3.27.1 \(\int \frac {x^2 \sqrt {-b x+a^2 x^2}}{(a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.27.2 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{(1+x) \sqrt {1+x^4}} \, dx\)
  3.27.3 \(\int \frac {-b+a x^2}{(-b+2 a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.27.4 \(\int \frac {-b+a x^2}{(-b+2 a x^3) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\)
  3.27.5 \(\int \frac {2 a b x-3 a x^2+x^3}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a^2+2 a x-(1+b d) x^2+d x^3)} \, dx\)
  3.27.6 \(\int \frac {(-2+k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d+(-2+d k^2) x^2+x^4)} \, dx\)
  3.27.7 \(\int \frac {(1+2 x) \sqrt [4]{x^3+x^4}}{-1+x+x^2} \, dx\)
  3.27.8 \(\int \frac {(-1+2 k^2) x-2 k^4 x^3+k^4 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d+(1-2 d k^2) x^2+d k^4 x^4)} \, dx\)
  3.27.9 \(\int \frac {(-a+x) (-b+x) (-2 a b+(a+b) x)}{\sqrt [3]{x (-a+x) (-b+x)} (a^2 b^2 d-2 a b (a+b) d x+(a^2+4 a b+b^2) d x^2-2 (a+b) d x^3+(-1+d) x^4)} \, dx\)
  3.27.10 \(\int \frac {\sqrt {b^2+a^2 x^3} (2 b^2+c x^3+a^2 x^6)}{x (b^2+a^2 x^6)} \, dx\)
  3.27.11 \(\int \frac {\sqrt {x+x^4} (b+a x^6)}{-d+c x^6} \, dx\)
  3.27.12 \(\int \frac {x (-1+k x) (1-2 k x+(-1+2 k) x^2)}{((1-x) x (1-k x))^{2/3} (-1+4 x+(-6+b) x^2+(4-2 b k) x^3+(-1+b k^2) x^4)} \, dx\)
  3.27.13 \(\int \frac {-3 a q+4 b p x^3+a p x^4}{\sqrt [3]{q+p x^4} (b^3 d+c q+3 a b^2 d x+3 a^2 b d x^2+a^3 d x^3+c p x^4)} \, dx\)
  3.27.14 \(\int \frac {x^2}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.27.15 \(\int \frac {x^2}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.27.16 \(\int \frac {3+(-1+2 k^2) x-3 k^2 x^2-k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d-(1+2 d) x-(d+k^2) x^2+k^2 x^3)} \, dx\)
  3.27.17 \(\int \frac {3+(1-2 k^2) x-3 k^2 x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d-(1+2 d) x+(d+k^2) x^2+k^2 x^3)} \, dx\)
  3.27.18 \(\int \frac {\sqrt {-b^4+a^4 x^4} (b^4+a^4 x^4)}{b^8-c x^4+a^8 x^8} \, dx\)
  3.27.19 \(\int \frac {-b^8+a^8 x^8}{\sqrt {-b^4+a^4 x^4} (b^8-c x^4+a^8 x^8)} \, dx\)
  3.27.20 \(\int \frac {\sqrt {a x+\sqrt {-b+a x}}}{x^2} \, dx\)
  3.27.21 \(\int \frac {-1+2 k x+(1-2 k) x^2}{((1-x) x (1-k x))^{2/3} (1-(2+b) x+(1+b k) x^2)} \, dx\)
  3.27.22 \(\int \frac {x^3 (3+x^2)}{(1+x^2) \sqrt [3]{1+x^2-x^3} (1+x^2+x^3)} \, dx\)
  3.27.23 \(\int \frac {(1+x^2) \sqrt [4]{-x^3+x^4}}{-1+x+2 x^2} \, dx\)
  3.27.24 \(\int \frac {\sqrt [4]{b x^2+a x^4} (b+a x^4+x^8)}{b+a x^4} \, dx\)
