3.30.1 \(\int \frac {(1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)} \, dx\)
  3.30.2 \(\int \frac {(1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)} \, dx\)
  3.30.3 \(\int \frac {x^2 \sqrt [4]{b x^3+a x^4}}{-b+a x^4} \, dx\)
  3.30.4 \(\int \frac {x^2 \sqrt [4]{b x^3+a x^4}}{-b+a x^4} \, dx\)
  3.30.5 \(\int \frac {(1+x^2) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.30.6 \(\int \frac {(1+x^2) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.30.7 \(\int \frac {x^3 (-b+x) (2 a b-3 a x+x^2)}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a^4+4 a^3 x-6 a^2 x^2+4 a x^3+(-1+b^2 d) x^4-2 b d x^5+d x^6)} \, dx\)
  3.30.8 \(\int \frac {(1+x^3)^{2/3} (-1+x^6)}{x^6 (-1-2 x^3+2 x^6)} \, dx\)
  3.30.9 \(\int \frac {1+x^4}{(-1+x^4) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.30.10 \(\int \frac {(b+2 a x) \sqrt [4]{b x^3+a x^4}}{-b+a x+x^2} \, dx\)
  3.30.11 \(\int \frac {(b+2 a x) \sqrt [4]{b x^3+a x^4}}{-b+a x+x^2} \, dx\)
  3.30.12 \(\int \frac {x^3}{\sqrt [3]{-x^2+x^4} (1+x^6)} \, dx\)
  3.30.13 \(\int \frac {x^4 \sqrt {b+a^2 x^2}}{x^2-\sqrt {a x-\sqrt {b+a^2 x^2}}} \, dx\)
  3.30.14 \(\int \frac {-1+x^2}{\sqrt [4]{\frac {b+a x}{d+c x}}} \, dx\)
  3.30.15 \(\int \frac {-b+a x^4}{\sqrt {b+a x^4} (b-c^2 x^2+a x^4)} \, dx\)
  3.30.16 \(\int \frac {(1+x^2) \sqrt [3]{-1-x^2+x^4+x^6}}{x} \, dx\)
  3.30.17 \(\int \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}} \sqrt [3]{a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}} \, dx\)
  3.30.18 \(\int \frac {-b+a x^2}{(-d+c x^2) \sqrt [3]{-x+x^3}} \, dx\)
  3.30.19 \(\int \frac {1}{(b+a x) \sqrt [3]{-b^3+a^3 x^3}} \, dx\)
  3.30.20 \(\int \frac {-b^{12}+a^{12} x^{12}}{\sqrt {b^4+a^4 x^4} (b^{12}+a^{12} x^{12})} \, dx\)
  3.30.21 \(\int \frac {(c+b x+a x^2)^{5/2}}{c+b x} \, dx\)
  3.30.22 \(\int \frac {(-b-a x^2+x^4) \sqrt [4]{b x^2+a x^4}}{b+a x^4} \, dx\)
  3.30.23 \(\int \frac {(-b-a x^2+x^4) \sqrt [4]{b x^2+a x^4}}{b+a x^4} \, dx\)
  3.30.24 \(\int \frac {\sqrt {1+x} (-1+x^2)}{(1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\)
  3.30.25 \(\int \frac {\sqrt {1+x} (-1+x^2)}{(1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\)
  3.30.26 \(\int \frac {-x^2+\sqrt {1+2 x^2}+(1+2 x^2)^{5/2}}{x^2-x (1+2 x^2)^{3/2}} \, dx\)
  3.30.27 \(\int \frac {(-b+x^3) (b+x^3) (-c+x^3)}{\sqrt [3]{a x^2+x^3}} \, dx\)
  3.30.28 \(\int \frac {x (-a+x) (-b+x) (a b-2 b x+x^2)}{(x (-a+x) (-b+x)^2)^{2/3} (-b^2+2 b x-(1-a^2 d) x^2-2 a d x^3+d x^4)} \, dx\)
  3.30.29 \(\int \frac {(-b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}}{b+a x^4} \, dx\)
  3.30.30 \(\int \frac {(-b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}}{b+a x^4} \, dx\)
  3.30.31 \(\int \frac {a b c-b^2 x+a^2 x^2}{\sqrt {c+b x+a x^2} (c+b x^2)} \, dx\)
  3.30.32 \(\int \frac {(b+a x^2+x^4) \sqrt [4]{-b x^2+a x^4}}{-b+a x^4} \, dx\)
  3.30.33 \(\int \frac {(b+a x^2+x^4) \sqrt [4]{-b x^2+a x^4}}{-b+a x^4} \, dx\)
  3.30.34 \(\int \frac {(-1+(-1+2 k) x) (1-2 x+x^2)}{\sqrt [3]{(1-x) x (1-k x)} (-b+4 b x+(1-6 b) x^2+(4 b-2 k) x^3+(-b+k^2) x^4)} \, dx\)
