3.24.1 \(\int \frac {1-x^4+2 x^8}{\sqrt [4]{1+x^4} (-1-2 x^4+x^8)} \, dx\)
  3.24.2 \(\int \frac {(-1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{(1+x^2) \sqrt {1+x^4}} \, dx\)
  3.24.3 \(\int \frac {x}{x+\sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.24.4 \(\int \frac {x}{x+\sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.24.5 \(\int \frac {1}{(1+x) \sqrt [3]{1-x+x^2}} \, dx\)
  3.24.6 \(\int \frac {(1+x^4) \sqrt [4]{-x^3+x^4}}{x^4 (-1+x^4)} \, dx\)
  3.24.7 \(\int \frac {(1+x^4) \sqrt [4]{-x^3+x^4}}{x^4 (-1+x^4)} \, dx\)
  3.24.8 \(\int \frac {\sqrt [3]{b x+a x^3} (b+a x^4)}{x^4} \, dx\)
  3.24.9 \(\int \frac {b^4+a^4 x^4}{\sqrt {-b^2 x+a^2 x^3} (-b^4+a^4 x^4)} \, dx\)
  3.24.10 \(\int \frac {1+x}{(-1+x^3) \sqrt [8]{256-256 x^2+96 x^4-16 x^6+x^8}} \, dx\)
  3.24.11 \(\int \frac {1}{x^2 \sqrt [3]{-1-x+5 x^2+2 x^3-10 x^4+2 x^5+7 x^6-5 x^7+x^8}} \, dx\)
  3.24.12 \(\int \frac {c x^6 (-4 b+a x^5)}{(b+a x^5)^{3/4} (b^2+2 a b x^5-c^2 x^8+a^2 x^{10})} \, dx\)
  3.24.13 \(\int \frac {x^2 \sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x}} \, dx\)
  3.24.14 \(\int \frac {a+b x^2+a k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (-1+k^4 x^4)} \, dx\)
  3.24.15 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (a q^2+2 a p q x^3+b x^4+a p^2 x^6)}{x^9} \, dx\)
  3.24.16 \(\int \frac {-1+x^3}{(1+x^3) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.24.17 \(\int \frac {5 x-4 (1+k) x^2+3 k x^3}{\sqrt [3]{(1-x) x (1-k x)} (-1+(1+k) x-k x^2+b x^5)} \, dx\)
  3.24.18 \(\int \frac {x^2 (8-7 (1+k) x+6 k x^2)}{\sqrt [3]{(1-x) x (1-k x)} (-1+(1+k) x-k x^2+b x^8)} \, dx\)
  3.24.19 \(\int \frac {x (-a b+x^2)}{(x^2 (-a+x) (-b+x))^{2/3} (a b-(a+b+d) x+x^2)} \, dx\)
  3.24.20 \(\int \frac {(b+x^3) (c+x^3)}{\sqrt [3]{a+x^3}} \, dx\)
  3.24.21 \(\int \frac {1}{(1+x^3) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.24.22 \(\int \frac {1}{(1+x^3) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.24.23 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^3 (a q+b x^2+a p x^3)} \, dx\)
  3.24.24 \(\int \frac {\sqrt [4]{x^2+x^6} (1+x^8)}{x^4 (-1+x^4)} \, dx\)
  3.24.25 \(\int \frac {\sqrt [4]{x^2+x^6} (1+x^8)}{x^4 (-1+x^4)} \, dx\)
  3.24.26 \(\int \frac {1}{x \sqrt [3]{2-3 x+x^2}} \, dx\)
  3.24.27 \(\int \frac {a b-x^2}{\sqrt [3]{x^2 (-a+x) (-b+x)} (a b-(a+b+d) x+x^2)} \, dx\)
  3.24.28 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^2+a (q+p x^3)^2)}{x^5} \, dx\)
  3.24.29 \(\int \frac {1+x}{(-1+x) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.24.30 \(\int \frac {1+x}{(-1+x) \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.24.31 \(\int \frac {1}{d+c x+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.24.32 \(\int \frac {1}{d+c x+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.24.33 \(\int \frac {-d+c x}{x^7 \sqrt [3]{-b+a x^3}} \, dx\)
  3.24.34 \(\int \frac {1+x^2+x^4}{(1-x^4) \sqrt [4]{x^3+x^5}} \, dx\)
