3.28.1 \(\int \frac {\sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}}}{1+x^2} \, dx\)
  3.28.2 \(\int \frac {x}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.28.3 \(\int \frac {x}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.28.4 \(\int \frac {\sqrt {b+a x} \sqrt {1+\sqrt {b+a x}}}{x^2 \sqrt {1+\sqrt {1+\sqrt {b+a x}}}} \, dx\)
  3.28.5 \(\int \frac {\sqrt {b+a x} \sqrt {1+\sqrt {b+a x}}}{x^2 \sqrt {1+\sqrt {1+\sqrt {b+a x}}}} \, dx\)
  3.28.6 \(\int \frac {x^4 \sqrt [4]{b x^2+a x^4}}{b+a x^2+x^4} \, dx\)
  3.28.7 \(\int \frac {x^4 \sqrt [4]{b x^2+a x^4}}{b+a x^2+x^4} \, dx\)
  3.28.8 \(\int \frac {(b+a x) (-3 a q+4 b p x^3+a p x^4)}{(q+p x^4)^{2/3} (b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+a^3 c x^3+d p x^4)} \, dx\)
  3.28.9 \(\int \frac {\sqrt {b^2+a^2 x^3} (2 b^2+c x^3+a^2 x^6)}{x^7 (b^2+a^2 x^6)} \, dx\)
  3.28.10 \(\int \frac {(-2+x^4) \sqrt {2+x^4}}{(2+x^2+x^4) (2+2 x^2+x^4)} \, dx\)
  3.28.11 \(\int \frac {x^2 (-2+x^8) \sqrt [4]{2-2 x^4+x^8}}{(2+x^8) (4-x^4+2 x^8)} \, dx\)
  3.28.12 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\)
  3.28.13 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\)
  3.28.14 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [3]{a x^2+x \sqrt {-b+a^2 x^2}}} \, dx\)
  3.28.15 \(\int \frac {\sqrt {-b+a x}}{1+\sqrt {a x+\sqrt {-b+a x}}} \, dx\)
  3.28.16 \(\int x \sqrt {1+\sqrt {2}+\sqrt {2} x+x^2} \, dx\)
  3.28.17 \(\int \frac {-a x+x^2}{(x^2 (-a+x))^{2/3} (a^2-2 a x+(1-d) x^2)} \, dx\)
  3.28.18 \(\int \frac {x}{\sqrt [3]{x^2 (-a+x)} (-a^2+2 a x+(-1+d) x^2)} \, dx\)
  3.28.19 \(\int \frac {-a b x^2+x^4}{(x^2 (-a+x) (-b+x))^{2/3} (a^2 b^2-2 a b (a+b) x+(a^2+4 a b+b^2-d) x^2-2 (a+b) x^3+x^4)} \, dx\)
  3.28.20 \(\int \frac {\sqrt [4]{\frac {1+4 x^2+a x^2+6 x^4+4 a x^4+4 x^6+6 a x^6+x^8+4 a x^8+a x^{10}}{x^2}}}{x} \, dx\)
  3.28.21 \(\int \frac {\sqrt [3]{2-8 x+8 x^2}}{3+x} \, dx\)
  3.28.22 \(\int \frac {(b+a x) (-a q+b p x^2)}{(q+p x^3)^{2/3} (b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+(a^3 c+d p) x^3)} \, dx\)
  3.28.23 \(\int \frac {(-b+x) (-a (a-2 b)-2 b x+x^2)}{((-a+x) (-b+x))^{2/3} (a^4-b^2 d-2 (2 a^3-b d) x+(6 a^2-d) x^2-4 a x^3+x^4)} \, dx\)
  3.28.24 \(\int \frac {\sqrt {1+x^5} (2+x^5)}{x^6 (-1-x^5+a x^{10})} \, dx\)
  3.28.25 \(\int \frac {(-2+x^5) \sqrt {-1+x^5}}{x^6 (1-x^5+a x^{10})} \, dx\)
  3.28.26 \(\int \frac {1}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.28.27 \(\int \frac {1}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.28.28 \(\int \frac {x (x^2 c_3-c_4)}{\sqrt {\frac {x c_0+x^2 c_3+c_4}{x c_1+x^2 c_3+c_4}} (x+3 x^2 c_3+3 c_4) (-x^2+x^4 c_3{}^2+2 x^2 c_3 c_4+c_4{}^2)} \, dx\)
