3.17.1 \(\int \frac {(2+x^6) (1-2 x^6+x^8+x^{12})}{x^8 \sqrt [4]{-1+x^6} (-1+x^4+x^6)} \, dx\)
  3.17.2 \(\int \frac {\sqrt {x+x^2}}{x \sqrt {x^2+x \sqrt {x+x^2}}} \, dx\)
  3.17.3 \(\int \frac {\sqrt {x^2+x \sqrt {x+x^2}}}{\sqrt {x+x^2}} \, dx\)
  3.17.4 \(\int \frac {1}{\sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.17.5 \(\int (b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}} \, dx\)
  3.17.6 \(\int \frac {1}{(1-3 x) \sqrt [3]{-x+x^3}} \, dx\)
  3.17.7 \(\int \frac {1}{(1+3 x) \sqrt [3]{-x+x^3}} \, dx\)
  3.17.8 \(\int \frac {x}{\sqrt [3]{-x^2+x^3}} \, dx\)
  3.17.9 \(\int \frac {(1-x^3)^{2/3} (-1+x^3)}{x^6 (-1+2 x^3)} \, dx\)
  3.17.10 \(\int \frac {2 b+a x}{(b+a x+x^2) \sqrt [4]{b x^2+a x^3}} \, dx\)
  3.17.11 \(\int \frac {x^3 \sqrt {x+x^4}}{-b+a x^3} \, dx\)
  3.17.12 \(\int x^9 \sqrt [3]{1+x^6} \, dx\)
  3.17.13 \(\int \frac {(-1+x^3)^{2/3} (2+x^3)}{x^6 (4+x^6)} \, dx\)
  3.17.14 \(\int \frac {(-1+x^3)^{2/3} (2+x^3)}{x^6 (4+x^6)} \, dx\)
  3.17.15 \(\int \frac {b-a x^3+x^6}{x^6 \sqrt [4]{b x+a x^4}} \, dx\)
  3.17.16 \(\int \frac {-b+a x^6}{x^6 \sqrt [4]{b x+a x^4}} \, dx\)
  3.17.17 \(\int \frac {b+a x^6}{x^6 \sqrt [4]{b x+a x^4}} \, dx\)
  3.17.18 \(\int \frac {-3 b+2 a x^5}{(2 b+x^3+2 a x^5) \sqrt [4]{b x+a x^6}} \, dx\)
  3.17.19 \(\int \frac {1}{\sqrt [3]{b^2 x^2+a^3 x^3} (2 b+a^6 x^6)} \, dx\)
  3.17.20 \(\int \frac {1}{\sqrt [3]{b^2 x^2+a^3 x^3} (2 b+a^6 x^6)} \, dx\)
  3.17.21 \(\int \frac {(-1+x^4) (1+x^2+3 x^4+x^6+x^8)}{(1+x^2+x^4)^{3/2} (1+3 x^2+5 x^4+3 x^6+x^8)} \, dx\)
  3.17.22 \(\int \frac {-b+a x^8}{\sqrt [4]{b+a x^4} (b+a x^8)} \, dx\)
  3.17.23 \(\int \frac {-b+a x^8}{\sqrt [4]{b+a x^4} (b+a x^8)} \, dx\)
  3.17.24 \(\int \frac {(-3+2 x+2 x^5) \sqrt {x-x^2+x^6}}{1-2 x+x^2-x^3+x^4+2 x^5-3 x^6-x^8+x^{10}} \, dx\)
  3.17.25 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{x^2 \sqrt {1+x}} \, dx\)
  3.17.26 \(\int \frac {\sqrt {x+\sqrt {1+x}}}{x \sqrt {1+x}} \, dx\)
  3.17.27 \(\int \frac {\sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x}} \, dx\)
  3.17.28 \(\int \frac {1-a x+b \sqrt {a+b x}}{\sqrt {a+b x} (x+a b \sqrt {a+b x})} \, dx\)
  3.17.29 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{x^2} \, dx\)
  3.17.30 \(\int \frac {1}{\sqrt {-b x+a^2 x^2} (a x^2+x \sqrt {-b x+a^2 x^2})^{3/2}} \, dx\)
  3.17.31 \(\int \frac {1}{1+\sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.17.32 \(\int \frac {-2+x}{(2+x^2) \sqrt [3]{-1+x+2 x^2}} \, dx\)
  3.17.33 \(\int \frac {(-a+x) (-b+x) (-2 a b+(a+b) x)}{(x^2 (-a+x) (-b+x))^{3/4} (-a b+(a+b) x+(-1+d) x^2)} \, dx\)
  3.17.34 \(\int \frac {1-x+x^2}{(-2+2 x+x^2) \sqrt {1+x^3}} \, dx\)
