3.8.1 \(\int \frac {(-b+a x^3) \sqrt {b+a x^3}}{x^4} \, dx\)
  3.8.2 \(\int \frac {1-2 x+k^2 x^2}{(-1+2 x-2 x^2+k^2 x^2) \sqrt {x-x^2-k^2 x^2+k^2 x^3}} \, dx\)
  3.8.3 \(\int \frac {2+x}{x \sqrt [4]{1+x^4}} \, dx\)
  3.8.4 \(\int x^6 \sqrt [4]{1+x^4} \, dx\)
  3.8.5 \(\int \frac {\sqrt [4]{-x+x^4}}{x^2} \, dx\)
  3.8.6 \(\int x \sqrt [4]{-x+x^4} \, dx\)
  3.8.7 \(\int \frac {(-b+a x^3) \sqrt {-x+x^4}}{x^3} \, dx\)
  3.8.8 \(\int \frac {\sqrt [4]{-x^3+x^4}}{x^2} \, dx\)
  3.8.9 \(\int \frac {x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx\)
  3.8.10 \(\int \frac {\sqrt {-1-x-x^2+x^4} (2+x+2 x^4)}{(-1-x+x^4) (-1-x+x^2+x^4)} \, dx\)
  3.8.11 \(\int \frac {1}{x (b+a x^4)^{3/4}} \, dx\)
  3.8.12 \(\int \frac {1}{x \sqrt [4]{b+a x^4}} \, dx\)
  3.8.13 \(\int \frac {1}{x (b+a x^5)^{3/4}} \, dx\)
  3.8.14 \(\int \frac {(1+2 x^3) \sqrt {-1+x^6}}{x} \, dx\)
  3.8.15 \(\int \frac {(-2+x^3) \sqrt [3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx\)
  3.8.16 \(\int \frac {(-2+x^3) \sqrt [3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx\)
  3.8.17 \(\int \frac {1}{x (b+a x^6)^{3/4}} \, dx\)
  3.8.18 \(\int \frac {-2 b+a x^4}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\)
  3.8.19 \(\int \frac {-2 b+a x^4}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\)
  3.8.20 \(\int \frac {x^2}{(b+a x^4)^{3/4} (b^2+a^2 x^8)} \, dx\)
  3.8.21 \(\int \frac {1}{(-1+x) \sqrt {-\sqrt {x}+x}} \, dx\)
  3.8.22 \(\int \frac {1}{(1+2 x) \sqrt [4]{1+2 x+2 x^2}} \, dx\)
  3.8.23 \(\int \frac {\sqrt {b+a x^3} (2 b+a x^3)}{x^4} \, dx\)
  3.8.24 \(\int \frac {(-2 q+p x^3) \sqrt {q+p x^3}}{x^2 (a q+b x^2+a p x^3)} \, dx\)
  3.8.25 \(\int \frac {-1+2 x}{\sqrt {-8+4 x-3 x^2-10 x^3+x^4}} \, dx\)
  3.8.26 \(\int \frac {-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx\)
  3.8.27 \(\int \frac {\sqrt {q+p x^5} (-2 q+3 p x^5)}{x^2 (a q+b x^2+a p x^5)} \, dx\)
  3.8.28 \(\int \frac {x^2 (-1+4 x^5)}{(1+x^5)^2 (a-x+a x^5) \sqrt {x+x^6}} \, dx\)
  3.8.29 \(\int \frac {\sqrt {-x+x^4} (-b+a x^6)}{x^6} \, dx\)
  3.8.30 \(\int \frac {(-2 q+p x^6) \sqrt {q+p x^6}}{x^3 (a q+b x^4+a p x^6)} \, dx\)
  3.8.31 \(\int \frac {2 (-2 q+p x^6) \sqrt {q+p x^6} (a q+b x^4+a p x^6)}{x^{11}} \, dx\)
  3.8.32 \(\int \frac {1}{x^3 \sqrt [8]{256-256 x^2+96 x^4-16 x^6+x^8}} \, dx\)
  3.8.33 \(\int \frac {x^3 (5 b+8 a x^3)}{\sqrt [4]{b x+a x^4} (-2+b x^5+a x^8)} \, dx\)
  3.8.34 \(\int \sqrt {1-x^2-y^4} \, dx\)
  3.8.35 \(\int \frac {1-2 k^2 x+k^2 x^2}{\sqrt {(1-x) x (1-k^2 x)} (-a-b x+(a k^2+b k^2) x^2)} \, dx\)
  3.8.36 \(\int \frac {a b c-(a+b+c) x^2+2 x^3}{\sqrt {x (-a+x) (-b+x) (-c+x)} (-a b c d+(-1+a b d+a c d+b c d) x-(a+b+c) d x^2+d x^3)} \, dx\)