  3.28.29 \(\int \frac {1}{(-b+a x^4)^2 \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.28.30 \(\int \frac {1}{(-b+a x^4)^2 \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.28.31 \(\int \frac {(-2 q+p x^3) (a q+b x^2+a p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^5 (c q+d x^2+c p x^3)} \, dx\)
  3.28.32 \(\int -\frac {(-1+x) x (-1+2 x+(-2 k+k^2) x^2)}{((1-x) x (1-k x))^{2/3} (1-4 k x+(-b+6 k^2) x^2+(2 b-4 k^3) x^3+(-b+k^4) x^4)} \, dx\)
  3.28.33 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (b x^8+a (q+p x^3)^4)}{x^{13}} \, dx\)
  3.28.34 \(\int \frac {x^2}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.28.35 \(\int \frac {x^2}{x^2-\sqrt {1+x} \sqrt {1+\sqrt {1+x}}} \, dx\)
  3.28.36 \(\int \frac {1}{x \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx\)
  3.28.37 \(\int \frac {1-x+x^2}{(-1+x^2) \sqrt [3]{x^2+x^4}} \, dx\)
  3.28.38 \(\int \frac {1+x+x^2}{(-1+x^2) \sqrt [3]{x^2+x^4}} \, dx\)
  3.28.39 \(\int \frac {(-1+x^2) \sqrt {1-x-x^2+x^3+x^4}}{x^2 (1+x^2)} \, dx\)
  3.28.40 \(\int \frac {(-1+x^2) \sqrt {1-x-x^2+x^3+x^4}}{x^2 (1+x^2)} \, dx\)
  3.28.41 \(\int \frac {(-1+x^3)^{2/3} (4+x^3)}{x^6 (-2-x^3+x^6)} \, dx\)
  3.28.42 \(\int \frac {\sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.28.43 \(\int \frac {(x+x^2) \sqrt [4]{x^3+x^4}}{-1+x+x^2} \, dx\)
  3.28.44 \(\int \frac {(b+x^4)^2}{\sqrt [4]{a b^4+4 a b^3 x^4+b^4 x^4+6 a b^2 x^8+4 b^3 x^8+4 a b x^{12}+6 b^2 x^{12}+a x^{16}+4 b x^{16}+x^{20}}} \, dx\)
  3.28.45 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^4+a (q+p x^3)^4)}{x^7} \, dx\)
  3.28.46 \(\int \frac {1-\sqrt {x-\sqrt {1+x^2}}}{x^4-2 x^2 \sqrt {1+x^2}} \, dx\)
  3.28.47 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [6]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.28.48 \(\int \frac {(1-2 k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d+(1-2 d k^2) x^2+d k^4 x^4)} \, dx\)
  3.28.49 \(\int \frac {(2-k^2) x-2 x^3+k^2 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d+(-2+d k^2) x^2+x^4)} \, dx\)
  3.28.50 \(\int \frac {(-1+x^4) \sqrt [4]{-x^2+x^4}}{-1-x^2+x^4} \, dx\)
  3.28.51 \(\int \frac {1+(3-2 k) x-(4+k) x^2+3 k x^3}{\sqrt [3]{(1-x) x (1-k x)} (-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5)} \, dx\)
  3.28.52 \(\int \frac {x^3}{\sqrt [3]{-x^2+x^3} (-1+x^6)} \, dx\)
