3.21.1 \(\int \frac {b+a x^4}{\sqrt [4]{-b+a x^4} (b+3 a x^4)} \, dx\)
  3.21.2 \(\int \frac {(2+x^6) (-1-x^4+x^6)}{\sqrt [4]{1-x^4-x^6} (-1+x^6)^2} \, dx\)
  3.21.3 \(\int \frac {(-2 b+a x^6) (b-c x^4+a x^6)}{x^2 (b+a x^6)^{3/4} (b+c x^4+a x^6)} \, dx\)
  3.21.4 \(\int \frac {\sqrt [4]{1+2 x^4} (-1-x^4+2 x^8)}{x^6 (2+x^4)} \, dx\)
  3.21.5 \(\int \frac {-b^8+2 a^4 x^4}{\sqrt [4]{-b^8+a^4 x^4} (-b^8-c x^4+a^8 x^8)} \, dx\)
  3.21.6 \(\int \frac {-1+x^2}{(1+x^2) \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.21.7 \(\int \frac {(1+x^2) \sqrt [3]{x+2 x^3}}{x^4 (-1+x^2)} \, dx\)
  3.21.8 \(\int \frac {(-b+a^3 x^3) \sqrt [3]{b+a^3 x^3}}{x^5} \, dx\)
  3.21.9 \(\int \frac {-3 b+a x^2}{\sqrt [4]{3 b-2 a x^2} (3 b-2 a x^2+3 x^4)} \, dx\)
  3.21.10 \(\int \frac {(-4 b+a x^5) (b-c x^4+a x^5)}{x^2 (b+a x^5)^{3/4} (b+c x^4+a x^5)} \, dx\)
  3.21.11 \(\int \frac {(-1+x^3) (1+x^6)^{2/3} (1-x^3+x^6)}{x^6 (1+x^3)} \, dx\)
  3.21.12 \(\int \frac {(-b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}}}{(b^2+a x^2)^2} \, dx\)
  3.21.13 \(\int \frac {(2+x^3) (1+2 x^3)^{2/3}}{x^6 (-1+x^3)} \, dx\)
  3.21.14 \(\int \frac {(-4+x^2) \sqrt [4]{2-x^2-2 x^4}}{x^2 (-2+x^2)} \, dx\)
  3.21.15 \(\int \frac {1}{(1+x) (-2+2 x+x^2-x^4)^{3/2}} \, dx\)
  3.21.16 \(\int \frac {(-3+2 x^4) (1+2 x^4)^{2/3}}{x^3 (2-x^3+4 x^4)} \, dx\)
  3.21.17 \(\int \frac {-b+a x^3}{x^6 (b+a x^3) \sqrt [4]{-b x+a x^4}} \, dx\)
  3.21.18 \(\int \frac {(-1+x^3)^{2/3} (4+4 x^3+x^6)}{x^9 (1+x^3)} \, dx\)
  3.21.19 \(\int \frac {(1+x^3)^{2/3} (-1-2 x^3+2 x^6)}{x^9 (-1+x^3)} \, dx\)
  3.21.20 \(\int \frac {1}{\sqrt [4]{-b^4+a^4 x^4} (-b^8-c x^4+a^8 x^8)} \, dx\)
  3.21.21 \(\int \frac {1}{\sqrt [4]{-b^4+a^4 x^4} (-b^8-c x^4+a^8 x^8)} \, dx\)
  3.21.22 \(\int \frac {x-\sqrt {1+x^2}}{\sqrt {1+\sqrt {1+x^2}}} \, dx\)
  3.21.23 \(\int \frac {(-4+x^3) (-2+x^3) (-1+x^3)^{2/3}}{x^9 (-2+3 x^3)} \, dx\)
  3.21.24 \(\int \frac {1}{(-1+x) (-2 x^2-3 x^3+x^4)^{3/2}} \, dx\)
  3.21.25 \(\int \frac {1}{(b+2 a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.21.26 \(\int \frac {\sqrt [3]{1-x^7} (-2+x^3+2 x^7) (3+4 x^7)}{x^2 (-1+x^7) (-4+x^3+4 x^7)} \, dx\)
  3.21.27 \(\int \frac {(-1+x^2) (1+x^2)^3 \sqrt {1+2 x^2+x^4}}{(1+x^4) (1-x^2+x^4-x^6+x^8)} \, dx\)
  3.21.28 \(\int \frac {1}{x^2 \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.21.29 \(\int \frac {\sqrt [4]{-b+a x^3}}{x} \, dx\)
  3.21.30 \(\int \frac {(-b+a x^3)^{3/4}}{x} \, dx\)
  3.21.31 \(\int \frac {(-1+x^4)^{2/3} (3+x^4) (-1-x^3+x^4)}{x^6 (-2-x^3+2 x^4)} \, dx\)
  3.21.32 \(\int \frac {(-b+a x^4)^{3/4}}{x} \, dx\)
  3.21.33 \(\int \frac {-3 a b^3+2 b^2 (3 a+b) x-3 b (a+b) x^2+x^4}{\sqrt [4]{x (-a+x) (-b+x)^3} (a b^3 d-b^2 (3 a+b) d x+3 b (a+b) d x^2-(1+a d+3 b d) x^3+d x^4)} \, dx\)
