, dx\)
  3.25.47 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^6 \sqrt {b^2+a x^2}} \, dx\)
  3.25.48 \(\int \sqrt {d+\sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.25.49 \(\int \frac {1}{(-b+a x^2) \sqrt [3]{-x+x^3}} \, dx\)
  3.25.50 \(\int \frac {1}{x^3 (-1+x^3) \sqrt [3]{x^2+x^3}} \, dx\)
  3.25.51 \(\int \frac {1}{x^3 (-1+x^3) \sqrt [3]{x^2+x^3}} \, dx\)
  3.25.52 \(\int \frac {1}{x^6 (-b+a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.25.53 \(\int \frac {1}{x^6 (-b+a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.25.54 \(\int \frac {(-1+x^2) (1+x+x^2) \sqrt {1+3 x^2+x^4}}{(1+x+x^2+x^3+x^4)^2} \, dx\)
  3.25.55 \(\int \frac {b+a x^4}{(-b+a x^4) \sqrt [4]{b^2+c x^4+a^2 x^8}} \, dx\)
  3.25.56 \(\int \frac {2 x^4-x^9}{\sqrt {-1+x^5} (a-a x^5+x^{10})} \, dx\)
  3.25.57 \(\int \frac {1+x^2}{(-1+x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.25.58 \(\int \frac {d+c x^2}{(-d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.25.59 \(\int \frac {d+c x^2}{(-d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.25.60 \(\int \frac {1}{x^6 (b+a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.25.61 \(\int \frac {1}{x^6 (b+a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.25.62 \(\int \frac {(-q+p x^2) (a q+b x+a p x^2) \sqrt {q^2+p^2 x^4}}{x^3 (c q+d x+c p x^2)} \, dx\)
  3.25.63 \(\int \frac {x (3+7 x^4)}{\sqrt [3]{1+x^4} (-4+x^3+x^7)} \, dx\)
  3.25.64 \(\int \frac {-d+c x^2}{(d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.25.65 \(\int \frac {-d+c x^2}{(d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.25.66 \(\int \frac {\sqrt {-b x+a^2 x^2}}{\sqrt {a x^2+x \sqrt {-b x+a^2 x^2}}} \, dx\)
  3.25.67 \(\int \frac {a-2 b+x}{\sqrt [3]{(-a+x) (-b+x)} (a^2+b d-(2 a+d) x+x^2)} \, dx\)
  3.25.68 \(\int \frac {-a (a-2 b)-2 b x+x^2}{((-a+x) (-b+x))^{2/3} (b+a^2 d-(1+2 a d) x+d x^2)} \, dx\)
  3.25.69 \(\int \frac {-1+(2-k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(b+2 k) x+(b+k^2) x^2)} \, dx\)
  3.25.70 \(\int \frac {-3 k-2 (1+k^2) x+k (1+k^2) x^2+4 k^2 x^3+k^3 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d-(2+d) k x-(d+k^2) x^2+d k x^3)} \, dx\)
  3.25.71 \(\int \frac {-1+2 x^4}{\sqrt [4]{1+x^4} (-1+x^4+x^8)} \, dx\)
  3.25.72 \(\int \frac {(-2 x+(1+k) x^2) (a-a (1+k) x+(1+a k) x^2)}{(-1+x) ((1-x) x (1-k x))^{2/3} (-1+k x) (b-b (1+k) x+(-1+b k) x^2)} \, dx\)
  3.25.73 \(\int \frac {-3 k+2 (1+k^2) x+k (1+k^2) x^2-4 k^2 x^3+k^3 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d-(2+d) k x+(d+k^2) x^2+d k x^3)} \, dx\)
  3.25.74 \(\int \frac {\sqrt [3]{-x+x^3} (-b+a x^6)}{-d+c x^6} \, dx\)
  3.25.75 \(\int \frac {\sqrt [3]{-x+x^3} (-b+a x^6)}{-d+c x^6} \, dx\)
  3.25.76 \(\int \frac {1}{1-x \sqrt {c+b x+a x^2}} \, dx\)
  3.25.77 \(\int \frac {-b+a x^2}{(-b+2 a x^2) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.25.78 \(\int \frac {-b+a x^2}{(-b+2 a x^2) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.25.79 \(\int \frac {b+a x^2}{(b+2 a x^2) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.25.80 \(\int \frac {b+a x^2}{(b+2 a x^2) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.25.81 \(\int \frac {x (4 a b-3 (a+b) x+2 x^2)}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a b+(a+b) x-x^2+d x^4)} \, dx\)
  3.25.82 \(\int \frac {\sqrt [4]{b+a x^4} (2 b+3 a x^4)}{x^6 (b+a x^8)} \, dx\)
  3.25.83 \(\int \frac {\sqrt [4]{b+a x^4} (2 b+3 a x^4)}{x^6 (b+a x^8)} \, dx\)
  3.25.84 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{1+x^2} \, dx\)
  3.25.85 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{1+x^2} \, dx\)
  3.25.86 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{x^2-\sqrt {1+x}} \, dx\)
  3.25.87 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{x^2-\sqrt {1+x}} \, dx\)
  3.25.88 \(\int \frac {x^2}{(x^2 (-a+x))^{2/3} (-a^2+2 a x+(-1+d) x^2)} \, dx\)
  3.25.89 \(\int \frac {(-2+(1+k) x) (1-(1+k) x+(a+k) x^2)}{x ((1-x) x (1-k x))^{2/3} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.25.90 \(\int \frac {-2 a^2 b x+a (3 a+2 b) x^2-4 a x^3+x^4}{(x^2 (-a+x) (-b+x))^{2/3} (-a^2+2 a x-(1+b d) x^2+d x^3)} \, dx\)
  3.25.91 \(\int \frac {1}{\sqrt [3]{-8+12 x+54 x^2-135 x^3+81 x^4}} \, dx\)
  3.25.92 \(\int \frac {1+x^2}{(-1-x+x^2) \sqrt [3]{-1+x^6}} \, dx\)
  3.25.93 \(\int \frac {1+x^2}{(-1-x+x^2) \sqrt [3]{-1+x^6}} \, dx\)
  3.25.94 \(\int \frac {(2-2 x^4+3 x^5+4 x^6) \sqrt [3]{-x+2 x^3-x^5+x^6+x^7}}{(-1+x^2-x^4+x^5+x^6)^2} \, dx\)
  3.25.95 \(\int \frac {-1+(-1+2 k) x}{\sqrt [3]{(1-x) x (1-k x)} (b-(1+2 b) x+(b+k) x^2)} \, dx\)
  3.25.96 \(\int \frac {\sqrt {b^2+a^2 x^3} (2 b^2+c x^3+a^2 x^6)}{x^7 (-b^2+a^2 x^6)} \, dx\)
  3.25.97 \(\int \frac {x^7 (-4 a+3 x)}{(x^2 (-a+x))^{2/3} (-a^2+2 a x-x^2+d x^8)} \, dx\)
  3.25.98 \(\int \frac {-1+2 x+(-2 k+k^2) x^2}{((1-x) x (1-k x))^{2/3} (b-(1+2 b k) x+(1+b k^2) x^2)} \, dx\)
  3.25.99 \(\int \frac {1}{\sqrt [3]{-x^2+x^3} (-1+x^4)} \, dx\)
  3.25.100 \(\int \frac {1}{\sqrt [3]{-x^2+x^3} (-1+x^4)} \, dx\)