3.24.1 \(\int \frac {1+x^4}{(-1+x^4) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.24.2 \(\int \frac {x^3}{\sqrt [3]{-x^2+x^4} (1+x^6)} \, dx\)
  3.24.3 \(\int \frac {-1+x^2}{\sqrt [4]{\frac {b+a x}{d+c x}}} \, dx\)
  3.24.4 \(\int \frac {-b+a x^4}{\sqrt {b+a x^4} (b-c^2 x^2+a x^4)} \, dx\)
  3.24.5 \(\int \frac {(1+x^2) \sqrt [3]{-1-x^2+x^4+x^6}}{x} \, dx\)
  3.24.6 \(\int \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}} \sqrt [3]{a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}} \, dx\)
  3.24.7 \(\int \frac {-b+a x^2}{(-d+c x^2) \sqrt [3]{-x+x^3}} \, dx\)
  3.24.8 \(\int \frac {1}{(b+a x) \sqrt [3]{-b^3+a^3 x^3}} \, dx\)
  3.24.9 \(\int \frac {(c+b x+a x^2)^{5/2}}{c+b x} \, dx\)
  3.24.10 \(\int \frac {(-b+x^3) (b+x^3) (-c+x^3)}{\sqrt [3]{a x^2+x^3}} \, dx\)
  3.24.11 \(\int \frac {x (-a+x) (-b+x) (a b-2 b x+x^2)}{(x (-a+x) (-b+x)^2)^{2/3} (-b^2+2 b x-(1-a^2 d) x^2-2 a d x^3+d x^4)} \, dx\)
  3.24.12 \(\int \frac {(-1+(-1+2 k) x) (1-2 x+x^2)}{\sqrt [3]{(1-x) x (1-k x)} (-b+4 b x+(1-6 b) x^2+(4 b-2 k) x^3+(-b+k^2) x^4)} \, dx\)
  3.24.13 \(\int \frac {1}{(b+a x) \sqrt [4]{b^2 x+a^2 x^3}} \, dx\)
  3.24.14 \(\int \frac {(-b+x) (-4 a+b+3 x)}{\sqrt [3]{(-a+x) (-b+x)^2} (a+b^4 d-(1+4 b^3 d) x+6 b^2 d x^2-4 b d x^3+d x^4)} \, dx\)
  3.24.15 \(\int \frac {1-x^4}{(1+x^2+x^4) \sqrt [4]{-x^3+x^5}} \, dx\)
  3.24.16 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt [3]{a x^2+x \sqrt {-b+a^2 x^2}}} \, dx\)
  3.24.17 \(\int \frac {x^3}{\sqrt {a+b x+c x^2+b x^3+a x^4} (1-x^6)} \, dx\)
  3.24.18 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^6+a (q+p x^3)^6)}{x^9} \, dx\)
  3.24.19 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (b x^{12}+a (q+p x^3)^6)}{x^{17}} \, dx\)
  3.24.20 \(\int \frac {-3 b+a x}{\sqrt [3]{b^2-a^2 x^2} (3 b^2+a^2 x^2)} \, dx\)
  3.24.21 \(\int \frac {x^3 (4 a b-3 (a+b) x+2 x^2)}{(x^2 (-a+x) (-b+x))^{2/3} (-a b d+(a+b) d x-d x^2+x^4)} \, dx\)
  3.24.22 \(\int \frac {x^3}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\)
  3.24.23 \(\int \frac {(c+b x+a x^2)^{5/2}}{(c+b x)^2} \, dx\)
  3.24.24 \(\int \frac {(1+x^4)^2}{(-1+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.24.25 \(\int \frac {\sqrt {a x+\sqrt {-b+a x}}}{1+\sqrt {-b+a x}} \, dx\)
  3.24.26 \(\int \frac {(b+a x^2) \sqrt [3]{x+x^3}}{d+c x^2} \, dx\)
  3.24.27 \(\int \frac {a b+a c-2 b c+(-2 a+b+c) x}{\sqrt [3]{(-a+x) (-b+x) (-c+x)} (a^2-b c d+(-2 a+b d+c d) x+(1-d) x^2)} \, dx\)
  3.24.28 \(\int \frac {(-2+x) (1-x+x^2)}{x^3 (-1+x+x^2) \sqrt [3]{\frac {1-x+2 x^2}{1-x+3 x^2}}} \, dx\)
  3.24.29 \(\int \frac {x^3 (5 b+9 a x^4)}{\sqrt [4]{b x+a x^5} (1+b x^5+a x^9)} \, dx\)
  3.24.30 \(\int \frac {(-2 x+(1+k) x^2) (1-(1+k) x+(a+k) x^2)}{((1-x) x (1-k x))^{2/3} (1-2 (1+k) x+(1+4 k+k^2) x^2-2 (k+k^2) x^3+(-b+k^2) x^4)} \, dx\)
  3.24.31 \(\int \frac {(-2+(1+k) x) (1-(1+k) x+(a+k) x^2)}{\sqrt [3]{(1-x) x (1-k x)} (1-(2+2 k) x+(1+4 k+k^2) x^2-2 (k+k^2) x^3+(-b+k^2) x^4)} \, dx\)
