3.8.1 \(\int \genfrac {}{}{}{}{(-b+a x^3) \sqrt {b+a x^3}}{x^4} \, dx\) [701]
  3.8.2 \(\int \genfrac {}{}{}{}{1-2 x+k^2 x^2}{(-1+2 x-2 x^2+k^2 x^2) \sqrt {x-x^2-k^2 x^2+k^2 x^3}} \, dx\) [702]
  3.8.3 \(\int \genfrac {}{}{}{}{2+x}{x \sqrt [4]{1+x^4}} \, dx\) [703]
  3.8.4 \(\int x^6 \sqrt [4]{1+x^4} \, dx\) [704]
  3.8.5 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x+x^4}}{x^2} \, dx\) [705]
  3.8.6 \(\int x \sqrt [4]{-x+x^4} \, dx\) [706]
  3.8.7 \(\int \genfrac {}{}{}{}{(-b+a x^3) \sqrt {-x+x^4}}{x^3} \, dx\) [707]
  3.8.8 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x^3+x^4}}{x^2} \, dx\) [708]
  3.8.9 \(\int \genfrac {}{}{}{}{x}{\sqrt {-17+18 x-11 x^2+6 x^3+x^4}} \, dx\) [709]
  3.8.10 \(\int \genfrac {}{}{}{}{\sqrt {-1-x-x^2+x^4} (2+x+2 x^4)}{(-1-x+x^4) (-1-x+x^2+x^4)} \, dx\) [710]
  3.8.11 \(\int \genfrac {}{}{}{}{1}{x (b+a x^4)^{3/4}} \, dx\) [711]
  3.8.12 \(\int \genfrac {}{}{}{}{1}{x \sqrt [4]{b+a x^4}} \, dx\) [712]
  3.8.13 \(\int \genfrac {}{}{}{}{1}{x (b+a x^5)^{3/4}} \, dx\) [713]
  3.8.14 \(\int \genfrac {}{}{}{}{(1+2 x^3) \sqrt {-1+x^6}}{x} \, dx\) [714]
  3.8.15 \(\int \genfrac {}{}{}{}{(-2+x^3) \sqrt [3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx\) [715]
  3.8.16 \(\int \genfrac {}{}{}{}{(-2+x^3) \sqrt [3]{x+x^3+x^4}}{1+x^2+2 x^3+x^4+x^5+x^6} \, dx\) [716]
  3.8.17 \(\int \genfrac {}{}{}{}{1}{x (b+a x^6)^{3/4}} \, dx\) [717]
  3.8.18 \(\int \genfrac {}{}{}{}{-2 b+a x^4}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\) [718]
  3.8.19 \(\int \genfrac {}{}{}{}{-2 b+a x^4}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\) [719]
  3.8.20 \(\int \genfrac {}{}{}{}{x^2}{(b+a x^4)^{3/4} (b^2+a^2 x^8)} \, dx\) [720]
  3.8.21 \(\int \genfrac {}{}{}{}{1}{(-1+x) \sqrt {-\sqrt {x}+x}} \, dx\) [721]
  3.8.22 \(\int \genfrac {}{}{}{}{1}{(1+2 x) \sqrt [4]{1+2 x+2 x^2}} \, dx\) [722]
  3.8.23 \(\int \genfrac {}{}{}{}{\sqrt {b+a x^3} (2 b+a x^3)}{x^4} \, dx\) [723]
  3.8.24 \(\int \genfrac {}{}{}{}{(-2 q+p x^3) \sqrt {q+p x^3}}{x^2 (a q+b x^2+a p x^3)} \, dx\) [724]
  3.8.25 \(\int \genfrac {}{}{}{}{-1+2 x}{\sqrt {-8+4 x-3 x^2-10 x^3+x^4}} \, dx\) [725]
  3.8.26 \(\int \genfrac {}{}{}{}{-1+x}{\sqrt {4-16 x+12 x^2-8 x^3+x^4}} \, dx\) [726]
  3.8.27 \(\int \genfrac {}{}{}{}{\sqrt {q+p x^5} (-2 q+3 p x^5)}{x^2 (a q+b x^2+a p x^5)} \, dx\) [727]
  3.8.28 \(\int \genfrac {}{}{}{}{x^2 (-1+4 x^5)}{(1+x^5)^2 (a-x+a x^5) \sqrt {x+x^6}} \, dx\) [728]