  3.28.53 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\)
  3.28.54 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\)
  3.28.55 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.28.56 \(\int \frac {(-b+x) (a b-2 b x+x^2)}{(x (-a+x) (-b+x)^2)^{2/3} (b-(1+a d) x+d x^2)} \, dx\)
  3.28.57 \(\int \frac {(a-5 b+4 x) (-a^3+3 a^2 x-3 a x^2+x^3)}{((-a+x) (-b+x))^{2/3} (-a^5+b d-(-5 a^4+d) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5)} \, dx\)
  3.28.58 \(\int \frac {1-x^3 \sqrt [3]{5+4 x}-x^3 (5+4 x)^{2/3}}{1-x \sqrt {5+4 x}} \, dx\)
  3.28.59 \(\int \frac {x^3 (x^3 c_3-2 c_4) \sqrt {\frac {x^2 c_0+x^3 c_3+c_4}{x^2 c_1+x^3 c_3+c_4}}}{(x^2+2 x^3 c_3+2 c_4) (-x^4+x^6 c_3{}^2+2 x^3 c_3 c_4+c_4{}^2)} \, dx\)
  3.28.60 \(\int \frac {x^5 (2 x^5 c_3-3 c_4) \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{(x^3+2 x^5 c_3+2 c_4) (-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2)} \, dx\)
  3.28.61 \(\int \frac {(-1+x^2)^2 (x+x^3)}{\sqrt {1+x^4} (1-2 x^2+4 x^4-2 x^6+x^8)} \, dx\)
  3.28.62 \(\int \frac {(-1+x+2 x^2) \sqrt [4]{-x^3+x^4}}{-1-x+x^2} \, dx\)
  3.28.63 \(\int \frac {(2+x^6) (-1+x^4+x^6)}{\sqrt [4]{-1+x^6} (1-2 x^6+x^8+x^{12})} \, dx\)
  3.28.64 \(\int \frac {1}{(d+c x)^2 \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.28.65 \(\int \frac {(1+x^2)^2}{(-1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.28.66 \(\int \frac {a (a b+a c-2 b c)-2 (a^2-b c) x+(2 a-b-c) x^2}{((-a+x) (-b+x) (-c+x))^{2/3} (a^2-b c d+(-2 a+b d+c d) x+(1-d) x^2)} \, dx\)
  3.28.67 \(\int \frac {1+x^4}{(-1+x^4) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.28.68 \(\int \frac {(-1+x^2)^2}{(1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.28.69 \(\int \frac {2 a b^2-b (2 a+b) x+x^3}{\sqrt [3]{x (-a+x) (-b+x)^2} (-a b^2+b (2 a+b) x-(a+2 b+d) x^2+x^3)} \, dx\)
  3.28.70 \(\int \frac {-d+c x}{x \sqrt [3]{-b+a x^3}} \, dx\)
  3.28.71 \(\int \frac {-b^4+c^2 x^2+a^4 x^4}{\sqrt {-b^4+a^4 x^4} (b^4+a^4 x^4)} \, dx\)
  3.28.72 \(\int \frac {x^2}{(1-x^4) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.28.73 \(\int \frac {x (-b+x) (-a^2 b+2 a^2 x+(-2 a+b) x^2)}{(x (-a+x) (-b+x))^{2/3} (-a^4+4 a^3 x+(-6 a^2+b^2 d) x^2+2 (2 a-b d) x^3+(-1+d) x^4)} \, dx\)
  3.28.74 \(\int \frac {(-1+x^3)^{2/3} (8-8 x^3+x^6)}{x^6 (-4+x^3) (-2+x^3)} \, dx\)
  3.28.75 \(\int \frac {(c+(a x+\sqrt {-b+a^2 x^2})^{3/4})^{4/3}}{\sqrt {-b+a^2 x^2}} \, dx\)
  3.28.76 \(\int \frac {1}{(-b+a x) \sqrt [3]{b^3+a^3 x^3}} \, dx\)