  3.17.35 \(\int \frac {-1+x}{x \sqrt [3]{-x^2+x^3}} \, dx\)
  3.17.36 \(\int \frac {1+x}{x \sqrt [3]{-x^2+x^3}} \, dx\)
  3.17.37 \(\int \frac {x^2}{\sqrt [3]{x^2+x^3}} \, dx\)
  3.17.38 \(\int \frac {(a-3 b+2 x) (-a^3+3 a^2 x-3 a x^2+x^3)}{(-b+x) \sqrt [4]{(-a+x) (-b+x)} (-a^3+b d-(-3 a^2+d) x-3 a x^2+x^3)} \, dx\)
  3.17.39 \(\int \frac {x^3 (3-2 (1+k) x+k x^2)}{(-1+x) \sqrt [4]{(1-x) x (1-k x)} (-1+k x) (-d+d (1+k) x-d k x^2+x^3)} \, dx\)
  3.17.40 \(\int \frac {(2+x^3) (1+2 x^3)^{2/3}}{x^6 (1+x^3)} \, dx\)
  3.17.41 \(\int \frac {3 a b^2-2 b (2 a+b) x+(a+2 b) x^2}{\sqrt [4]{x (-a+x) (-b+x)^2} (-a b^2 d+b (2 a+b) d x-(a+2 b) d x^2+(-1+d) x^3)} \, dx\)
  3.17.42 \(\int \frac {(d+c x) \sqrt [4]{-b x^3+a x^4}}{x^2} \, dx\)
  3.17.43 \(\int \frac {(3+x^5) \sqrt [3]{-2+x^3+x^5}}{x^2 (-2+x^5)} \, dx\)
  3.17.44 \(\int \frac {(-3+x^5) (2+x^3+x^5)^{2/3}}{x^3 (2+x^5)} \, dx\)
  3.17.45 \(\int \frac {\sqrt [3]{-1+x^6} (1+x^6)}{x^9} \, dx\)
  3.17.46 \(\int \frac {1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-2 b+a^6 x^6)} \, dx\)
  3.17.47 \(\int \frac {1}{\sqrt [3]{b^2 x^2+a^3 x^3} (-2 b+a^6 x^6)} \, dx\)
  3.17.48 \(\int \frac {1}{\sqrt [4]{-1-3 x^4-2 x^8+2 x^{12}+3 x^{16}+x^{20}}} \, dx\)
  3.17.49 \(\int \frac {1+x^2}{\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\)
  3.17.50 \(\int \frac {x^2}{\sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.17.51 \(\int x^2 \sqrt [3]{-x+x^3} \, dx\)
  3.17.52 \(\int x^6 \sqrt [3]{x+x^3} \, dx\)
  3.17.53 \(\int \frac {-3+2 x}{x \sqrt [4]{-1+x^4}} \, dx\)
  3.17.54 \(\int \frac {\sqrt [3]{-1+x^3-x^4} (-3+x^4)}{x^2 (1+x^4)} \, dx\)
  3.17.55 \(\int \frac {x^3 \sqrt {-x+x^4}}{-b+a x^3} \, dx\)
  3.17.56 \(\int \frac {1+2 x^4}{(-1+x^4) \sqrt [4]{x^2+x^4}} \, dx\)
  3.17.57 \(\int \frac {b+a x^2}{x^2 (-b+a x^2) \sqrt [4]{b x^2+a x^4}} \, dx\)
  3.17.58 \(\int x \sqrt [4]{b x^3+a x^4} \, dx\)
  3.17.59 \(\int \frac {-2 b+a x^3}{(b+x^2+a x^3) \sqrt [4]{b x^2+a x^5}} \, dx\)
  3.17.60 \(\int \frac {-b+a x^2}{(b+x+a x^2) \sqrt [4]{b x^3+a x^5}} \, dx\)
  3.17.61 \(\int \frac {x^{13}}{\sqrt [3]{-1+x^6}} \, dx\)
  3.17.62 \(\int x^9 \sqrt [3]{-1+x^6} \, dx\)
  3.17.63 \(\int x^7 (-1+x^6)^{2/3} \, dx\)
  3.17.64 \(\int \frac {x^{13}}{\sqrt [3]{1+x^6}} \, dx\)
  3.17.65 \(\int x^7 (1+x^6)^{2/3} \, dx\)
  3.17.66 \(\int \frac {(1+x^3)^{2/3} (4+x^3)}{x^6 (8-4 x^3+x^6)} \, dx\)
  3.17.67 \(\int \frac {(1+x^3)^{2/3} (4+x^3)}{x^6 (8-4 x^3+x^6)} \, dx\)
  3.17.68 \(\int \frac {(1+x^3)^{2/3} (2+x^3) (4+3 x^3)}{x^6 (4+2 x^3+x^6)} \, dx\)
  3.17.69 \(\int \frac {(1+x^3)^{2/3} (2+x^3) (4+3 x^3)}{x^6 (4+2 x^3+x^6)} \, dx\)
  3.17.70 \(\int \frac {(-1+x^3)^{2/3} (4+x^6)}{x^6 (4+2 x^3+x^6)} \, dx\)