  3.24.32 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt {a x+\sqrt {-b+a^2 x^2}} \sqrt [6]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.24.33 \(\int \frac {x}{\sqrt {1+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.24.34 \(\int \frac {(d+c x^2) (a x+\sqrt {-b+a^2 x^2})^{5/4}}{(-b+a^2 x^2)^{3/2}} \, dx\)
  3.24.35 \(\int \frac {(-b+a x^2) \sqrt [3]{-x+x^3}}{-d+c x^2} \, dx\)
  3.24.36 \(\int \frac {(-a b+(2 a-b) x) (a^2-2 a x+x^2)}{\sqrt [3]{x (-a+x) (-b+x)} (a^4 d-4 a^3 d x+(-b^2+6 a^2 d) x^2+2 (b-2 a d) x^3+(-1+d) x^4)} \, dx\)
  3.24.37 \(\int \frac {b+d x}{x^4 \sqrt [4]{\frac {b+a x}{d+c x}}} \, dx\)
  3.24.38 \(\int \frac {1+x^6}{\sqrt [4]{-x^3+x^5} (1-x^6)} \, dx\)
  3.24.39 \(\int \frac {\sqrt {-b+a^2 x^2} (d+c x^4) \sqrt {a x+\sqrt {-b+a^2 x^2}}}{x^2} \, dx\)
  3.24.40 \(\int \frac {\sqrt {-b+a^2 x^2} (d+c x^4) \sqrt {a x+\sqrt {-b+a^2 x^2}}}{x} \, dx\)
  3.24.41 \(\int \frac {x^5 (7 b+10 a x^3)}{\sqrt [4]{b x^3+a x^6} (1+b x^7+a x^{10})} \, dx\)
  3.24.42 \(\int \frac {x^4 (-2 q+p x^3) \sqrt {q+p x^3}}{b x^8+a (q+p x^3)^4} \, dx\)
  3.24.43 \(\int \frac {(1+(-2+k) x) (1-2 k x+k^2 x^2)}{\sqrt [3]{(1-x) x (1-k x)} (b-4 b k x+(-1+6 b k^2) x^2+(2-4 b k^3) x^3+(-1+b k^4) x^4)} \, dx\)
  3.24.44 \(\int \frac {(a-2 b+x) (a^2-2 a x+x^2)}{\sqrt [3]{(-a+x) (-b+x)} (-b^2+a^4 d+2 (b-2 a^3 d) x+(-1+6 a^2 d) x^2-4 a d x^3+d x^4)} \, dx\)
  3.24.45 \(\int \frac {\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{x-\sqrt {b+a x}} \, dx\)
  3.24.46 \(\int \frac {1+x}{(1-a x) \sqrt [4]{\frac {1-b x}{c+x}}} \, dx\)
  3.24.47 \(\int \frac {x^5 (-7 b+9 a x^2)}{\sqrt [4]{-b x^3+a x^5} (1-b x^7+a x^9)} \, dx\)
  3.24.48 \(\int \frac {b+a x^4}{\sqrt {-b+a x^4} (-b+c^2 x^2+a x^4)} \, dx\)
  3.24.49 \(\int \frac {x (-a+x) (a b-2 b x+x^2)}{\sqrt [3]{x (-a+x) (-b+x)^2} (-b^2+2 b x+(-1+a^2 d) x^2-2 a d x^3+d x^4)} \, dx\)
  3.24.50 \(\int \frac {b+a x}{(-b+a x) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.24.51 \(\int \frac {1}{\sqrt [3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx\)
  3.24.52 \(\int \frac {(-4-3 x+2 x^2) (1+x-x^2+x^4) \sqrt [3]{\frac {1+x-x^2+2 x^4}{1+x-x^2+3 x^4}}}{x^5 (-1-x+x^2+x^4)} \, dx\)
  3.24.53 \(\int \frac {-b+a x}{(b+a x) \sqrt [3]{-b^2 x^2+a^3 x^3}} \, dx\)
  3.24.54 \(\int \frac {1-x^3+x^6}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\)
  3.24.55 \(\int \frac {1+x^3+x^6}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\)
  3.24.56 \(\int \frac {\sqrt {-b+a^2 x^2} \sqrt {a x+\sqrt {-b+a^2 x^2}}}{\sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.24.57 \(\int \frac {(-1+a x^8) (1+a x^8)^{3/4}}{1+x^8+a^2 x^{16}} \, dx\)
  3.24.58 \(\int \frac {-b+a x}{(b+a x) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.24.59 \(\int \frac {1}{(-1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.24.60 \(\int \frac {(-b+x)^2}{((-a+x) (-b+x)^2)^{2/3} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\)
  3.24.61 \(\int \frac {b+a x}{(-b+a x) \sqrt [3]{-b^2 x^2+a^3 x^3}} \, dx\)
  3.24.62 \(\int \frac {1}{\sqrt [3]{a x+\sqrt {-b+a^2 x^2}} \sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.24.63 \(\int \frac {x^4}{\sqrt [4]{-b+a x^4} (-b+2 a x^4+x^8)} \, dx\)
  3.24.64 \(\int \frac {(d+c x^2) (a x+\sqrt {-b+a^2 x^2})^{3/4}}{(-b+a^2 x^2)^{5/2}} \, dx\)