  3.28.77 \(\int \frac {\sqrt [3]{a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}}{\sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}} \, dx\)
  3.28.78 \(\int \frac {\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\)
  3.28.79 \(\int \frac {\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\)
  3.28.80 \(\int \frac {-b+x}{((-a+x) (-b+x)^2)^{2/3} (b-a d+(-1+d) x)} \, dx\)
  3.28.81 \(\int \frac {-a q x+b p x^3}{\sqrt {q+p x^4} (b^2 c+d q+2 a b c x^2+(a^2 c+d p) x^4)} \, dx\)
  3.28.82 \(\int \frac {(b+a x)^2 (-2 a q+3 b p x^2+a p x^3)}{\sqrt {q+p x^3} (b^4 c+d q^2+4 a b^3 c x+6 a^2 b^2 c x^2+(4 a^3 b c+2 d p q) x^3+a^4 c x^4+d p^2 x^6)} \, dx\)
  3.28.83 \(\int \frac {(1+x^2) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.28.84 \(\int \frac {(1+x^2) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.28.85 \(\int \frac {-1+k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (a+b x^2+a k^4 x^4)} \, dx\)
  3.28.86 \(\int \frac {x^5 (-4 a+3 x)}{\sqrt [3]{x^2 (-a+x)} (-a^2+2 a x-x^2+d x^8)} \, dx\)
  3.28.87 \(\int \frac {\sqrt {1-x}}{8 (1+x)^{7/2}} \, dx\)
  3.28.88 \(\int \frac {2 a b^2-b (2 a+b) x+x^3}{\sqrt [3]{x (-a+x) (-b+x)^2} (-a b^2 d+b (2 a+b) d x-(1+a d+2 b d) x^2+d x^3)} \, dx\)
  3.28.89 \(\int \frac {(-x+x^2) \sqrt [4]{-x^3+x^4}}{-1-x+x^2} \, dx\)
  3.28.90 \(\int \frac {\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{x \sqrt {d+\sqrt {c+\sqrt {b+a x}}}} \, dx\)
  3.28.91 \(\int \frac {\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{x \sqrt {d+\sqrt {c+\sqrt {b+a x}}}} \, dx\)
  3.28.92 \(\int \frac {1}{\sqrt {1+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.28.93 \(\int \frac {(-1+x) (-1+k x) (-2 x+(1+k) x^2)}{((1-x) x (1-k x))^{2/3} (b-2 b (1+k) x+(b+4 b k+b k^2) x^2-2 b k (1+k) x^3+(-1+b k^2) x^4)} \, dx\)
  3.28.94 \(\int \frac {(-1+2 (-2+k) x+3 k x^2) (-1+3 x-3 x^2+x^3)}{((1-x) x (1-k x))^{2/3} (-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5)} \, dx\)
  3.28.95 \(\int \frac {\sqrt [4]{2 b+a x^4} (-4 b+a x^8)}{x^6 (-4 b+c x^4+a x^8)} \, dx\)
  3.28.96 \(\int \frac {\sqrt [4]{2 b+a x^4} (-4 b+a x^8)}{x^6 (-4 b+c x^4+a x^8)} \, dx\)
  3.28.97 \(\int \frac {-b^{12}+a^{12} x^{12}}{\sqrt {-b^4+a^4 x^4} (b^{12}+a^{12} x^{12})} \, dx\)
  3.28.98 \(\int \frac {1}{1-(1+x) \sqrt {c+b x+a x^2}} \, dx\)
  3.28.99 \(\int \frac {(1-x^4) \sqrt [4]{1-x-4 x^2+4 x^3+6 x^4-6 x^5-4 x^6+4 x^7+x^8-x^9}}{1+x^4} \, dx\)
  3.28.100 \(\int \frac {-a (a-5 b)-(3 a+5 b) x+4 x^2}{\sqrt [3]{(-a+x) (-b+x)} (b-a^5 d-(1-5 a^4 d) x-10 a^3 d x^2+10 a^2 d x^3-5 a d x^4+d x^5)} \, dx\)