  3.30.35 \(\int \frac {1}{(b+a x) \sqrt [4]{b^2 x+a^2 x^3}} \, dx\)
  3.30.36 \(\int \frac {(-b+a x^4) \sqrt [4]{-b x^2+a x^4}}{-b-a x^2+x^4} \, dx\)
  3.30.37 \(\int \frac {(-b+a x^4) \sqrt [4]{-b x^2+a x^4}}{-b-a x^2+x^4} \, dx\)
  3.30.38 \(\int \frac {(-b+x) (-4 a+b+3 x)}{\sqrt [3]{(-a+x) (-b+x)^2} (a+b^4 d-(1+4 b^3 d) x+6 b^2 d x^2-4 b d x^3+d x^4)} \, dx\)
  3.30.39 \(\int \frac {(d+c x^2) \sqrt {a x+\sqrt {b^2+a^2 x^2}}}{f+e x^2} \, dx\)
  3.30.40 \(\int \frac {(1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)} \, dx\)
  3.30.41 \(\int \frac {(1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)} \, dx\)
  3.30.42 \(\int \frac {1-x^4}{(1+x^2+x^4) \sqrt [4]{-x^3+x^5}} \, dx\)
  3.30.43 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt [3]{a x^2+x \sqrt {-b+a^2 x^2}}} \, dx\)
  3.30.44 \(\int \frac {(b+a^2 x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(-b+a^2 x^2) \sqrt {b+a^2 x^4}} \, dx\)
  3.30.45 \(\int \frac {(b+a^2 x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(-b+a^2 x^2) \sqrt {b+a^2 x^4}} \, dx\)
  3.30.46 \(\int \frac {x^3}{\sqrt {a+b x+c x^2+b x^3+a x^4} (1-x^6)} \, dx\)
  3.30.47 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^6+a (q+p x^3)^6)}{x^9} \, dx\)
  3.30.48 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (b x^{12}+a (q+p x^3)^6)}{x^{17}} \, dx\)
  3.30.49 \(\int \frac {(-q+p x^4) \sqrt {q+p x^4}}{b x^4+a (q+p x^4)^2} \, dx\)
  3.30.50 \(\int \frac {-3 b+a x}{\sqrt [3]{b^2-a^2 x^2} (3 b^2+a^2 x^2)} \, dx\)
  3.30.51 \(\int \frac {x+\sqrt {1+4 x+7 x^2+8 x^3+5 x^4+2 x^5}}{1-\sqrt {1+4 x+7 x^2+8 x^3+5 x^4+2 x^5}} \, dx\)
  3.30.52 \(\int \frac {x^3 (4 a b-3 (a+b) x+2 x^2)}{(x^2 (-a+x) (-b+x))^{2/3} (-a b d+(a+b) d x-d x^2+x^4)} \, dx\)
  3.30.53 \(\int \frac {x^3}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\)
  3.30.54 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {1+x^2}} \, dx\)
  3.30.55 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {1+x^2}} \, dx\)
  3.30.56 \(\int \frac {\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.30.57 \(\int \frac {\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.30.58 \(\int \frac {\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.30.59 \(\int \frac {(c+b x+a x^2)^{5/2}}{(c+b x)^2} \, dx\)
  3.30.60 \(\int \frac {(1+x^4)^2}{(-1+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.30.61 \(\int \frac {\sqrt {a x+\sqrt {-b+a x}}}{1+\sqrt {-b+a x}} \, dx\)
  3.30.62 \(\int \frac {(b x+a x^2) \sqrt [4]{b x^3+a x^4}}{-b+a x+x^2} \, dx\)
  3.30.63 \(\int \frac {(b x+a x^2) \sqrt [4]{b x^3+a x^4}}{-b+a x+x^2} \, dx\)
  3.30.64 \(\int \frac {-b^{10}+a^{10} x^{10}}{\sqrt {b^4+a^4 x^4} (b^{10}+a^{10} x^{10})} \, dx\)
  3.30.65 \(\int \frac {-b^{10}+a^{10} x^{10}}{\sqrt {b^4+a^4 x^4} (b^{10}+a^{10} x^{10})} \, dx\)
  3.30.66 \(\int \frac {(b+a x^2) \sqrt [3]{x+x^3}}{d+c x^2} \, dx\)
  3.30.67 \(\int \frac {x^2 (b+a x^3) (-b p+3 a q+2 a p x^3)}{(q+p x^3)^{2/3} (b^3 c+d q+(3 a b^2 c+d p) x^3+3 a^2 b c x^6+a^3 c x^9)} \, dx\)
  3.30.68 \(\int \frac {a b+a c-2 b c+(-2 a+b+c) x}{\sqrt [3]{(-a+x) (-b+x) (-c+x)} (a^2-b c d+(-2 a+b d+c d) x+(1-d) x^2)} \, dx\)