  3.8.29 \(\int \genfrac {}{}{}{}{\sqrt {-x+x^4} (-b+a x^6)}{x^6} \, dx\) [729]
  3.8.30 \(\int \genfrac {}{}{}{}{(-2 q+p x^6) \sqrt {q+p x^6}}{x^3 (a q+b x^4+a p x^6)} \, dx\) [730]
  3.8.31 \(\int \genfrac {}{}{}{}{2 (-2 q+p x^6) \sqrt {q+p x^6} (a q+b x^4+a p x^6)}{x^{11}} \, dx\) [731]
  3.8.32 \(\int \genfrac {}{}{}{}{1}{x^3 \sqrt [8]{256-256 x^2+96 x^4-16 x^6+x^8}} \, dx\) [732]
  3.8.33 \(\int \genfrac {}{}{}{}{x^3 (5 b+8 a x^3)}{\sqrt [4]{b x+a x^4} (-2+b x^5+a x^8)} \, dx\) [733]
  3.8.34 \(\int \sqrt {1-x^2-y^4} \, dx\) [734]
  3.8.35 \(\int \genfrac {}{}{}{}{1-2 k^2 x+k^2 x^2}{\sqrt {(1-x) x (1-k^2 x)} (-a-b x+(a k^2+b k^2) x^2)} \, dx\) [735]
  3.8.36 \(\int \genfrac {}{}{}{}{a b c-(a+b+c) x^2+2 x^3}{\sqrt {x (-a+x) (-b+x) (-c+x)} (-a b c d+(-1+a b d+a c d+b c d) x-(a+b+c) d x^2+d x^3)} \, dx\) [736]
  3.8.37 \(\int x^6 \sqrt [4]{-1+x^4} \, dx\) [737]
  3.8.38 \(\int \genfrac {}{}{}{}{(-1+2 x) \sqrt [4]{x^3+x^4}}{x} \, dx\) [738]
  3.8.39 \(\int \genfrac {}{}{}{}{\sqrt {-1+x^2-2 x^3+x^4} (1-x^3+x^4)}{(-1-2 x^3+x^4) (-2-x^2-4 x^3+2 x^4)} \, dx\) [739]
  3.8.40 \(\int \genfrac {}{}{}{}{x^2}{(b+a x^4)^{3/4}} \, dx\) [740]
  3.8.41 \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{b+a x^4} (-b+a x^8)} \, dx\) [741]
  3.8.42 \(\int \genfrac {}{}{}{}{-b+a x^8}{\sqrt [4]{b+a x^8} (b-c x^4+a x^8)} \, dx\) [742]
  3.8.43 \(\int \genfrac {}{}{}{}{(-3+2 x^5) (1+2 x^5+x^6+x^{10})}{x^6 (1-x^3+x^5) \sqrt [4]{x+x^6}} \, dx\) [743]
  3.8.44 \(\int \sqrt {x^2+\sqrt {1+x^4}} \, dx\) [744]
  3.8.45 \(\int \genfrac {}{}{}{}{-1-x+x^2}{(1+x^2) \sqrt {-x+x^3}} \, dx\) [745]
  3.8.46 \(\int \genfrac {}{}{}{}{-1+x+x^2}{(1+x^2) \sqrt {-x+x^3}} \, dx\) [746]
  3.8.47 \(\int \genfrac {}{}{}{}{-7+x+7 x^2}{(1+x^2) \sqrt {-x+x^3}} \, dx\) [747]
  3.8.48 \(\int \genfrac {}{}{}{}{1}{(-2+x) \sqrt [4]{-x^2+x^3}} \, dx\) [748]
  3.8.49 \(\int (b+a x^3) \sqrt {-x+x^4} \, dx\) [749]
  3.8.50 \(\int \genfrac {}{}{}{}{-2-x+2 x^2}{(1+x^2) \sqrt {1+x^2+x^4}} \, dx\) [750]
  3.8.51 \(\int \genfrac {}{}{}{}{x^3 (-5 b+9 a x^4)}{\sqrt [4]{-b x+a x^5} (-2-b x^5+a x^9)} \, dx\) [751]
  3.8.52 \(\int \genfrac {}{}{}{}{1+x^2}{(-1+x^2) \sqrt {x+x^2+x^3}} \, dx\) [752]
  3.8.53 \(\int \genfrac {}{}{}{}{a b c-(a+b+c) x^2+2 x^3}{\sqrt {x (-a+x) (-b+x) (-c+x)} (-a b c+(a b+a c+b c-d) x-(a+b+c) x^2+x^3)} \, dx\) [753]
  3.8.54 \(\int \genfrac {}{}{}{}{(-b+a x^3) \sqrt {b+a x^3}}{x^7} \, dx\) [754]