  3.27.25 \(\int \frac {\sqrt [4]{b x^2+a x^4} (b+a x^4+x^8)}{b+a x^4} \, dx\)
  3.27.26 \(\int \frac {1}{\sqrt [3]{-1+x^2} (3+x^2)} \, dx\)
  3.27.27 \(\int \frac {1+x}{(1+3 x+x^2) \sqrt [3]{1-x^3}} \, dx\)
  3.27.28 \(\int \frac {3 k+2 (1+k^2) x-k (1+k^2) x^2-4 k^2 x^3-k^3 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d-(1+2 d) k x-(1+d k^2) x^2+k x^3)} \, dx\)
  3.27.29 \(\int \frac {\sqrt {-x+x^4} (b+a x^6)}{-d+c x^6} \, dx\)
  3.27.30 \(\int \frac {a^2 b-2 a^2 x+(2 a-b) x^2}{(x (-a+x) (-b+x))^{2/3} (a^2 d+(b-2 a d) x+(-1+d) x^2)} \, dx\)
  3.27.31 \(\int \frac {2 a b^2 x-b (2 a+b) x^2+x^4}{(x (-a+x) (-b+x)^2)^{2/3} (-a b^2+b (2 a+b) x-(a+2 b+d) x^2+x^3)} \, dx\)
  3.27.32 \(\int \frac {-3 k+2 (1+k^2) x+k (1+k^2) x^2-4 k^2 x^3+k^3 x^4}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d-(1+2 d) k x+(1+d k^2) x^2+k x^3)} \, dx\)
  3.27.33 \(\int \frac {1-((-1+3 x) (3+4 x))^{3/2}}{1+((-1+3 x) (3+4 x))^{3/2}} \, dx\)
  3.27.34 \(\int \frac {1}{(-b x+a^2 x^2)^{3/2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.27.35 \(\int \frac {1}{x \sqrt [3]{(-1+x) (q-2 q x+x^2)}} \, dx\)
  3.27.36 \(\int \frac {a b+(-2 a+b) x}{\sqrt [3]{x (-a+x) (-b+x)} (a^2 d+(b-2 a d) x+(-1+d) x^2)} \, dx\)
  3.27.37 \(\int \frac {1+x^4}{(-1-x^2+x^4) \sqrt [4]{-x^2+x^4}} \, dx\)
  3.27.38 \(\int \frac {x^3 \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}{\sqrt {a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}} \, dx\)
  3.27.39 \(\int \frac {\sqrt [3]{-x+x^3} (-2+x^4)}{x^4 (1+x^2)} \, dx\)
  3.27.40 \(\int \frac {2 (3 a q x-2 b p x^3+a p x^5)}{\sqrt [3]{q+p x^4} (b^3 d+c q+3 a b^2 d x^2+(3 a^2 b d+c p) x^4+a^3 d x^6)} \, dx\)
  3.27.41 \(\int \frac {(b^2-2 b x+x^2) (-a^2 b+4 a b x-(2 a+3 b) x^2+2 x^3)}{(x (-a+x)^2 (-b+x)^3)^{3/4} (b d+(a^2-d) x-2 a x^2+x^3)} \, dx\)
  3.27.42 \(\int \frac {(-2+(1+k) x) (1-2 (1+k) x+(1+4 k+k^2) x^2-2 (k+k^2) x^3+(a+k^2) x^4)}{x^3 ((1-x) x (1-k x))^{2/3} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.27.43 \(\int \frac {(1+x^3) \sqrt [3]{-x^2+x^3}}{1+x^6} \, dx\)
  3.27.44 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(d+c x^2) \sqrt {b+a^2 x^4}} \, dx\)
  3.27.45 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(d+c x^2) \sqrt {b+a^2 x^4}} \, dx\)
  3.27.46 \(\int \frac {\sqrt {a x+\sqrt {b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}}}{(b+a^2 x^2)^{3/2}} \, dx\)
  3.27.47 \(\int \frac {\sqrt {a x+\sqrt {b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}}}{(b+a^2 x^2)^{3/2}} \, dx\)