  3.17.71 \(\int \frac {(-1+x^3)^{2/3} (4+x^6)}{x^6 (4+2 x^3+x^6)} \, dx\)
  3.17.72 \(\int \frac {(-1+x^3)^{2/3} (1-x^3+x^6)}{x^6 (-2-x^3+2 x^6)} \, dx\)
  3.17.73 \(\int \frac {(-1+x^3)^{2/3} (1-x^3+x^6)}{x^6 (-2-x^3+2 x^6)} \, dx\)
  3.17.74 \(\int \frac {(1+x^3)^{2/3} (4+6 x^3+3 x^6)}{x^6 (8+6 x^3+3 x^6)} \, dx\)
  3.17.75 \(\int \frac {(1+x^3)^{2/3} (4+6 x^3+3 x^6)}{x^6 (8+6 x^3+3 x^6)} \, dx\)
  3.17.76 \(\int \frac {\sqrt [3]{-1+2 x^3+x^8} (3+5 x^8)}{x^2 (-1+x^3+x^8)} \, dx\)
  3.17.77 \(\int \frac {(-1+x^4) \sqrt {1+\sqrt {1+x^2}}}{1+x^4} \, dx\)
  3.17.78 \(\int \frac {(-1+x^4) \sqrt {1+\sqrt {1+x^2}}}{1+x^4} \, dx\)
  3.17.79 \(\int \frac {\sqrt {b^2+a^2 x^2}}{\sqrt {a x+\sqrt {b^2+a^2 x^2}}} \, dx\)
  3.17.80 \(\int \frac {-2 a+b+x}{\sqrt [4]{(-a+x) (-b+x)^2} (b^2+a d-(2 b+d) x+x^2)} \, dx\)
  3.17.81 \(\int x \sqrt [3]{x^2+x^3} \, dx\)
  3.17.82 \(\int \frac {-((2 a-3 b) b)+2 (a-2 b) x+x^2}{\sqrt [4]{(-a+x) (-b+x)^2} (-a^3-b^2 d+(3 a^2+2 b d) x-(3 a+d) x^2+x^3)} \, dx\)
  3.17.83 \(\int \frac {(-1+x)^3 (-1+2 (-1+k) x+k x^2)}{x \sqrt [4]{(1-x) x (1-k x)} (-1+k x) (-1+(3+d) x-(3+d k) x^2+x^3)} \, dx\)
  3.17.84 \(\int \frac {b+a x^2}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
  3.17.85 \(\int \frac {(a^2-2 a x+x^2) (-((2 a-3 b) b)+2 (a-2 b) x+x^2)}{((-a+x) (-b+x)^2)^{3/4} (-b^2-a^3 d+(2 b+3 a^2 d) x-(1+3 a d) x^2+d x^3)} \, dx\)
  3.17.86 \(\int \frac {(-1+x^3) \sqrt [4]{x^3+x^4}}{1+x^3} \, dx\)
  3.17.87 \(\int \frac {-b+a x^2}{x^2 (b+a x^2) \sqrt [4]{-b x^2+a x^4}} \, dx\)
  3.17.88 \(\int \frac {(-b+x) (-6 a+b+5 x)}{\sqrt [4]{(-a+x) (-b+x)^2} (b^6+a d-(6 b^5+d) x+15 b^4 x^2-20 b^3 x^3+15 b^2 x^4-6 b x^5+x^6)} \, dx\)
  3.17.89 \(\int \frac {(-6 a+b+5 x) (-b^5+5 b^4 x-10 b^3 x^2+10 b^2 x^3-5 b x^4+x^5)}{((-a+x) (-b+x)^2)^{3/4} (a+b^6 d-(1+6 b^5 d) x+15 b^4 d x^2-20 b^3 d x^3+15 b^2 d x^4-6 b d x^5+d x^6)} \, dx\)
  3.17.90 \(\int \frac {x^4 \sqrt [4]{x^2+x^4}}{-1+x^8} \, dx\)
  3.17.91 \(\int \frac {x^4 \sqrt [4]{x^2+x^4}}{-1+x^8} \, dx\)
  3.17.92 \(\int \frac {x^4}{\sqrt [4]{x^2+x^4} (1+x^4+x^8)} \, dx\)
  3.17.93 \(\int \frac {x^4}{\sqrt [4]{x^2+x^4} (1+x^4+x^8)} \, dx\)
  3.17.94 \(\int \frac {x^6 (4+x^3)}{(1+x^3)^{3/4} (-1-2 x^3-x^6+x^8)} \, dx\)
  3.17.95 \(\int x^{10} \sqrt [3]{-1+x^3} \, dx\)
  3.17.96 \(\int \frac {x}{(-1+x) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.17.97 \(\int \frac {1+x}{(-1+x) \sqrt [3]{-x^2+x^3}} \, dx\)
  3.17.98 \(\int \frac {-2 b+a x}{(-b+a x+x^2) \sqrt [4]{-b x^2+a x^3}} \, dx\)
  3.17.99 \(\int \frac {(1+x^2) \sqrt [3]{-x+2 x^3}}{x^2 (1+x^4)} \, dx\)
  3.17.100 \(\int \frac {-1+x}{(1+x+x^2) \sqrt [4]{1+x^4}} \, dx\)