3.15.1 \(\int \frac {x^3 (3-2 (1+k) x+k x^2)}{(-1+x) \sqrt [4]{(1-x) x (1-k x)} (-1+k x) (-d+d (1+k) x-d k x^2+x^3)} \, dx\)
  3.15.2 \(\int \frac {(2+x^3) (1+2 x^3)^{2/3}}{x^6 (1+x^3)} \, dx\)
  3.15.3 \(\int \frac {3 a b^2-2 b (2 a+b) x+(a+2 b) x^2}{\sqrt [4]{x (-a+x) (-b+x)^2} (-a b^2 d+b (2 a+b) d x-(a+2 b) d x^2+(-1+d) x^3)} \, dx\)
  3.15.4 \(\int \frac {(d+c x) \sqrt [4]{-b x^3+a x^4}}{x^2} \, dx\)
  3.15.5 \(\int \frac {(3+x^5) \sqrt [3]{-2+x^3+x^5}}{x^2 (-2+x^5)} \, dx\)
  3.15.6 \(\int \frac {(-3+x^5) (2+x^3+x^5)^{2/3}}{x^3 (2+x^5)} \, dx\)
  3.15.7 \(\int \frac {\sqrt [3]{-1+x^6} (1+x^6)}{x^9} \, dx\)
  3.15.8 \(\int \frac {1}{\sqrt [4]{-1-3 x^4-2 x^8+2 x^{12}+3 x^{16}+x^{20}}} \, dx\)
  3.15.9 \(\int \frac {1+x^2}{\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.15.10 \(\int \frac {x^2}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.15.11 \(\int x^2 \sqrt [3]{-x+x^3} \, dx\)
  3.15.12 \(\int x^6 \sqrt [3]{x+x^3} \, dx\)
  3.15.13 \(\int \frac {-3+2 x}{x \sqrt [4]{-1+x^4}} \, dx\)
  3.15.14 \(\int \frac {\sqrt [3]{-1+x^3-x^4} (-3+x^4)}{x^2 (1+x^4)} \, dx\)
  3.15.15 \(\int \frac {x^3 \sqrt {-x+x^4}}{-b+a x^3} \, dx\)
  3.15.16 \(\int \frac {1+2 x^4}{(-1+x^4) \sqrt [4]{x^2+x^4}} \, dx\)
  3.15.17 \(\int \frac {b+a x^2}{x^2 (-b+a x^2) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.15.18 \(\int x \sqrt [4]{b x^3+a x^4} \, dx\)
  3.15.19 \(\int \frac {-2 b+a x^3}{(b+x^2+a x^3) \sqrt [4]{b x^2+a x^5}} \, dx\)
  3.15.20 \(\int \frac {-b+a x^2}{(b+x+a x^2) \sqrt [4]{b x^3+a x^5}} \, dx\)
  3.15.21 \(\int \frac {x^{13}}{\sqrt [3]{-1+x^6}} \, dx\)
  3.15.22 \(\int x^9 \sqrt [3]{-1+x^6} \, dx\)
  3.15.23 \(\int x^7 (-1+x^6)^{2/3} \, dx\)
  3.15.24 \(\int \frac {x^{13}}{\sqrt [3]{1+x^6}} \, dx\)
  3.15.25 \(\int x^7 (1+x^6)^{2/3} \, dx\)
  3.15.26 \(\int \frac {\sqrt [3]{-1+2 x^3+x^8} (3+5 x^8)}{x^2 (-1+x^3+x^8)} \, dx\)
  3.15.27 \(\int \frac {\sqrt {b^2+a^2 x^2}}{\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.15.28 \(\int \frac {-2 a+b+x}{\sqrt [4]{(-a+x) (-b+x)^2} (b^2+a d-(2 b+d) x+x^2)} \, dx\)
  3.15.29 \(\int x \sqrt [3]{x^2+x^3} \, dx\)
  3.15.30 \(\int \frac {-((2 a-3 b) b)+2 (a-2 b) x+x^2}{\sqrt [4]{(-a+x) (-b+x)^2} (-a^3-b^2 d+(3 a^2+2 b d) x-(3 a+d) x^2+x^3)} \, dx\)
  3.15.31 \(\int \frac {(-1+x)^3 (-1+2 (-1+k) x+k x^2)}{x \sqrt [4]{(1-x) x (1-k x)} (-1+k x) (-1+(3+d) x-(3+d k) x^2+x^3)} \, dx\)
  3.15.32 \(\int \frac {b+a x^2}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
  3.15.33 \(\int \frac {(a^2-2 a x+x^2) (-((2 a-3 b) b)+2 (a-2 b) x+x^2)}{((-a+x) (-b+x)^2)^{3/4} (-b^2-a^3 d+(2 b+3 a^2 d) x-(1+3 a d) x^2+d x^3)} \, dx\)