  3.27.48 \(\int \frac {1+a k x+k x^2}{(-1+k x^2) \sqrt {(1-x^2) (1-k^2 x^2)}} \, dx\)
  3.27.49 \(\int \frac {3 k+(2-k^2) x-3 k x^2-k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d-(1+2 d) k x+(-1-d k^2) x^2+k x^3)} \, dx\)
  3.27.50 \(\int \frac {3 k+(-2+k^2) x-3 k x^2+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d-(1+2 d) k x+(1+d k^2) x^2+k x^3)} \, dx\)
  3.27.51 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{d+c x^2} \, dx\)
  3.27.52 \(\int \frac {\sqrt [4]{-b x^3+a x^4}}{d+c x^2} \, dx\)
  3.27.53 \(\int \frac {d+c x^4}{x \sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.27.54 \(\int \frac {\sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.27.55 \(\int \sqrt {1+x^2} \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.27.56 \(\int \frac {\sqrt [4]{-x^3+x^4}}{x (-b+a x)} \, dx\)
  3.27.57 \(\int \frac {x^3 (-2 a b+(a+b) x)}{(x (-a+x) (-b+x))^{2/3} (-a^2 b^2+2 a b (a+b) x-(a^2+4 a b+b^2) x^2+2 (a+b) x^3+(-1+d) x^4)} \, dx\)
  3.27.58 \(\int \frac {1+2 x^6}{\sqrt [3]{x+x^3} (-1+x^6)} \, dx\)
  3.27.59 \(\int \frac {1+2 x^6}{\sqrt [3]{x+x^3} (-1+x^6)} \, dx\)
  3.27.60 \(\int \frac {(-4 b+a x^3) \sqrt [3]{b+a x^3}}{x^5 (-2 b+a x^3)} \, dx\)
  3.27.61 \(\int \frac {-2 a^2 b x+a (3 a+2 b) x^2-4 a x^3+x^4}{(x^2 (-a+x) (-b+x))^{2/3} (-a^2 d+2 a d x-(b+d) x^2+x^3)} \, dx\)
  3.27.62 \(\int \frac {(-2+(1+k) x) (1-2 (1+k) x+(1+4 k+k^2) x^2-2 (k+k^2) x^3+(a+k^2) x^4)}{x^4 \sqrt [3]{(1-x) x (1-k x)} (1-(1+k) x+(-b+k) x^2)} \, dx\)
  3.27.63 \(\int \frac {x^6 \sqrt {x+x^4}}{b+a x^6} \, dx\)
  3.27.64 \(\int \frac {\sqrt [4]{b x^2+a x^4} (-b-a x^4+x^8)}{-b+a x^4} \, dx\)
  3.27.65 \(\int \frac {\sqrt [4]{b x^2+a x^4} (-b-a x^4+x^8)}{-b+a x^4} \, dx\)
  3.27.66 \(\int \frac {(-2+2 x^4+5 x^7) \sqrt [3]{x-x^3+x^5+x^8}}{(2+x^2+2 x^4+2 x^7)^2} \, dx\)
  3.27.67 \(\int \frac {-b^5+a^5 x^5}{\sqrt {b^2 x+a^2 x^3} (b^5+a^5 x^5)} \, dx\)
  3.27.68 \(\int \frac {b^5+a^5 x^5}{\sqrt {b^2 x+a^2 x^3} (-b^5+a^5 x^5)} \, dx\)
  3.27.69 \(\int \frac {-2 b-a x^4+2 x^8}{x^4 \sqrt [4]{-b+a x^4} (-b+2 a x^4)} \, dx\)
  3.27.70 \(\int \frac {-1+x^{16}}{\sqrt {-1+x^4} (1+x^8+x^{16})} \, dx\)
  3.27.71 \(\int \frac {2 a b x-3 a x^2+x^3}{\sqrt [3]{x^2 (-a+x) (-b+x)} (-a^2 d+2 a d x-(b+d) x^2+x^3)} \, dx\)
  3.27.72 \(\int \frac {(d+c x^2) \sqrt [4]{b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\)
  3.27.73 \(\int \frac {(d+c x^2) \sqrt [4]{b x^3+a x^4}}{x^2 (-d+c x^2)} \, dx\)
