3.31.1 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.31.2 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.31.3 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.31.4 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.31.5 \(\int \frac {(1+(-2+k) x) (1-2 k x+k^2 x^2)}{\sqrt [3]{(1-x) x (1-k x)} (b-4 b k x+(-1+6 b k^2) x^2+(2-4 b k^3) x^3+(-1+b k^4) x^4)} \, dx\)
  3.31.6 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.31.7 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.31.8 \(\int \frac {(a-2 b+x) (a^2-2 a x+x^2)}{\sqrt [3]{(-a+x) (-b+x)} (-b^2+a^4 d+2 (b-2 a^3 d) x+(-1+6 a^2 d) x^2-4 a d x^3+d x^4)} \, dx\)
  3.31.9 \(\int \frac {(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^4) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.31.10 \(\int \frac {(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^4) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.31.11 \(\int \frac {\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{x-\sqrt {b+a x}} \, dx\)
  3.31.12 \(\int \frac {1+x}{(1-a x) \sqrt [4]{\frac {1-b x}{c+x}}} \, dx\)
  3.31.13 \(\int \frac {x^5 (-7 b+9 a x^2)}{\sqrt [4]{-b x^3+a x^5} (1-b x^7+a x^9)} \, dx\)
  3.31.14 \(\int \frac {b+a x^4}{\sqrt {-b+a x^4} (-b+c^2 x^2+a x^4)} \, dx\)
  3.31.15 \(\int \frac {x (-a+x) (a b-2 b x+x^2)}{\sqrt [3]{x (-a+x) (-b+x)^2} (-b^2+2 b x+(-1+a^2 d) x^2-2 a d x^3+d x^4)} \, dx\)
  3.31.16 \(\int \frac {b+a x}{(-b+a x) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.31.17 \(\int \frac {\sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{-b+a^2 x^4} \, dx\)
  3.31.18 \(\int \frac {\sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{-b+a^2 x^4} \, dx\)
  3.31.19 \(\int \frac {1}{\sqrt [3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx\)
  3.31.20 \(\int \frac {(-4-3 x+2 x^2) (1+x-x^2+x^4) \sqrt [3]{\frac {1+x-x^2+2 x^4}{1+x-x^2+3 x^4}}}{x^5 (-1-x+x^2+x^4)} \, dx\)
  3.31.21 \(\int \frac {-b+a x}{(b+a x) \sqrt [3]{-b^2 x^2+a^3 x^3}} \, dx\)
  3.31.22 \(\int \frac {(-q+p x^4) \sqrt {q+p x^4}}{c x^4+b x^2 (q+p x^4)+a (q+p x^4)^2} \, dx\)
  3.31.23 \(\int \frac {(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\sqrt {1+x^2} (1-x^4)} \, dx\)
  3.31.24 \(\int \frac {(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\sqrt {1+x^2} (1-x^4)} \, dx\)
  3.31.25 \(\int \frac {1-x^3+x^6}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\)
  3.31.26 \(\int \frac {1+x^3+x^6}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\)
  3.31.27 \(\int \frac {\sqrt {-b+a^2 x^2} \sqrt {a x+\sqrt {-b+a^2 x^2}}}{\sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.31.28 \(\int \frac {(-1+a x^8) (1+a x^8)^{3/4}}{1+x^8+a^2 x^{16}} \, dx\)
  3.31.29 \(\int \frac {-b+a x}{(b+a x) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.31.30 \(\int \frac {1}{(-1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.31.31 \(\int \frac {(c+b x+a x^2)^{3/2}}{1-x \sqrt {c+b x+a x^2}} \, dx\)
  3.31.32 \(\int \frac {(-b+x)^2}{((-a+x) (-b+x)^2)^{2/3} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\)
  3.31.33 \(\int \frac {b+a x}{(-b+a x) \sqrt [3]{-b^2 x^2+a^3 x^3}} \, dx\)
  3.31.34 \(\int \frac {1}{\sqrt [3]{a x+\sqrt {-b+a^2 x^2}} \sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.31.35 \(\int \frac {x^4}{\sqrt [4]{-b+a x^4} (-b+2 a x^4+x^8)} \, dx\)
  3.31.36 \(\int \frac {(d+c x^2) (a x+\sqrt {-b+a^2 x^2})^{3/4}}{(-b+a^2 x^2)^{5/2}} \, dx\)
  3.31.37 \(\int \frac {x^2}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\)
  3.31.38 \(\int \frac {x^2}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\)
  3.31.39 \(\int \frac {-1+x^4}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\)
  3.31.40 \(\int \frac {(-b+a x^4)^{3/4}}{-b+2 a x^4+x^8} \, dx\)
  3.31.41 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^{5/2}} \, dx\)
  3.31.42 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^{5/2}} \, dx\)
  3.31.43 \(\int \frac {x^2 \sqrt {b+a x}}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.31.44 \(\int \frac {x^2 \sqrt {b+a x}}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.31.45 \(\int \sqrt {b+a^2 x^2} \sqrt {a x+\sqrt {b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.31.46 \(\int \frac {x^4}{\sqrt [4]{b+a x^4} (b+2 a x^4+2 x^8)} \, dx\)
  3.31.47 \(\int \frac {x^4 (-q+p x^4) \sqrt {q+p x^4}}{b x^8+a (q+p x^4)^4} \, dx\)
  3.31.48 \(\int \frac {1}{\sqrt [3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}}} \, dx\)
  3.31.49 \(\int \frac {(b+a x^4)^{3/4}}{b+2 a x^4+2 x^8} \, dx\)