  3.15.34 \(\int \frac {-b+a x^2}{x^2 (b+a x^2) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.15.35 \(\int \frac {(-b+x) (-6 a+b+5 x)}{\sqrt [4]{(-a+x) (-b+x)^2} (b^6+a d-(6 b^5+d) x+15 b^4 x^2-20 b^3 x^3+15 b^2 x^4-6 b x^5+x^6)} \, dx\)
  3.15.36 \(\int \frac {(-6 a+b+5 x) (-b^5+5 b^4 x-10 b^3 x^2+10 b^2 x^3-5 b x^4+x^5)}{((-a+x) (-b+x)^2)^{3/4} (a+b^6 d-(1+6 b^5 d) x+15 b^4 d x^2-20 b^3 d x^3+15 b^2 d x^4-6 b d x^5+d x^6)} \, dx\)
  3.15.37 \(\int \frac {x^6 (4+x^3)}{(1+x^3)^{3/4} (-1-2 x^3-x^6+x^8)} \, dx\)
  3.15.38 \(\int x^{10} \sqrt [3]{-1+x^3} \, dx\)
  3.15.39 \(\int \frac {x}{(-1+x) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.15.40 \(\int \frac {1+x}{(-1+x) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.15.41 \(\int \frac {-2 b+a x}{(-b+a x+x^2) \sqrt [4]{-b x^2+a x^3}} \, dx\)
  3.15.42 \(\int \frac {-1+x}{(1+x+x^2) \sqrt [4]{1+x^4}} \, dx\)
  3.15.43 \(\int \frac {x^2 \sqrt [4]{x^3+x^4}}{-1+x} \, dx\)
  3.15.44 \(\int \frac {(-b+a x^3) (-b+2 a x^3)}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.15.45 \(\int \frac {-b+a x^4+x^8}{x^8 (-b+a x^4) \sqrt [4]{b+a x^4}} \, dx\)
  3.15.46 \(\int \frac {1+x^4}{x^4 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.15.47 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^2 \sqrt {b^2+a x^2}} \, dx\)
  3.15.48 \(\int \frac {2+x^2}{x (2-2 x+x^2) \sqrt [3]{1-x+x^2}} \, dx\)
  3.15.49 \(\int \frac {-1+x}{x^{10} \sqrt [3]{1+x^3}} \, dx\)
  3.15.50 \(\int \frac {1}{x \sqrt [3]{b+a x^3}} \, dx\)
  3.15.51 \(\int \frac {(-1-2 (-1+k) x+k x^2) (-1+3 k x-3 k^2 x^2+k^3 x^3)}{(-1+x) x \sqrt [4]{(1-x) x (1-k x)} (-1+(d+3 k) x-(d+3 k^2) x^2+k^3 x^3)} \, dx\)
  3.15.52 \(\int \frac {(3+x^4) (-1-x^3+x^4)^{2/3}}{x^3 (-1+x^4)} \, dx\)
  3.15.53 \(\int \frac {2-x+x^2}{\sqrt [3]{-1+x^2} (3+4 x+x^2)} \, dx\)
  3.15.54 \(\int \frac {x (-1+k x) (-1+2 (-1+k) x+k x^2)}{(-1+x) ((1-x) x (1-k x))^{3/4} (-d+(1+3 d) x-(3 d+k) x^2+d x^3)} \, dx\)
  3.15.55 \(\int \frac {(-1+x) x (-1-2 (-1+k) x+k x^2)}{((1-x) x (1-k x))^{3/4} (-1+k x) (-d+(1+3 d k) x-(1+3 d k^2) x^2+d k^3 x^3)} \, dx\)
  3.15.56 \(\int \frac {2 b+a x^3}{(-b+x^2+a x^3) \sqrt [4]{-b x^2+a x^5}} \, dx\)
  3.15.57 \(\int \frac {b+a x^2}{(-b+x+a x^2) \sqrt [4]{-b x^3+a x^5}} \, dx\)
  3.15.58 \(\int \frac {b+a x^4}{(-b+x^2+a x^4) \sqrt [4]{-b x^2+a x^6}} \, dx\)
  3.15.59 \(\int \frac {b+2 a x^3}{(-b+x+a x^3) \sqrt [4]{-b x^3+a x^6}} \, dx\)
  3.15.60 \(\int x^4 \sqrt [3]{-x+x^3} \, dx\)
  3.15.61 \(\int \frac {x}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
  3.15.62 \(\int \frac {\sqrt {b x+a x^3}}{-b^2+a^2 x^4} \, dx\)
  3.15.63 \(\int \frac {x^{19}}{\sqrt [3]{-1+x^6}} \, dx\)
  3.15.64 \(\int x^{15} \sqrt [3]{-1+x^6} \, dx\)
  3.15.65 \(\int \frac {x^{19}}{\sqrt [3]{1+x^6}} \, dx\)
  3.15.66 \(\int x^{15} \sqrt [3]{1+x^6} \, dx\)
