3.22.1 \(\int \frac {-b^8+a^8 x^8}{\sqrt {-b^4+a^4 x^4} (b^8-c x^4+a^8 x^8)} \, dx\)
  3.22.2 \(\int \frac {-1+2 k x+(1-2 k) x^2}{((1-x) x (1-k x))^{2/3} (1-(2+b) x+(1+b k) x^2)} \, dx\)
  3.22.3 \(\int \frac {x^3 (3+x^2)}{(1+x^2) \sqrt [3]{1+x^2-x^3} (1+x^2+x^3)} \, dx\)
  3.22.4 \(\int \frac {(1+x^2) \sqrt [4]{-x^3+x^4}}{-1+x+2 x^2} \, dx\)
  3.22.5 \(\int \frac {1}{\sqrt [3]{-1+x^2} (3+x^2)} \, dx\)
  3.22.6 \(\int \frac {1+x}{(1+3 x+x^2) \sqrt [3]{1-x^3}} \, dx\)
  3.22.7 \(\int \frac {3 k+2 (1+k^2) x-k (1+k^2) x^2-4 k^2 x^3-k^3 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d-(1+2 d) k x-(1+d k^2) x^2+k x^3)} \, dx\)
  3.22.8 \(\int \frac {\sqrt {-x+x^4} (b+a x^6)}{-d+c x^6} \, dx\)
  3.22.9 \(\int \frac {a^2 b-2 a^2 x+(2 a-b) x^2}{(x (-a+x) (-b+x))^{2/3} (a^2 d+(b-2 a d) x+(-1+d) x^2)} \, dx\)
  3.22.10 \(\int \frac {2 a b^2 x-b (2 a+b) x^2+x^4}{(x (-a+x) (-b+x)^2)^{2/3} (-a b^2+b (2 a+b) x-(a+2 b+d) x^2+x^3)} \, dx\)
  3.22.11 \(\int \frac {-3 k+2 (1+k^2) x+k (1+k^2) x^2-4 k^2 x^3+k^3 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d-(1+2 d) k x+(1+d k^2) x^2+k x^3)} \, dx\)
  3.22.12 \(\int \frac {1}{(-b x+a^2 x^2)^{3/2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.22.13 \(\int \frac {1}{x \sqrt [3]{(-1+x) (q-2 q x+x^2)}} \, dx\)
  3.22.14 \(\int \frac {a b+(-2 a+b) x}{\sqrt [3]{x (-a+x) (-b+x)} (a^2 d+(b-2 a d) x+(-1+d) x^2)} \, dx\)
  3.22.15 \(\int \frac {1+x^4}{(-1-x^2+x^4) \sqrt [4]{-x^2+x^4}} \, dx\)
  3.22.16 \(\int \frac {x^3 \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}{\sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}} \, dx\)
  3.22.17 \(\int \frac {\sqrt [3]{-x+x^3} (-2+x^4)}{x^4 (1+x^2)} \, dx\)
  3.22.18 \(\int \frac {2 (3 a q x-2 b p x^3+a p x^5)}{\sqrt [3]{q+p x^4} (b^3 d+c q+3 a b^2 d x^2+(3 a^2 b d+c p) x^4+a^3 d x^6)} \, dx\)
  3.22.19 \(\int \frac {(b^2-2 b x+x^2) (-a^2 b+4 a b x-(2 a+3 b) x^2+2 x^3)}{(x (-a+x)^2 (-b+x)^3)^{3/4} (b d+(a^2-d) x-2 a x^2+x^3)} \, dx\)
  3.22.20 \(\int \frac {(-2+(1+k) x) (1-2 (1+k) x+(1+4 k+k^2) x^2-2 (k+k^2) x^3+(a+k^2) x^4)}{x^3 ((1-x) x (1-k x))^{2/3} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.22.21 \(\int \frac {1+a k x+k x^2}{(-1+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.22.22 \(\int \frac {3 k+(2-k^2) x-3 k x^2-k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d-(1+2 d) k x+(-1-d k^2) x^2+k x^3)} \, dx\)
  3.22.23 \(\int \frac {3 k+(-2+k^2) x-3 k x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d-(1+2 d) k x+(1+d k^2) x^2+k x^3)} \, dx\)