  3.31.50 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(d+c x) \sqrt {b+a^2 x^4}} \, dx\)
  3.31.51 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(d+c x) \sqrt {b+a^2 x^4}} \, dx\)
  3.31.52 \(\int \frac {1}{\sqrt {c+b x+a x^2} (c^3+a^3 b^3 x^3)} \, dx\)
  3.31.53 \(\int \frac {(-d+c x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\)
  3.31.54 \(\int \frac {(-d+c x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\)
  3.31.55 \(\int \sqrt {\frac {-1+a x-2 x^2+2 a x^3-x^4+a x^5}{1+a x-2 x^2-2 a x^3+x^4+a x^5}} \, dx\)
  3.31.56 \(\int \frac {1+x}{(-3+x^2) \sqrt [3]{1+x^2}} \, dx\)
  3.31.57 \(\int \frac {1-x^4}{(1+x^4) \sqrt [4]{-x^3+x^5}} \, dx\)
  3.31.58 \(\int \frac {-1+x^8}{\sqrt [4]{-x^2+x^6} (1+x^8)} \, dx\)
  3.31.59 \(\int \frac {-1+x^8}{\sqrt [4]{-x^2+x^6} (1+x^8)} \, dx\)
  3.31.60 \(\int \frac {\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}{\sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.31.61 \(\int \frac {b^2+a x}{(-b^2+a x) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.31.62 \(\int \frac {(-b+a x^4)^{3/4}}{b-2 a x^4+2 x^8} \, dx\)
  3.31.63 \(\int \frac {-d+c x^2}{(d+c x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\)
  3.31.64 \(\int \frac {-d+c x^2}{(d+c x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\)
  3.31.65 \(\int \frac {x^4}{\sqrt [4]{-b+a x^4} (b-2 a x^4+2 x^8)} \, dx\)
  3.31.66 \(\int \frac {x^3 (-5 b+6 a x)}{\sqrt [4]{-b x+a x^2} (c-b x^5+a x^6)} \, dx\)
  3.31.67 \(\int \frac {-a+x}{\sqrt [3]{(-a+x) (-b+x)^2} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.31.68 \(\int \frac {b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b-2 a x^4+x^8)} \, dx\)
  3.31.69 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.31.70 \(\int \frac {1+x}{\sqrt [3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx\)
  3.31.71 \(\int \frac {-1+k^2 x^4}{\sqrt {(1-x^2) (1-k^2 x^2)} (1+k^2 x^4)} \, dx\)
  3.31.72 \(\int \frac {1+2 x}{\sqrt [3]{-1+x^2} (3+x^2)} \, dx\)
  3.31.73 \(\int \frac {x}{\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}} \, dx\)
  3.31.74 \(\int \frac {\sqrt [4]{-x^2+x^6} (1-x^4+x^8)}{x^4 (1+x^4)} \, dx\)
  3.31.75 \(\int \frac {\sqrt [4]{-x^2+x^6} (1-x^4+x^8)}{x^4 (1+x^4)} \, dx\)
  3.31.76 \(\int \frac {\sqrt [4]{-x^2+x^6} (1+x^4+x^8)}{x^4 (1+x^4)} \, dx\)
  3.31.77 \(\int \frac {\sqrt [4]{-x^2+x^6} (1+x^4+x^8)}{x^4 (1+x^4)} \, dx\)
  3.31.78 \(\int \frac {\sqrt [3]{b^2 x^2+a^3 x^3}}{-b+a x} \, dx\)
  3.31.79 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt {a x+\sqrt {-b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.31.80 \(\int \frac {(-3+x^2) (1-2 x^2+x^4+x^6)}{x^{10} \sqrt [4]{\frac {-a+a x^2+b x^3}{-c+c x^2+d x^3}}} \, dx\)
  3.31.81 \(\int \frac {(1+x^4) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^4} \, dx\)
  3.31.82 \(\int \frac {(1+x^4) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^4} \, dx\)
  3.31.83 \(\int \sqrt {b+a^2 x^2} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.31.84 \(\int \frac {\sqrt {(-81+27 x+135 x^2-150 x^3+65 x^4-13 x^5+x^6)^3}}{-1+x} \, dx\)
  3.31.85 \(\int \frac {(1+x^2+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)^2} \, dx\)
  3.31.86 \(\int \frac {(1+x^2+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)^2} \, dx\)
  3.31.87 \(\int \frac {(-q+p x^4) \sqrt {q+p x^4}}{x^2 (a q+b x^2+a p x^4)} \, dx\)
  3.31.88 \(\int \frac {\sqrt [3]{b^2 x^2+a^3 x^3}}{b+a x} \, dx\)
  3.31.89 \(\int \frac {(-b+a^2 x^2)^{3/2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x} \, dx\)
  3.31.90 \(\int \frac {(b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}}{-b^2+a x^2} \, dx\)
  3.31.91 \(\int \frac {d+c x^4}{x \sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.31.92 \(\int \frac {(-b+a^2 x^2)^{3/2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x^2} \, dx\)
  3.31.93 \(\int \frac {b-x}{\sqrt [3]{(-a+x) (-b+x)^2} (a^2-b^2 d-2 (a-b d) x+(1-d) x^2)} \, dx\)
  3.31.94 \(\int \frac {-b+x}{\sqrt [3]{(-a+x) (-b+x)^2} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\)
  3.31.95 \(\int \frac {b^2+a x^2}{(-b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.31.96 \(\int \frac {1}{\sqrt [3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx\)
  3.31.97 \(\int \frac {\sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\)
  3.31.98 \(\int \frac {\sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\)
  3.31.99 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{1+a x} \, dx\)
  3.31.100 \(\int \frac {1}{\sqrt {c_4+\sqrt {\frac {c_0+x c_1}{c_2+x c_3}} c_5} (c_6+x c_7)} \, dx\)