  3.21.34 \(\int \frac {(-b+a x^5)^{3/4}}{x} \, dx\)
  3.21.35 \(\int \frac {(-1+x^3)^{2/3} (4+x^3+x^6)}{x^9 (-2+x^3)} \, dx\)
  3.21.36 \(\int \frac {-3-4 x+3 x^6}{(1+2 x+x^6) \sqrt [3]{1+2 x+2 x^3+x^6}} \, dx\)
  3.21.37 \(\int \frac {(-b+a x^6)^{3/4}}{x} \, dx\)
  3.21.38 \(\int \frac {b+a x^6}{\sqrt [3]{-x+x^3}} \, dx\)
  3.21.39 \(\int \frac {\sqrt [4]{a x^2+b x \sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}}}{\sqrt {-\frac {a}{b^2}+\frac {a^2 x^2}{b^2}}} \, dx\)
  3.21.40 \(\int \frac {1}{\sqrt [3]{x^2 (-a+x)} (a+(-1+d) x)} \, dx\)
  3.21.41 \(\int \frac {(2+x-x^3-x^4)^{2/3} (6+2 x+x^4) (-2-x+x^3+x^4)}{x^6 (-2-x+2 x^3+x^4)} \, dx\)
  3.21.42 \(\int \frac {(-3+x^4) (1+x^4)^{2/3} (2+x^3+2 x^4)}{x^6 (4-x^3+4 x^4)} \, dx\)
  3.21.43 \(\int \frac {(-1-x^4+2 x^6) \sqrt [3]{x-x^5+x^7}}{(1+x^2-x^4+x^6)^2} \, dx\)
  3.21.44 \(\int \frac {x^4 (-4 b+a x^3)}{\sqrt [4]{-b+a x^3} (-b^2+2 a b x^3-a^2 x^6+x^8)} \, dx\)
  3.21.45 \(\int \frac {\sqrt {-1+x^2} \sqrt {x^2+x \sqrt {-1+x^2}}}{1+x^2} \, dx\)
  3.21.46 \(\int \frac {x}{(x^2 (-a+x))^{2/3} (a+(-1+d) x)} \, dx\)
  3.21.47 \(\int \frac {2+x+x^2}{(3+2 x+x^2) \sqrt [3]{x^2+x^3}} \, dx\)
  3.21.48 \(\int \frac {2+x+x^2}{(3+2 x+x^2) \sqrt [3]{x^2+x^3}} \, dx\)
  3.21.49 \(\int \frac {b-c x+a x^2}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
  3.21.50 \(\int \frac {b+c x+a x^2}{(-b+a x^2) \sqrt {b x+a x^3}} \, dx\)
  3.21.51 \(\int \frac {(1+x) \sqrt [4]{-x^3+x^4}}{1-x+x^2} \, dx\)
  3.21.52 \(\int \frac {(1+x) \sqrt [4]{-x^3+x^4}}{1-x+x^2} \, dx\)
  3.21.53 \(\int \frac {\sqrt [3]{b-a x^6} (b+a x^6)}{x^2 (-b+c x^3+a x^6)} \, dx\)
  3.21.54 \(\int \frac {x^2 (4+7 x^3)}{\sqrt [3]{x+x^4} (-1+x^4+x^7)} \, dx\)
  3.21.55 \(\int \frac {2 d+c x^4}{\sqrt [4]{-b+a x^4} (-2 f+e x^8)} \, dx\)
  3.21.56 \(\int \frac {\sqrt {1+x} (1+x^2)}{(-1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\)
  3.21.57 \(\int \frac {\sqrt {1+x} (1+x^2)}{(-1+x^2) \sqrt {x+\sqrt {1+x}}} \, dx\)
  3.21.58 \(\int \frac {\sqrt {x-\sqrt {-1+x^2}}}{x^2} \, dx\)
  3.21.59 \(\int \frac {(a x+\sqrt {-b x+a^2 x^2})^{3/4}}{\sqrt {-b x+a^2 x^2}} \, dx\)
  3.21.60 \(\int \frac {(1+x) \sqrt [4]{x^3+x^4}}{x (-1+x^3)} \, dx\)
  3.21.61 \(\int \frac {\sqrt [4]{-b x^3+a x^4} (-d+c x^4)}{x^4} \, dx\)
  3.21.62 \(\int \frac {(1+x^3)^{2/3} (2+x^3)}{x^6 (4+x^3)} \, dx\)
  3.21.63 \(\int \frac {(-1+x^3) (1+3 x^3)^{2/3}}{x^6 (1+x^3)} \, dx\)
  3.21.64 \(\int \frac {3-8 x+8 x^2-12 x^4}{x \sqrt [3]{\frac {1-2 x^2}{1+2 x^2}} (1+2 x^2) (3-7 x+7 x^2-6 x^3+2 x^4)} \, dx\)
  3.21.65 \(\int \frac {x^2}{\sqrt {b x+a x^3} (-b^2+a^2 x^4)} \, dx\)
  3.21.66 \(\int \frac {b+a x^6}{x^6 (-b+a x^3) \sqrt [4]{b x+a x^4}} \, dx\)