  3.8.55 \(\int \genfrac {}{}{}{}{\sqrt {b+a x^3} (2 b+a x^3)}{x^7} \, dx\) [755]
  3.8.56 \(\int \genfrac {}{}{}{}{3 a b c x-2 (a b+a c+b c) x^2+(a+b+c) x^3}{\sqrt {x (-a+x) (-b+x) (-c+x)} (a b c-(a b+a c+b c) x+(a+b+c) x^2+(-1+d) x^3)} \, dx\) [756]
  3.8.57 \(\int \genfrac {}{}{}{}{x (3 a b c-2 (a b+a c+b c) x+(a+b+c) x^2)}{\sqrt {x (-a+x) (-b+x) (-c+x)} (-a b c d+(a b+a c+b c) d x-(a+b+c) d x^2+(-1+d) x^3)} \, dx\) [757]
  3.8.58 \(\int \sqrt [4]{-x^2+x^4} \, dx\) [758]
  3.8.59 \(\int x^2 \sqrt [4]{x^2+x^4} \, dx\) [759]
  3.8.60 \(\int \genfrac {}{}{}{}{(-1+2 x^4) \sqrt {1+3 x^2+2 x^4}}{(1+2 x^2+2 x^4)^2} \, dx\) [760]
  3.8.61 \(\int \genfrac {}{}{}{}{\sqrt {-2+x^2-2 x^3+2 x^4} (2-x^3+2 x^4)}{(-1-x^3+x^4) (-2-x^2-2 x^3+2 x^4)} \, dx\) [761]
  3.8.62 \(\int \genfrac {}{}{}{}{-b+a x^2}{(b+a x^2) \sqrt {b^2+a^2 x^4}} \, dx\) [762]
  3.8.63 \(\int \genfrac {}{}{}{}{3 b+a x^4}{(-b-x^3+a x^4) \sqrt [4]{-b x+a x^5}} \, dx\) [763]
  3.8.64 \(\int \genfrac {}{}{}{}{(-1+x^3) \sqrt {-1+x^6}}{x} \, dx\) [764]
  3.8.65 \(\int \genfrac {}{}{}{}{x (3+4 x) \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx\) [765]
  3.8.66 \(\int \genfrac {}{}{}{}{x (3+4 x) \sqrt [3]{-1-2 x+x^3}}{-2-8 x-8 x^2+x^6} \, dx\) [766]
  3.8.67 \(\int \genfrac {}{}{}{}{(3+2 x) (1+x+x^3)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx\) [767]
  3.8.68 \(\int \genfrac {}{}{}{}{(3+2 x) (1+x+x^3)^{2/3}}{1+2 x+x^2+x^3+x^4+x^6} \, dx\) [768]
  3.8.69 \(\int \genfrac {}{}{}{}{(2+x^3) \sqrt [3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx\) [769]
  3.8.70 \(\int \genfrac {}{}{}{}{(2+x^3) \sqrt [3]{x+x^3-x^4}}{1+x^2-2 x^3+x^4-x^5+x^6} \, dx\) [770]
  3.8.71 \(\int \genfrac {}{}{}{}{(3+x^2) (1+x^2+x^3)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx\) [771]
  3.8.72 \(\int \genfrac {}{}{}{}{(3+x^2) (1+x^2+x^3)^{2/3}}{-1-2 x^2+x^3-x^4+x^5+x^6} \, dx\) [772]
  3.8.73 \(\int \genfrac {}{}{}{}{b+a x^8}{\sqrt [4]{b-a x^8} (-b+c x^4+a x^8)} \, dx\) [773]
  3.8.74 \(\int \genfrac {}{}{}{}{x \sqrt [3]{2-x^3+x^8} (-6+5 x^8)}{4+x^6+4 x^8+x^{16}} \, dx\) [774]
  3.8.75 \(\int \genfrac {}{}{}{}{a b+a c-b c-2 a x+x^2}{\sqrt {(-a+x) (-b+x) (-c+x)} (b c+a d-(b+c+d) x+x^2)} \, dx\) [775]
  3.8.76 \(\int \genfrac {}{}{}{}{a b+a c-b c-2 a x+x^2}{\sqrt {(-a+x) (-b+x) (-c+x)} (a+b c d-(1+b d+c d) x+d x^2)} \, dx\) [776]