  3.15.67 \(\int \frac {-b-a x^3+x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.15.68 \(\int \frac {-3-x^4+3 x^6}{(1-x^4+x^6) \sqrt [3]{1-x^3-x^4+x^6}} \, dx\)
  3.15.69 \(\int \frac {-b+a x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.15.70 \(\int \frac {b+a x^6}{x^6 \sqrt [4]{-b x+a x^4}} \, dx\)
  3.15.71 \(\int \frac {\sqrt [4]{x^2+x^4} (-1-x^4+x^8)}{-1+x^4} \, dx\)
  3.15.72 \(\int \frac {\sqrt {c x^2-x \sqrt {-b x+a x^2}}}{x^3 \sqrt {-b x+a x^2}} \, dx\)
  3.15.73 \(\int \frac {b+x^3}{\sqrt [3]{a+x^3}} \, dx\)
  3.15.74 \(\int \frac {b+a x^2}{\sqrt [3]{x+x^3}} \, dx\)
  3.15.75 \(\int \sqrt [3]{-x^2+x^3} \, dx\)
  3.15.76 \(\int x^2 \sqrt [3]{x^2+x^3} \, dx\)
  3.15.77 \(\int \frac {(-3+x^4) (1-x^3+x^4) (1+x^3+x^4)^{2/3}}{x^6 (1+x^4)} \, dx\)
  3.15.78 \(\int \frac {1+x^2}{(-1+x^2) \sqrt [3]{x+x^5}} \, dx\)
  3.15.79 \(\int \frac {(-1+x^2) \sqrt [4]{x^2+x^6}}{x^2 (1+x^2)} \, dx\)
  3.15.80 \(\int \frac {(-1+x^2) \sqrt [4]{x^2+x^6}}{x^2 (1+x^2)} \, dx\)
  3.15.81 \(\int \frac {(-1+x^3)^{2/3} (1-5 x^3+4 x^6)}{x^6 (-1+2 x^3)^2} \, dx\)
  3.15.82 \(\int \frac {\sqrt {1+x} \sqrt {1+\sqrt {1+x}}}{x-\sqrt {1+x}} \, dx\)
  3.15.83 \(\int \frac {\sqrt {b+a x}}{\sqrt {a b x+\sqrt {b+a x}}} \, dx\)
  3.15.84 \(\int \frac {\sqrt {b+a^2 x^4}}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\)
  3.15.85 \(\int \frac {-a b+(-a+2 b) x}{\sqrt [4]{x (-a+x) (-b+x)^2} (-b^2+(2 b-a d) x+(-1+d) x^2)} \, dx\)
  3.15.86 \(\int x^{13} \sqrt [3]{-1+x^3} \, dx\)
  3.15.87 \(\int \frac {a b^2-2 (2 a-b) b x+(3 a-2 b) x^2}{\sqrt [4]{x (-a+x) (-b+x)^2} (a^3+(-3 a^2+b^2 d) x+(3 a-2 b d) x^2+(-1+d) x^3)} \, dx\)
  3.15.88 \(\int \frac {(1+x^6) (-1-x^3+x^6)^{2/3}}{x^3 (-1+x^6)} \, dx\)
  3.15.89 \(\int \frac {(4+x^6) \sqrt [4]{-2-x^4+x^6}}{x^2 (-2+x^6)} \, dx\)
  3.15.90 \(\int \sqrt [4]{b x^7+a x^8} \, dx\)
  3.15.91 \(\int \frac {-1+x^{10}}{\sqrt {1+x^4} (1+x^{10})} \, dx\)
  3.15.92 \(\int \frac {1+x^{10}}{\sqrt {1+x^4} (-1+x^{10})} \, dx\)
  3.15.93 \(\int \frac {1+x^{16}}{\sqrt {1+x^4} (-1+x^{16})} \, dx\)
  3.15.94 \(\int \frac {\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{1-\sqrt {b+a x}} \, dx\)
  3.15.95 \(\int x \sqrt {-1+x^2} \sqrt {x^2+x \sqrt {-1+x^2}} \, dx\)
  3.15.96 \(\int \frac {(-q+p x^2) \sqrt {q^2+p^2 x^4} (b x^3+a (q+p x^2)^3)}{x^6} \, dx\)
  3.15.97 \(\int \frac {(-1+x^2) \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4}} \, dx\)
  3.15.98 \(\int \frac {x \sqrt {1+x}}{x+\sqrt {1+\sqrt {1+x}}} \, dx\)
  3.15.99 \(\int \frac {b+a x^8}{x^6 (-b+a x^4) (b+a x^4)^{3/4}} \, dx\)
  3.15.100 \(\int \frac {-a b-a c+3 b c+2 (a-b-c) x+x^2}{\sqrt [4]{(-a+x) (-b+x) (-c+x)} (-a^3-b c d+(3 a^2+b d+c d) x-(3 a+d) x^2+x^3)} \, dx\)