  3.24.35 \(\int \frac {\sqrt {-1+2 x^4} (-1+2 x^8)}{x^7 (-1+2 x^4+x^8)} \, dx\)
  3.24.36 \(\int \frac {\sqrt {1+x} \sqrt {1+\sqrt {1+x}}}{x \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx\)
  3.24.37 \(\int \frac {1+x}{(3+x) (1+2 x) \sqrt [3]{1+x^2}} \, dx\)
  3.24.38 \(\int \frac {\sqrt [3]{-x^2+x^3}}{1+x+x^2} \, dx\)
  3.24.39 \(\int \frac {\sqrt [3]{-x^2+x^3}}{1+x+x^2} \, dx\)
  3.24.40 \(\int \frac {x (5-4 (1+k) x+3 k x^2)}{\sqrt [3]{(1-x) x (1-k x)} (-b+(b+b k) x-b k x^2+x^5)} \, dx\)
  3.24.41 \(\int \frac {1+x^4}{(1-x^4) \sqrt [4]{x^3+x^5}} \, dx\)
  3.24.42 \(\int \frac {(1+x^3)^{2/3} (2+x^3+x^6)}{x^6 (-2+x^3)^2} \, dx\)
  3.24.43 \(\int \frac {1+x^8}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\)
  3.24.44 \(\int \frac {1+x^8}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\)
  3.24.45 \(\int \frac {x^2 (8-7 (1+k) x+6 k x^2)}{\sqrt [3]{(1-x) x (1-k x)} (-b+b (1+k) x-b k x^2+x^8)} \, dx\)
  3.24.46 \(\int \frac {1}{(1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.24.47 \(\int \frac {x (-a+x) (a b+(a-2 b) x)}{(x (-a+x) (-b+x)^2)^{3/4} (b^2 d+(a-2 b d) x+(-1+d) x^2)} \, dx\)
  3.24.48 \(\int \frac {(1+x^2) (1-3 x^2+x^4)}{x^2 \sqrt {\frac {-2+x+2 x^2}{-1+x+x^2}} (1-x-3 x^2+x^3+x^4)} \, dx\)
  3.24.49 \(\int \frac {x^3 (5-4 (1+k) x+3 k x^2)}{((1-x) x (1-k x))^{2/3} (-1+(1+k) x-k x^2+b x^5)} \, dx\)
  3.24.50 \(\int \frac {(-2+x^4) \sqrt {2+x^4}}{4+3 x^4+x^8} \, dx\)
  3.24.51 \(\int \frac {\sqrt [3]{-1-x+5 x^2+2 x^3-10 x^4+2 x^5+7 x^6-5 x^7+x^8}}{x^2} \, dx\)
  3.24.52 \(\int \frac {(-b+a^2 x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{\sqrt {b+a^2 x^4}} \, dx\)
  3.24.53 \(\int \frac {\sqrt {1+x}}{x+\sqrt {x+\sqrt {1+x}}} \, dx\)
  3.24.54 \(\int \frac {\sqrt {1+x}}{x+\sqrt {x+\sqrt {1+x}}} \, dx\)
  3.24.55 \(\int \frac {-i+\sqrt {k} x}{(i+\sqrt {k} x) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.24.56 \(\int \frac {i+\sqrt {k} x}{(-i+\sqrt {k} x) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.24.57 \(\int \frac {1}{\sqrt [4]{-1+3 x-3 x^2+x^3} (-1-2 x+x^2+3 x^3)^4} \, dx\)
  3.24.58 \(\int \frac {\sqrt [4]{b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\)
  3.24.59 \(\int \frac {\sqrt [4]{b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\)
  3.24.60 \(\int \frac {x^4}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\)
  3.24.61 \(\int \frac {x^4}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\)
  3.24.62 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1-x^4+x^8} \, dx\)
  3.24.63 \(\int \frac {(-1+x^4) \sqrt [4]{x^2+x^6}}{1-x^4+x^8} \, dx\)
  3.24.64 \(\int \frac {1-x^4+x^8}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\)
  3.24.65 \(\int \frac {1-x^4+x^8}{\sqrt [4]{x^2+x^6} (-1+x^8)} \, dx\)
  3.24.66 \(\int \frac {1}{(-b+a x) \sqrt [4]{-x^3+x^4}} \, dx\)
  3.24.67 \(\int \frac {-x+x^2}{\sqrt {(1-x) x (1-k^2 x)} (1-2 x+k^2 x^2)} \, dx\)