  3.8.77 \(\int \genfrac {}{}{}{}{-1+k^2 x^2}{\sqrt {(1-x) x (1-k^2 x)} (1+k^2 x^2)} \, dx\) [777]
  3.8.78 \(\int \genfrac {}{}{}{}{a (a b+a c-3 b c)+(-2 a^2+a b+a c+3 b c) x+(a-2 b-2 c) x^2+x^3}{\sqrt {(-a+x) (-b+x) (-c+x)} (-a^3-b c d+(3 a^2+b d+c d) x-(3 a+d) x^2+x^3)} \, dx\) [778]
  3.8.79 \(\int \genfrac {}{}{}{}{(-2 c+a x^3) \sqrt {c+b x^2+a x^3}}{(c+a x^3)^2} \, dx\) [779]
  3.8.80 \(\int \genfrac {}{}{}{}{-b+a^2 x^2}{(b+2 a b x+a^2 x^2) \sqrt {b x+a^2 x^3}} \, dx\) [780]
  3.8.81 \(\int \genfrac {}{}{}{}{a (a b+a c-3 b c)+(-2 a^2+a b+a c+3 b c) x+(a-2 b-2 c) x^2+x^3}{\sqrt {(-a+x) (-b+x) (-c+x)} (-b c-a^3 d+(b+c+3 a^2 d) x-(1+3 a d) x^2+d x^3)} \, dx\) [781]
  3.8.82 \(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {1+x^4}}{x^5} \, dx\) [782]
  3.8.83 \(\int \genfrac {}{}{}{}{(-1+x^2) \sqrt {1+x^4}}{x^3} \, dx\) [783]
  3.8.84 \(\int \genfrac {}{}{}{}{(1+2 x^3) \sqrt {-1+x^6}}{x^7} \, dx\) [784]
  3.8.85 \(\int \genfrac {}{}{}{}{(1+2 x^3) \sqrt {-1+x^6}}{x^4} \, dx\) [785]
  3.8.86 \(\int \genfrac {}{}{}{}{b^6+a^6 x^6}{\sqrt {-b^2 x+a^2 x^3} (-b^6+c x^3+a^6 x^6)} \, dx\) [786]
  3.8.87 \(\int \genfrac {}{}{}{}{b^6+a^6 x^6}{\sqrt {-b^2 x+a^2 x^3} (-b^6+c x^3+a^6 x^6)} \, dx\) [787]
  3.8.88 \(\int \genfrac {}{}{}{}{x-3 x^5}{\sqrt {x+x^5} (1-a x^2+2 x^4+x^8)} \, dx\) [788]
  3.8.89 \(\int \genfrac {}{}{}{}{\sqrt {1-2 x^8} (-1+2 x^8) (1+2 x^8)}{x^7 (-1+x^4+2 x^8)} \, dx\) [789]
  3.8.90 \(\int \genfrac {}{}{}{}{-x+3 x^5}{\sqrt {x+x^5} (a-x^2+2 a x^4+a x^8)} \, dx\) [790]
  3.8.91 \(\int \genfrac {}{}{}{}{x^5 (7 b+9 a x^2)}{\sqrt [4]{b x^3+a x^5} (-2+b x^7+a x^9)} \, dx\) [791]
  3.8.92 \(\int \genfrac {}{}{}{}{x^2}{(1+x^2) \sqrt [5]{243-5265 x+47250 x^2-225810 x^3+615255 x^4-954733 x^5+820340 x^6-401440 x^7+112000 x^8-16640 x^9+1024 x^{10}}} \, dx\) [792]
  3.8.93 \(\int \genfrac {}{}{}{}{\sqrt [3]{1-2 x+x^2}}{2+x^2} \, dx\) [793]
  3.8.94 \(\int \genfrac {}{}{}{}{\sqrt [3]{1+2 x+x^2}}{3+x^2} \, dx\) [794]
  3.8.95 \(\int \genfrac {}{}{}{}{1}{(-1+x) \sqrt [4]{x+x^3}} \, dx\) [795]
  3.8.96 \(\int \genfrac {}{}{}{}{-1+x^4}{\sqrt {x+x^3} (1+x^4)} \, dx\) [796]
  3.8.97 \(\int \genfrac {}{}{}{}{1+x^3}{(-1+x^3) \sqrt {1+x^4}} \, dx\) [797]
  3.8.98 \(\int \genfrac {}{}{}{}{-1+x}{x \sqrt [4]{1+x^4}} \, dx\) [798]
  3.8.99 \(\int \genfrac {}{}{}{}{x^2}{(-b+a x^4)^{3/4}} \, dx\) [799]
  3.8.100 \(\int \genfrac {}{}{}{}{(6+x^4) \sqrt {-2 x+x^4+x^5}}{(-2+x^4) (-2-x^3+x^4)} \, dx\) [800]