  3.22.24 \(\int \frac {d+c x^4}{x \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.22.25 \(\int \frac {\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.22.26 \(\int \sqrt {1+x^2} \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.22.27 \(\int \frac {\sqrt [4]{-x^3+x^4}}{x (-b+a x)} \, dx\)
  3.22.28 \(\int \frac {x^3 (-2 a b+(a+b) x)}{(x (-a+x) (-b+x))^{2/3} (-a^2 b^2+2 a b (a+b) x-(a^2+4 a b+b^2) x^2+2 (a+b) x^3+(-1+d) x^4)} \, dx\)
  3.22.29 \(\int \frac {(-4 b+a x^3) \sqrt [3]{b+a x^3}}{x^5 (-2 b+a x^3)} \, dx\)
  3.22.30 \(\int \frac {-2 a^2 b x+a (3 a+2 b) x^2-4 a x^3+x^4}{(x^2 (-a+x) (-b+x))^{2/3} (-a^2 d+2 a d x-(b+d) x^2+x^3)} \, dx\)
  3.22.31 \(\int \frac {(-2+(1+k) x) (1-2 (1+k) x+(1+4 k+k^2) x^2-2 (k+k^2) x^3+(a+k^2) x^4)}{x^4 \sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.22.32 \(\int \frac {x^6 \sqrt {x+x^4}}{b+a x^6} \, dx\)
  3.22.33 \(\int \frac {(-2+2 x^4+5 x^7) \sqrt [3]{x-x^3+x^5+x^8}}{(2+x^2+2 x^4+2 x^7)^2} \, dx\)
  3.22.34 \(\int \frac {-b^5+a^5 x^5}{\sqrt {b^2 x+a^2 x^3} (b^5+a^5 x^5)} \, dx\)
  3.22.35 \(\int \frac {b^5+a^5 x^5}{\sqrt {b^2 x+a^2 x^3} (-b^5+a^5 x^5)} \, dx\)
  3.22.36 \(\int \frac {-2 b-a x^4+2 x^8}{x^4 \sqrt [4]{-b+a x^4} (-b+2 a x^4)} \, dx\)
  3.22.37 \(\int \frac {-1+x^{16}}{\sqrt {-1+x^4} (1+x^8+x^{16})} \, dx\)
  3.22.38 \(\int \frac {2 a b x-3 a x^2+x^3}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a^2 d+2 a d x-(b+d) x^2+x^3)} \, dx\)
  3.22.39 \(\int \frac {(-2+k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d+(-2 d+k^2) x^2+d x^4)} \, dx\)
  3.22.40 \(\int \frac {(-1+2 k^2) x-2 k^4 x^3+k^4 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d+(d-2 k^2) x^2+k^4 x^4)} \, dx\)
  3.22.41 \(\int \frac {(-2+x^6) (1-x^4+x^6)}{\sqrt [4]{1+x^6} (1+2 x^6+x^8+x^{12})} \, dx\)
  3.22.42 \(\int \frac {(-q+2 p x^3) (a q+b x+a p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^3 (c q+d x+c p x^3)} \, dx\)
  3.22.43 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.22.44 \(\int \frac {(-1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{1+x^2} \, dx\)
  3.22.45 \(\int \sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.22.46 \(\int \frac {x (-a+x)}{(x^2 (-a+x))^{2/3} (a^2 d-2 a d x+(-1+d) x^2)} \, dx\)
  3.22.47 \(\int \frac {x}{\sqrt [3]{x^2 (-a+x)} (a^2 d-2 a d x+(-1+d) x^2)} \, dx\)
  3.22.48 \(\int \frac {-a x+x^2}{(x^2 (-a+x))^{2/3} (a^2 d-2 a d x+(-1+d) x^2)} \, dx\)
  3.22.49 \(\int \frac {-1+x}{(1+x) \sqrt [3]{-1+x^3}} \, dx\)
  3.22.50 \(\int \frac {(1+x^2) \sqrt [3]{-x^2+x^3}}{-1+x^2} \, dx\)