  3.24.65 \(\int \frac {x^2}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\)
  3.24.66 \(\int \frac {x^2}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\)
  3.24.67 \(\int \frac {-1+x^4}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\)
  3.24.68 \(\int \frac {(-b+a x^4)^{3/4}}{-b+2 a x^4+x^8} \, dx\)
  3.24.69 \(\int \sqrt {b+a^2 x^2} \sqrt {a x+\sqrt {b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.24.70 \(\int \frac {x^4}{\sqrt [4]{b+a x^4} (b+2 a x^4+2 x^8)} \, dx\)
  3.24.71 \(\int \frac {x^4 (-q+p x^4) \sqrt {q+p x^4}}{b x^8+a (q+p x^4)^4} \, dx\)
  3.24.72 \(\int \frac {(b+a x^4)^{3/4}}{b+2 a x^4+2 x^8} \, dx\)
  3.24.73 \(\int \sqrt {\frac {-1+a x-2 x^2+2 a x^3-x^4+a x^5}{1+a x-2 x^2-2 a x^3+x^4+a x^5}} \, dx\)
  3.24.74 \(\int \frac {1+x}{(-3+x^2) \sqrt [3]{1+x^2}} \, dx\)
  3.24.75 \(\int \frac {1-x^4}{(1+x^4) \sqrt [4]{-x^3+x^5}} \, dx\)
  3.24.76 \(\int \frac {-1+x^8}{\sqrt [4]{-x^2+x^6} (1+x^8)} \, dx\)
  3.24.77 \(\int \frac {-1+x^8}{\sqrt [4]{-x^2+x^6} (1+x^8)} \, dx\)
  3.24.78 \(\int \frac {\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}{\sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.24.79 \(\int \frac {b^2+a x}{(-b^2+a x) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.24.80 \(\int \frac {(-b+a x^4)^{3/4}}{b-2 a x^4+2 x^8} \, dx\)
  3.24.81 \(\int \frac {x^4}{\sqrt [4]{-b+a x^4} (b-2 a x^4+2 x^8)} \, dx\)
  3.24.82 \(\int \frac {x^3 (-5 b+6 a x)}{\sqrt [4]{-b x+a x^2} (c-b x^5+a x^6)} \, dx\)
  3.24.83 \(\int \frac {-a+x}{\sqrt [3]{(-a+x) (-b+x)^2} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.24.84 \(\int \frac {b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b-2 a x^4+x^8)} \, dx\)
  3.24.85 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.24.86 \(\int \frac {1+x}{\sqrt [3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx\)
  3.24.87 \(\int \frac {-1+k^2 x^4}{\sqrt {(1-x^2) (1-k^2 x^2)} (1+k^2 x^4)} \, dx\)
  3.24.88 \(\int \frac {1+2 x}{\sqrt [3]{-1+x^2} (3+x^2)} \, dx\)
  3.24.89 \(\int \frac {x}{\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}} \, dx\)
  3.24.90 \(\int \frac {\sqrt [4]{-x^2+x^6} (1-x^4+x^8)}{x^4 (1+x^4)} \, dx\)
  3.24.91 \(\int \frac {\sqrt [4]{-x^2+x^6} (1-x^4+x^8)}{x^4 (1+x^4)} \, dx\)
  3.24.92 \(\int \frac {\sqrt [4]{-x^2+x^6} (1+x^4+x^8)}{x^4 (1+x^4)} \, dx\)
  3.24.93 \(\int \frac {\sqrt [4]{-x^2+x^6} (1+x^4+x^8)}{x^4 (1+x^4)} \, dx\)
  3.24.94 \(\int \frac {\sqrt [3]{b^2 x^2+a^3 x^3}}{-b+a x} \, dx\)
  3.24.95 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt {a x+\sqrt {-b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.24.96 \(\int \frac {(-3+x^2) (1-2 x^2+x^4+x^6)}{x^{10} \sqrt [4]{\frac {-a+a x^2+b x^3}{-c+c x^2+d x^3}}} \, dx\)
  3.24.97 \(\int \sqrt {b+a^2 x^2} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.24.98 \(\int \frac {\sqrt {(-81+27 x+135 x^2-150 x^3+65 x^4-13 x^5+x^6)^3}}{-1+x} \, dx\)
  3.24.99 \(\int \frac {(-q+p x^4) \sqrt {q+p x^4}}{x^2 (a q+b x^2+a p x^4)} \, dx\)
  3.24.100 \(\int \frac {\sqrt [3]{b^2 x^2+a^3 x^3}}{b+a x} \, dx\)