  3.30.69 \(\int \frac {(-2+x) (1-x+x^2)}{x^3 (-1+x+x^2) \sqrt [3]{\frac {1-x+2 x^2}{1-x+3 x^2}}} \, dx\)
  3.30.70 \(\int \frac {x^3 (5 b+9 a x^4)}{\sqrt [4]{b x+a x^5} (1+b x^5+a x^9)} \, dx\)
  3.30.71 \(\int \frac {\sqrt {1+x^2} (1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^4} \, dx\)
  3.30.72 \(\int \frac {\sqrt {1+x^2} (1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^4} \, dx\)
  3.30.73 \(\int \frac {b^{12}+a^{12} x^{12}}{\sqrt {-b^4+a^4 x^4} (-b^{12}+a^{12} x^{12})} \, dx\)
  3.30.74 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{\sqrt {b+a^2 x^4} (d+c x^4)} \, dx\)
  3.30.75 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{\sqrt {b+a^2 x^4} (d+c x^4)} \, dx\)
  3.30.76 \(\int \frac {x}{x-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.30.77 \(\int \frac {x}{x-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.30.78 \(\int \frac {(-2 x+(1+k) x^2) (1-(1+k) x+(a+k) x^2)}{((1-x) x (1-k x))^{2/3} (1-2 (1+k) x+(1+4 k+k^2) x^2-2 (k+k^2) x^3+(-b+k^2) x^4)} \, dx\)
  3.30.79 \(\int \frac {(-2+(1+k) x) (1-(1+k) x+(a+k) x^2)}{\sqrt [3]{(1-x) x (1-k x)} (1-(2+2 k) x+(1+4 k+k^2) x^2-2 (k+k^2) x^3+(-b+k^2) x^4)} \, dx\)
  3.30.80 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt {a x+\sqrt {-b+a^2 x^2}} \sqrt [6]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.30.81 \(\int \frac {x}{\sqrt {1+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.30.82 \(\int \frac {(d+c x^2) (a x+\sqrt {-b+a^2 x^2})^{5/4}}{(-b+a^2 x^2)^{3/2}} \, dx\)
  3.30.83 \(\int \frac {(-b+a x^2) \sqrt [3]{-x+x^3}}{-d+c x^2} \, dx\)
  3.30.84 \(\int \frac {(-a b+(2 a-b) x) (a^2-2 a x+x^2)}{\sqrt [3]{x (-a+x) (-b+x)} (a^4 d-4 a^3 d x+(-b^2+6 a^2 d) x^2+2 (b-2 a d) x^3+(-1+d) x^4)} \, dx\)
  3.30.85 \(\int \frac {b+d x}{x^4 \sqrt [4]{\frac {b+a x}{d+c x}}} \, dx\)
  3.30.86 \(\int \frac {f+e x}{d+c x+\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.30.87 \(\int \frac {1+x^6}{\sqrt [4]{-x^3+x^5} (1-x^6)} \, dx\)
  3.30.88 \(\int \frac {\sqrt {-b+a^2 x^2} (d+c x^4) \sqrt {a x+\sqrt {-b+a^2 x^2}}}{x^2} \, dx\)
  3.30.89 \(\int \frac {(1+x^2)^{3/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.30.90 \(\int \frac {(1+x^2)^{3/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.30.91 \(\int \frac {(1+x^2)^{3/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.30.92 \(\int \frac {(1+x^2+x^4) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)} \, dx\)
  3.30.93 \(\int \frac {(1+x^2+x^4) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)} \, dx\)
  3.30.94 \(\int \frac {\sqrt {-b+a^2 x^2} (d+c x^4) \sqrt {a x+\sqrt {-b+a^2 x^2}}}{x} \, dx\)
  3.30.95 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\)
  3.30.96 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\)
  3.30.97 \(\int \frac {x^5 (7 b+10 a x^3)}{\sqrt [4]{b x^3+a x^6} (1+b x^7+a x^{10})} \, dx\)
  3.30.98 \(\int \frac {x^4 (-2 q+p x^3) \sqrt {q+p x^3}}{b x^8+a (q+p x^3)^4} \, dx\)
  3.30.99 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^2} \, dx\)
  3.30.100 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^2} \, dx\)