  3.22.51 \(\int \frac {(1-2 k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d+(d-2 k^2) x^2+k^4 x^4)} \, dx\)
  3.22.52 \(\int \frac {(2-k^2) x-2 x^3+k^2 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d+(-2 d+k^2) x^2+d x^4)} \, dx\)
  3.22.53 \(\int \frac {1}{x^4 \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.22.54 \(\int \frac {-a (a-5 b)-(3 a+5 b) x+4 x^2}{\sqrt [3]{(-a+x) (-b+x)} (-a^5+b d-(-5 a^4+d) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5)} \, dx\)
  3.22.55 \(\int \frac {x^6 \sqrt {-x+x^4}}{b+a x^6} \, dx\)
  3.22.56 \(\int \frac {b^6+a^6 x^6}{\sqrt {-b^2 x+a^2 x^3} (-b^6+a^6 x^6)} \, dx\)
  3.22.57 \(\int \frac {a^2 b-2 a^2 x+(2 a-b) x^2}{(x (-a+x) (-b+x))^{2/3} (a^2+(-2 a+b d) x+(1-d) x^2)} \, dx\)
  3.22.58 \(\int \frac {b^6+a^6 x^6}{\sqrt {b^2 x+a^2 x^3} (-b^6+a^6 x^6)} \, dx\)
  3.22.59 \(\int \frac {(2+5 x^7) \sqrt [3]{-x-x^3+x^8}}{(-1+x^7) (-1+x^2+x^7)} \, dx\)
  3.22.60 \(\int \frac {x^6 (-4+x^3)}{(-1+x^3)^{3/4} (1-2 x^3+x^6+x^8)} \, dx\)
  3.22.61 \(\int \frac {x^6 (4+x^5)}{(-1+x^5)^{3/4} (1-2 x^5+x^8+x^{10})} \, dx\)
  3.22.62 \(\int \frac {\sqrt {1+x^4} \sqrt {x^2+\sqrt {1+x^4}}}{1+x^2} \, dx\)
  3.22.63 \(\int \frac {(b+a x) (-3 a q+4 b p x^3+a p x^4)}{(q+p x^4)^{2/3} (b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+a^3 c x^3+d p x^4)} \, dx\)
  3.22.64 \(\int \frac {\sqrt {b^2+a^2 x^3} (2 b^2+c x^3+a^2 x^6)}{x^7 (b^2+a^2 x^6)} \, dx\)
  3.22.65 \(\int \frac {x^2 (-2+x^8) \sqrt [4]{2-2 x^4+x^8}}{(2+x^8) (4-x^4+2 x^8)} \, dx\)
  3.22.66 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [3]{a x^2+x \sqrt {-b+a^2 x^2}}} \, dx\)
  3.22.67 \(\int \frac {\sqrt {-b+a x}}{1+\sqrt {a x+\sqrt {-b+a x}}} \, dx\)
  3.22.68 \(\int x \sqrt {1+\sqrt {2}+\sqrt {2} x+x^2} \, dx\)
  3.22.69 \(\int \frac {-a x+x^2}{(x^2 (-a+x))^{2/3} (a^2-2 a x+(1-d) x^2)} \, dx\)
  3.22.70 \(\int \frac {x}{\sqrt [3]{x^2 (-a+x)} (-a^2+2 a x+(-1+d) x^2)} \, dx\)
  3.22.71 \(\int \frac {-a b x^2+x^4}{(x^2 (-a+x) (-b+x))^{2/3} (a^2 b^2-2 a b (a+b) x+(a^2+4 a b+b^2-d) x^2-2 (a+b) x^3+x^4)} \, dx\)
  3.22.72 \(\int \frac {\sqrt [4]{\frac {1+4 x^2+a x^2+6 x^4+4 a x^4+4 x^6+6 a x^6+x^8+4 a x^8+a x^{10}}{x^2}}}{x} \, dx\)
  3.22.73 \(\int \frac {\sqrt [3]{2-8 x+8 x^2}}{3+x} \, dx\)
  3.22.74 \(\int \frac {(b+a x) (-a q+b p x^2)}{(q+p x^3)^{2/3} (b^3 c+d q+3 a b^2 c x+3 a^2 b c x^2+(a^3 c+d p) x^3)} \, dx\)
  3.22.75 \(\int \frac {(-b+x) (-a (a-2 b)-2 b x+x^2)}{((-a+x) (-b+x))^{2/3} (a^4-b^2 d-2 (2 a^3-b d) x+(6 a^2-d) x^2-4 a x^3+x^4)} \, dx\)