  3.8.37 \(\int x^6 \sqrt [4]{-1+x^4} \, dx\)
  3.8.38 \(\int \frac {(-1+2 x) \sqrt [4]{x^3+x^4}}{x} \, dx\)
  3.8.39 \(\int \frac {\sqrt {-1+x^2-2 x^3+x^4} (1-x^3+x^4)}{(-1-2 x^3+x^4) (-2-x^2-4 x^3+2 x^4)} \, dx\)
  3.8.40 \(\int \frac {x^2}{(b+a x^4)^{3/4}} \, dx\)
  3.8.41 \(\int \frac {1}{\sqrt [4]{b+a x^4} (-b+a x^8)} \, dx\)
  3.8.42 \(\int \frac {-b+a x^8}{\sqrt [4]{b+a x^8} (b-c x^4+a x^8)} \, dx\)
  3.8.43 \(\int \frac {(-3+2 x^5) (1+2 x^5+x^6+x^{10})}{x^6 (1-x^3+x^5) \sqrt [4]{x+x^6}} \, dx\)
  3.8.44 \(\int \sqrt {x^2+\sqrt {1+x^4}} \, dx\)
  3.8.45 \(\int \frac {-1-x+x^2}{(1+x^2) \sqrt {-x+x^3}} \, dx\)
  3.8.46 \(\int \frac {-1+x+x^2}{(1+x^2) \sqrt {-x+x^3}} \, dx\)
  3.8.47 \(\int \frac {-7+x+7 x^2}{(1+x^2) \sqrt {-x+x^3}} \, dx\)
  3.8.48 \(\int \frac {1}{(-2+x) \sqrt [4]{-x^2+x^3}} \, dx\)
  3.8.49 \(\int (b+a x^3) \sqrt {-x+x^4} \, dx\)
  3.8.50 \(\int \frac {-2-x+2 x^2}{(1+x^2) \sqrt {1+x^2+x^4}} \, dx\)
  3.8.51 \(\int \frac {x^3 (-5 b+9 a x^4)}{\sqrt [4]{-b x+a x^5} (-2-b x^5+a x^9)} \, dx\)
  3.8.52 \(\int \frac {1+x^2}{(-1+x^2) \sqrt {x+x^2+x^3}} \, dx\)
  3.8.53 \(\int \frac {a b c-(a+b+c) x^2+2 x^3}{\sqrt {x (-a+x) (-b+x) (-c+x)} (-a b c+(a b+a c+b c-d) x-(a+b+c) x^2+x^3)} \, dx\)
  3.8.54 \(\int \frac {(-b+a x^3) \sqrt {b+a x^3}}{x^7} \, dx\)
  3.8.55 \(\int \frac {\sqrt {b+a x^3} (2 b+a x^3)}{x^7} \, dx\)
  3.8.56 \(\int \frac {3 a b c x-2 (a b+a c+b c) x^2+(a+b+c) x^3}{\sqrt {x (-a+x) (-b+x) (-c+x)} (a b c-(a b+a c+b c) x+(a+b+c) x^2+(-1+d) x^3)} \, dx\)
  3.8.57 \(\int \frac {x (3 a b c-2 (a b+a c+b c) x+(a+b+c) x^2)}{\sqrt {x (-a+x) (-b+x) (-c+x)} (-a b c d+(a b+a c+b c) d x-(a+b+c) d x^2+(-1+d) x^3)} \, dx\)
  3.8.58 \(\int \sqrt [4]{-x^2+x^4} \, dx\)
  3.8.59 \(\int x^2 \sqrt [4]{x^2+x^4} \, dx\)
  3.8.60 \(\int \frac {(-1+2 x^4) \sqrt {1+3 x^2+2 x^4}}{(1+2 x^2+2 x^4)^2} \, dx\)
  3.8.61 \(\int \frac {\sqrt {-2+x^2-2 x^3+2 x^4} (2-x^3+2 x^4)}{(-1-x^3+x^4) (-2-x^2-2 x^3+2 x^4)} \, dx\)
  3.8.62 \(\int \frac {-b+a x^2}{(b+a x^2) \sqrt {b^2+a^2 x^4}} \, dx\)
  3.8.63 \(\int \frac {3 b+a x^4}{(-b-x^3+a x^4) \sqrt [4]{-b x+a x^5}} \, dx\)
  3.8.64 \(\int \frac {(-1+x^3) \sqrt {-1+x^6}}{x} \, dx\)
  3.8.65 \(\int \frac {x (3+4 x) \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx\)
  3.8.66 \(\int \frac {x (3+4 x) \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx\)
  3.8.67 \(\int \frac {(3+2 x) (1+x+x^3)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx\)
  3.8.68 \(\int \frac {(3+2 x) (1+x+x^3)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx\)
  3.8.69 \(\int \frac {(2+x^3) \sqrt [3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx\)