  3.27.74 \(\int \frac {-1+x^4}{(1+x^4) \sqrt {a+b x+c x^2+b x^3+a x^4}} \, dx\)
  3.27.75 \(\int \frac {(-2+k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (-1+d+(-2 d+k^2) x^2+d x^4)} \, dx\)
  3.27.76 \(\int \frac {(-1+2 k^2) x-2 k^4 x^3+k^4 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (1-d+(d-2 k^2) x^2+k^4 x^4)} \, dx\)
  3.27.77 \(\int \frac {(-2+x^6) (1-x^4+x^6)}{\sqrt [4]{1+x^6} (1+2 x^6+x^8+x^{12})} \, dx\)
  3.27.78 \(\int \frac {(-q+2 p x^3) (a q+b x+a p x^3) \sqrt {q^2-2 p q x^2+2 p q x^3+p^2 x^6}}{x^3 (c q+d x+c p x^3)} \, dx\)
  3.27.79 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.27.80 \(\int \frac {(-1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{1+x^2} \, dx\)
  3.27.81 \(\int \sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.27.82 \(\int \frac {x (-a+x)}{(x^2 (-a+x))^{2/3} (a^2 d-2 a d x+(-1+d) x^2)} \, dx\)
  3.27.83 \(\int \frac {x}{\sqrt [3]{x^2 (-a+x)} (a^2 d-2 a d x+(-1+d) x^2)} \, dx\)
  3.27.84 \(\int \frac {-a x+x^2}{(x^2 (-a+x))^{2/3} (a^2 d-2 a d x+(-1+d) x^2)} \, dx\)
  3.27.85 \(\int \frac {-1+x}{(1+x) \sqrt [3]{-1+x^3}} \, dx\)
  3.27.86 \(\int \frac {(1+x^2) \sqrt [3]{-x^2+x^3}}{-1+x^2} \, dx\)
  3.27.87 \(\int \frac {b+a x^4}{(-b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.27.88 \(\int \frac {b+a x^4}{(-b-a x^2+x^4) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.27.89 \(\int \frac {(1-2 k^2) x+k^2 x^3}{\sqrt [3]{(1-x^2) (1-k^2 x^2)} (1-d+(d-2 k^2) x^2+k^4 x^4)} \, dx\)
  3.27.90 \(\int \frac {(2-k^2) x-2 x^3+k^2 x^5}{((1-x^2) (1-k^2 x^2))^{2/3} (-1+d+(-2 d+k^2) x^2+d x^4)} \, dx\)
  3.27.91 \(\int \frac {1}{x^4 \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.27.92 \(\int \frac {-a (a-5 b)-(3 a+5 b) x+4 x^2}{\sqrt [3]{(-a+x) (-b+x)} (-a^5+b d-(-5 a^4+d) x-10 a^3 x^2+10 a^2 x^3-5 a x^4+x^5)} \, dx\)
  3.27.93 \(\int \frac {x^6 \sqrt {-x+x^4}}{b+a x^6} \, dx\)
  3.27.94 \(\int \frac {b^6+a^6 x^6}{\sqrt {-b^2 x+a^2 x^3} (-b^6+a^6 x^6)} \, dx\)
  3.27.95 \(\int \frac {a^2 b-2 a^2 x+(2 a-b) x^2}{(x (-a+x) (-b+x))^{2/3} (a^2+(-2 a+b d) x+(1-d) x^2)} \, dx\)
  3.27.96 \(\int \frac {b^6+a^6 x^6}{\sqrt {b^2 x+a^2 x^3} (-b^6+a^6 x^6)} \, dx\)
  3.27.97 \(\int \frac {(2+5 x^7) \sqrt [3]{-x-x^3+x^8}}{(-1+x^7) (-1+x^2+x^7)} \, dx\)
  3.27.98 \(\int \frac {x^6 (-4+x^3)}{(-1+x^3)^{3/4} (1-2 x^3+x^6+x^8)} \, dx\)
  3.27.99 \(\int \frac {x^6 (4+x^5)}{(-1+x^5)^{3/4} (1-2 x^5+x^8+x^{10})} \, dx\)
  3.27.100 \(\int \frac {\sqrt {b+a x} (-g+f x^2)}{(e+d x^2) \sqrt {c+\sqrt {b+a x}}} \, dx\)