  3.22.76 \(\int \frac {\sqrt {1+x^5} (2+x^5)}{x^6 (-1-x^5+a x^{10})} \, dx\)
  3.22.77 \(\int \frac {(-2+x^5) \sqrt {-1+x^5}}{x^6 (1-x^5+a x^{10})} \, dx\)
  3.22.78 \(\int \frac {(-2 q+p x^3) (a q+b x^2+a p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6}}{x^5 (c q+d x^2+c p x^3)} \, dx\)
  3.22.79 \(\int -\frac {(-1+x) x (-1+2 x+(-2 k+k^2) x^2)}{((1-x) x (1-k x))^{2/3} (1-4 k x+(-b+6 k^2) x^2+(2 b-4 k^3) x^3+(-b+k^4) x^4)} \, dx\)
  3.22.80 \(\int \frac {(-2 q+p x^3) \sqrt {q^2+2 p q x^3-2 p q x^4+p^2 x^6} (b x^8+a (q+p x^3)^4)}{x^{13}} \, dx\)
  3.22.81 \(\int \frac {1}{x \sqrt [5]{1-4 x+6 x^2-4 x^3+x^4}} \, dx\)
  3.22.82 \(\int \frac {1-x+x^2}{(-1+x^2) \sqrt [3]{x^2+x^4}} \, dx\)
  3.22.83 \(\int \frac {1+x+x^2}{(-1+x^2) \sqrt [3]{x^2+x^4}} \, dx\)
  3.22.84 \(\int \frac {(-1+x^3)^{2/3} (4+x^3)}{x^6 (-2-x^3+x^6)} \, dx\)
  3.22.85 \(\int \frac {\sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.22.86 \(\int \frac {(x+x^2) \sqrt [4]{x^3+x^4}}{-1+x+x^2} \, dx\)
  3.22.87 \(\int \frac {(b+x^4)^2}{\sqrt [4]{a b^4+4 a b^3 x^4+b^4 x^4+6 a b^2 x^8+4 b^3 x^8+4 a b x^{12}+6 b^2 x^{12}+a x^{16}+4 b x^{16}+x^{20}}} \, dx\)
  3.22.88 \(\int \frac {(-q+2 p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6} (b x^4+a (q+p x^3)^4)}{x^7} \, dx\)
  3.22.89 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [6]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.22.90 \(\int \frac {(1-2 k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d+(1-2 d k^2) x^2+d k^4 x^4)} \, dx\)
  3.22.91 \(\int \frac {(2-k^2) x-2 x^3+k^2 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d+(-2+d k^2) x^2+x^4)} \, dx\)
  3.22.92 \(\int \frac {(-1+x^4) \sqrt [4]{-x^2+x^4}}{-1-x^2+x^4} \, dx\)
  3.22.93 \(\int \frac {1+(3-2 k) x-(4+k) x^2+3 k x^3}{\sqrt [3]{(1-x) x (1-k x)} (-b+(1+5 b) x-(10 b+k) x^2+10 b x^3-5 b x^4+b x^5)} \, dx\)
  3.22.94 \(\int \frac {1}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.22.95 \(\int \frac {(-b+x) (a b-2 b x+x^2)}{(x (-a+x) (-b+x)^2)^{2/3} (b-(1+a d) x+d x^2)} \, dx\)
  3.22.96 \(\int \frac {(a-5 b+4 x) (-a^3+3 a^2 x-3 a x^2+x^3)}{((-a+x) (-b+x))^{2/3} (-a^5+b d-(-5 a^4+d) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5)} \, dx\)
  3.22.97 \(\int \frac {(-1+x+2 x^2) \sqrt [4]{-x^3+x^4}}{-1-x+x^2} \, dx\)
  3.22.98 \(\int \frac {(2+x^6) (-1+x^4+x^6)}{\sqrt [4]{-1+x^6} (1-2 x^6+x^8+x^{12})} \, dx\)
  3.22.99 \(\int \frac {1}{(d+c x)^2 \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.22.100 \(\int \frac {(1+x^2)^2}{(-1+x^2)^2 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)