  3.21.67 \(\int \frac {\sqrt [3]{-1+2 x^3+x^8} (3+5 x^8)}{x^2 (-1+x^8)} \, dx\)
  3.21.68 \(\int \frac {\sqrt {b^2+a x^2}}{\sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.21.69 \(\int \frac {\sqrt {b+\sqrt {b^2+a x^2}}}{(b^2+a x^2)^3} \, dx\)
  3.21.70 \(\int \frac {(-b+a x^2)^{3/4}}{x^3} \, dx\)
  3.21.71 \(\int \frac {(1+x^3) (-1+2 x^3)^{2/3}}{x^6 (1+2 x^3)} \, dx\)
  3.21.72 \(\int \frac {(1-x^3)^{2/3} (-1+4 x^3)}{x^6 (-2+3 x^3)} \, dx\)
  3.21.73 \(\int \frac {\sqrt [4]{-b+a x^3}}{x^4} \, dx\)
  3.21.74 \(\int \frac {(-b+a x^3)^{3/4}}{x^4} \, dx\)
  3.21.75 \(\int \frac {(-a+x) (-3 a b+(a+2 b) x) (-b^3+3 b^2 x-3 b x^2+x^3)}{x (x (-a+x) (-b+x)^2)^{3/4} (a b^2-b (2 a+b) x+(a+2 b) x^2+(-1+d) x^3)} \, dx\)
  3.21.76 \(\int \frac {(-b+a x^5)^{3/4}}{x^6} \, dx\)
  3.21.77 \(\int \frac {(-b+a x^6)^{3/4}}{x^7} \, dx\)
  3.21.78 \(\int \frac {(-4+5 x^7) \sqrt [3]{-2 x+2 x^3-x^8}}{(2+x^7) (2-2 x^2+x^7)} \, dx\)
  3.21.79 \(\int \frac {b-2 a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-2 b-a x^4+x^8)} \, dx\)
  3.21.80 \(\int \frac {-b+2 a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\)
  3.21.81 \(\int \frac {-b+2 a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b+a x^4+x^8)} \, dx\)
  3.21.82 \(\int \frac {\sqrt {-b^4+a^4 x^4} (b^4+a^4 x^4)}{b^8+a^8 x^8} \, dx\)
  3.21.83 \(\int \frac {-b^8+a^8 x^8}{\sqrt {-b^4+a^4 x^4} (b^8+a^8 x^8)} \, dx\)
  3.21.84 \(\int \frac {x^3 \sqrt {x+x^2}}{\sqrt {x^2+x \sqrt {x+x^2}}} \, dx\)
  3.21.85 \(\int \frac {(-b+a x^2)^{3/4} (3 b+2 a x^2)}{x} \, dx\)
  3.21.86 \(\int \frac {(-6+x^2) (2-x^2+x^3)^{2/3}}{x^3 (-2+x^2+x^3)} \, dx\)
  3.21.87 \(\int \frac {x^3 (-4 a+3 x)}{(x^2 (-a+x))^{2/3} (a d-d x+x^4)} \, dx\)
  3.21.88 \(\int \frac {-1+k^4 x^4}{\sqrt {(1-x) x (1-k^2 x)} (1+k^4 x^4)} \, dx\)
  3.21.89 \(\int \frac {1-x^4}{(1+x^4) \sqrt [4]{x^3+x^5}} \, dx\)
  3.21.90 \(\int \frac {(1+x^3)^{2/3} (2+x^6)}{x^6 (-1+x^3)^2} \, dx\)
  3.21.91 \(\int \frac {(-1+x^3)^{2/3} (-2+2 x^3+x^6)}{x^6 (1+x^3)^2} \, dx\)
  3.21.92 \(\int \frac {(2 b+a x^6) (-b-c x^4+a x^6)}{x^2 (-b+a x^6)^{3/4} (-b+c x^4+a x^6)} \, dx\)
  3.21.93 \(\int \frac {\sqrt {c+d \sqrt {b+a x^2}}}{x} \, dx\)
  3.21.94 \(\int \frac {(-b+a^2 x^4) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{\sqrt {b+a^2 x^4}} \, dx\)
  3.21.95 \(\int \sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}} \, dx\)
  3.21.96 \(\int \frac {1}{(2 b+a x) \sqrt [4]{b x^2+a x^3}} \, dx\)
  3.21.97 \(\int \frac {x (-4 a+3 x)}{\sqrt [3]{x^2 (-a+x)} (a d-d x+x^4)} \, dx\)
  3.21.98 \(\int \frac {(-b+a x^5)^{3/4} (4 b+a x^5)}{x^4 (-b+c x^4+a x^5)} \, dx\)
  3.21.99 \(\int \frac {(1+x^8)^{3/4}}{-1+x^8} \, dx\)
  3.21.100 \(\int \frac {x^4}{\sqrt [4]{-1+x^4} (-1+2 x^4+x^8)} \, dx\)