  3.24.68 \(\int \frac {-b+a^3 x^2}{(b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\)
  3.24.69 \(\int \frac {-b+a^3 x^2}{(b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\)
  3.24.70 \(\int \frac {1+x^2}{(-1+x^2) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.24.71 \(\int \frac {x^4 \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx\)
  3.24.72 \(\int \frac {x^4 \sqrt [4]{-x^2+x^4}}{1+x^4+x^8} \, dx\)
  3.24.73 \(\int \frac {(-2 q+p x^3) \sqrt {q+p x^3}}{c x^4+b x^2 (q+p x^3)+a (q+p x^3)^2} \, dx\)
  3.24.74 \(\int \frac {(-1+x^4)^2}{(1+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.24.75 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{(1+x^2)^2 \sqrt {1+x^4}} \, dx\)
  3.24.76 \(\int \frac {\sqrt {q+p x^5} (-2 q+3 p x^5)}{c x^4+b x^2 (q+p x^5)+a (q+p x^5)^2} \, dx\)
  3.24.77 \(\int \frac {1}{x \sqrt {a x+\sqrt {-b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.24.78 \(\int \frac {1}{\sqrt [3]{1+x^2} (9+x^2)} \, dx\)
  3.24.79 \(\int \frac {b+a^3 x^2}{(-b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\)
  3.24.80 \(\int \frac {b+a^3 x^2}{(-b+a^3 x^2) \sqrt [3]{-b x^2+a^3 x^3}} \, dx\)
  3.24.81 \(\int \frac {-3-2 (1+k^2) x+(1+k^2) x^2+4 k^2 x^3+k^2 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d-(2+d) x-(1+d k^2) x^2+d k^2 x^3)} \, dx\)
  3.24.82 \(\int \frac {\sqrt [4]{x^3+x^5} (1+x^4+x^8)}{x^4 (-1+x^4)} \, dx\)
  3.24.83 \(\int \frac {1}{(b+a x^2) \sqrt [3]{x+x^3}} \, dx\)
  3.24.84 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\)
  3.24.85 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\)
  3.24.86 \(\int \frac {\sqrt [3]{x+x^3} (b+a x^6)}{d+c x^6} \, dx\)
  3.24.87 \(\int \frac {\sqrt [3]{x+x^3} (b+a x^6)}{d+c x^6} \, dx\)
  3.24.88 \(\int \frac {(-1+2 x^6) \sqrt [3]{x+x^7}}{(1-2 x^2+x^6) (1-x^2+x^6)} \, dx\)
  3.24.89 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^3+a (q+p x^3)^3)}{x^6} \, dx\)
  3.24.90 \(\int \frac {-1+(-1+2 k) x}{\sqrt [3]{(1-x) x (1-k x)} (1-(2+b) x+(1+b k) x^2)} \, dx\)
  3.24.91 \(\int \frac {-3+2 (1+k^2) x+(1+k^2) x^2-4 k^2 x^3+k^2 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d-(2+d) x+(1+d k^2) x^2+d k^2 x^3)} \, dx\)
  3.24.92 \(\int \frac {b-3 a x^3+3 x^6}{x^6 (-b+2 a x^3) \sqrt [4]{-b x+a x^4}} \, dx\)
  3.24.93 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (b x^6+a (q+p x^3)^3)}{x^{11}} \, dx\)
  3.24.94 \(\int \frac {x \sqrt {1+x}}{x+\sqrt {x+\sqrt {1+x}}} \, dx\)
  3.24.95 \(\int \frac {x \sqrt {1+x}}{x+\sqrt {x+\sqrt {1+x}}} \, dx\)
  3.24.96 \(\int \frac {x^2}{\sqrt {\frac {b+a x}{d+c x}}} \, dx\)
  3.24.97 \(\int \frac {b+2 a x}{(-b+a x) (2 b+a x) \sqrt [4]{-1+b x+a x^2}} \, dx\)
  3.24.98 \(\int \frac {-1+a k x+k x^2}{(1+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.24.99 \(\int \frac {(-b+x^3) (b+x^3)}{\sqrt [3]{a x^2+x^3}} \, dx\)
  3.24.100 \(\int \frac {x}{(1-x^2) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)