  3.8.70 \(\int \frac {(2+x^3) \sqrt [3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx\)
  3.8.71 \(\int \frac {(3+x^2) (1+x^2+x^3)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx\)
  3.8.72 \(\int \frac {(3+x^2) (1+x^2+x^3)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx\)
  3.8.73 \(\int \frac {b+a x^8}{\sqrt [4]{b-a x^8} (-b+c x^4+a x^8)} \, dx\)
  3.8.74 \(\int \frac {x \sqrt [3]{2-x^3+x^8} (-6+5 x^8)}{4+x^6+4 x^8+x^{16}} \, dx\)
  3.8.75 \(\int \frac {a b+a c-b c-2 a x+x^2}{\sqrt {(-a+x) (-b+x) (-c+x)} (b c+a d-(b+c+d) x+x^2)} \, dx\)
  3.8.76 \(\int \frac {a b+a c-b c-2 a x+x^2}{\sqrt {(-a+x) (-b+x) (-c+x)} (a+b c d-(1+b d+c d) x+d x^2)} \, dx\)
  3.8.77 \(\int \frac {-1+k^2 x^2}{\sqrt {(1-x) x (1-k^2 x)} (1+k^2 x^2)} \, dx\)
  3.8.78 \(\int \frac {a (a b+a c-3 b c)+(-2 a^2+a b+a c+3 b c) x+(a-2 b-2 c) x^2+x^3}{\sqrt {(-a+x) (-b+x) (-c+x)} (-a^3-b c d+(3 a^2+b d+c d) x-(3 a+d) x^2+x^3)} \, dx\)
  3.8.79 \(\int \frac {(-2 c+a x^3) \sqrt {c+b x^2+a x^3}}{(c+a x^3)^2} \, dx\)
  3.8.80 \(\int \frac {-b+a^2 x^2}{(b+2 a b x+a^2 x^2) \sqrt {b x+a^2 x^3}} \, dx\)
  3.8.81 \(\int \frac {a (a b+a c-3 b c)+(-2 a^2+a b+a c+3 b c) x+(a-2 b-2 c) x^2+x^3}{\sqrt {(-a+x) (-b+x) (-c+x)} (-b c-a^3 d+(b+c+3 a^2 d) x-(1+3 a d) x^2+d x^3)} \, dx\)
  3.8.82 \(\int \frac {(-1+x^2) \sqrt {1+x^4}}{x^5} \, dx\)
  3.8.83 \(\int \frac {(-1+x^2) \sqrt {1+x^4}}{x^3} \, dx\)
  3.8.84 \(\int \frac {(1+2 x^3) \sqrt {-1+x^6}}{x^7} \, dx\)
  3.8.85 \(\int \frac {(1+2 x^3) \sqrt {-1+x^6}}{x^4} \, dx\)
  3.8.86 \(\int \frac {b^6+a^6 x^6}{\sqrt {-b^2 x+a^2 x^3} (-b^6+c x^3+a^6 x^6)} \, dx\)
  3.8.87 \(\int \frac {b^6+a^6 x^6}{\sqrt {-b^2 x+a^2 x^3} (-b^6+c x^3+a^6 x^6)} \, dx\)
  3.8.88 \(\int \frac {x-3 x^5}{\sqrt {x+x^5} (1-a x^2+2 x^4+x^8)} \, dx\)
  3.8.89 \(\int \frac {\sqrt {1-2 x^8} (-1+2 x^8) (1+2 x^8)}{x^7 (-1+x^4+2 x^8)} \, dx\)
  3.8.90 \(\int \frac {-x+3 x^5}{\sqrt {x+x^5} (a-x^2+2 a x^4+a x^8)} \, dx\)
  3.8.91 \(\int \frac {x^5 (7 b+9 a x^2)}{\sqrt [4]{b x^3+a x^5} (-2+b x^7+a x^9)} \, dx\)
  3.8.92 \(\int \frac {x^2}{(1+x^2) \sqrt [5]{243-5265 x+47250 x^2-225810 x^3+615255 x^4-954733 x^5+820340 x^6-401440 x^7+112000 x^8-16640 x^9+1024 x^{10}}} \, dx\)
  3.8.93 \(\int \frac {\sqrt [3]{1-2 x+x^2}}{2+x^2} \, dx\)
  3.8.94 \(\int \frac {\sqrt [3]{1+2 x+x^2}}{3+x^2} \, dx\)
  3.8.95 \(\int \frac {1}{(-1+x) \sqrt [4]{x+x^3}} \, dx\)
  3.8.96 \(\int \frac {-1+x^4}{\sqrt {x+x^3} (1+x^4)} \, dx\)
  3.8.97 \(\int \frac {1+x^3}{(-1+x^3) \sqrt {1+x^4}} \, dx\)
  3.8.98 \(\int \frac {-1+x}{x \sqrt [4]{1+x^4}} \, dx\)
  3.8.99 \(\int \frac {x^2}{(-b+a x^4)^{3/4}} \, dx\)
  3.8.100 \(\int \frac {(6+x^4) \sqrt {-2 x+x^4+x^5}}{(-2+x^4) (-2-x^3+x^4)} \, dx\)