3.32.1 \(\int \frac {-b+x}{\sqrt [3]{(-a+x) (-b+x)^2} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.32.2 \(\int \frac {(b^2+a x^2)^2}{(-b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.32.3 \(\int \frac {\sqrt {a x+\sqrt {-b+a x}}}{\sqrt {-b+a x} (1+a^2 x^2)} \, dx\)
  3.32.4 \(\int \frac {(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^4} \, dx\)
  3.32.5 \(\int \frac {(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^4} \, dx\)
  3.32.6 \(\int \frac {(1+x^2)^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.32.7 \(\int \frac {(1+x^2)^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.32.8 \(\int \frac {\sqrt {1+x^4}}{(1+x)^3 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.32.9 \(\int \frac {x^2}{\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}} \, dx\)
  3.32.10 \(\int \frac {(1+x^2) (-a-b x+a x^2)}{x^2 (-c+d x+c x^2) \sqrt [3]{\frac {-1+x^2-x c_0}{-1+x^2-x c_1}}} \, dx\)
  3.32.11 \(\int \frac {(1+x^2)^2 \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.32.12 \(\int \frac {(1+x^2)^2 \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
  3.32.13 \(\int \frac {(1+x^2)^2 \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.32.14 \(\int \frac {(1+x^2)^2 \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
  3.32.15 \(\int \frac {x^2}{\sqrt {1+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.32.16 \(\int \sqrt [3]{\frac {x}{-1-a x+3 x^2+3 a x^3-3 x^4-3 a x^5+x^6+a x^7}} \, dx\)
  3.32.17 \(\int \frac {\sqrt {-b+a^2 x^2} \sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}{\sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.32.18 \(\int \frac {\sqrt [6]{a x+\sqrt {-b+a^2 x^2}}}{x^3 \sqrt {-b+a^2 x^2}} \, dx\)
  3.32.19 \(\int \frac {x^2 (x^2 c_3-c_4) \sqrt [4]{\frac {x c_0+x^2 c_3+c_4}{x c_1+x^2 c_3+c_4}}}{(-x+x^2 c_3+c_4) (x+x^2 c_3+c_4) (x^2+x^4 c_3{}^2+2 x^2 c_3 c_4+c_4{}^2)} \, dx\)
  3.32.20 \(\int \frac {1}{\sqrt [4]{a x+\sqrt {-b+a^2 x^2}} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.32.21 \(\int \frac {1}{\sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.32.22 \(\int \sqrt [4]{\frac {1+a x-4 x^2-4 a x^3+6 x^4+6 a x^5-4 x^6-4 a x^7+x^8+a x^9}{-c+b x}} \, dx\)
  3.32.23 \(\int \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.32.24 \(\int \frac {\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x (-b+a^2 x^2)^{3/2}} \, dx\)
  3.32.25 \(\int \frac {x (2 x^3 c_3-c_4)}{(-x+x^3 c_3+c_4) \sqrt [3]{\frac {x c_0+x^3 c_3+c_4}{x c_1+x^3 c_3+c_4}} (x^2+x^4 c_3+x^6 c_3{}^2+x c_4+2 x^3 c_3 c_4+c_4{}^2)} \, dx\)
  3.32.26 \(\int \frac {(-d+c x) \sqrt {a x+\sqrt {b^2+a^2 x^2}}}{d+c x} \, dx\)
  3.32.27 \(\int \frac {\sqrt [3]{\frac {x}{-1-a x+3 x^2+3 a x^3-3 x^4-3 a x^5+x^6+a x^7}}}{x^3} \, dx\)
  3.32.28 \(\int \frac {1}{a b c-(c+a b x)^2 \sqrt {c+b x+a x^2}} \, dx\)
  3.32.29 \(\int \frac {\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x^2 (-b+a^2 x^2)^{3/2}} \, dx\)
  3.32.30 \(\int \frac {(-1+x^2) \sqrt {c_4+\sqrt {\frac {c_0+x c_1}{c_2+x c_3}} c_5}}{1+x^2} \, dx\)
  3.32.31 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.32.32 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt [3]{a x+\sqrt {-b+a^2 x^2}} \sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.32.33 \(\int \frac {(b+a x^4) \sqrt {-b-c x^2+a x^4}}{(-b+a x^4)^2} \, dx\)
  3.32.34 \(\int \frac {-a-b c+(1+c) x}{((-a+x) (-b+x)^2)^{2/3} (a-b d+(-1+d) x)} \, dx\)
  3.32.35 \(\int \frac {-a-b c+(1+c) x}{(-b+x) \sqrt [3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx\)
  3.32.36 \(\int \frac {(d+c x^2) (a x+\sqrt {-b+a^2 x^2})^{5/4}}{x (-b+a^2 x^2)^{5/2}} \, dx\)
  3.32.37 \(\int \frac {1}{\sqrt {c_4+\sqrt {\frac {c_0+x c_1}{c_2+x c_3}} c_5} (c_6+x c_7){}^2} \, dx\)
  3.32.38 \(\int \frac {\sqrt [6]{\frac {1-b x}{c+x}} (1+d x^2)}{(1+b x) (1+c x)} \, dx\)
  3.32.39 \(\int \frac {\sqrt {-b+a^2 x^2} (a x+\sqrt {-b+a^2 x^2})^{3/4}}{(c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}})^{2/3}} \, dx\)
  3.32.40 \(\int \frac {c_6+x c_7}{\sqrt {c_4+\sqrt {\frac {c_0+x c_1}{c_2+x c_3}} c_5}} \, dx\)
  3.32.41 \(\int \frac {\sqrt {-b+a^2 x^2}}{(c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}})^{2/3}} \, dx\)
  3.32.42 \(\int (b+a^2 x^2)^{3/2} \sqrt {a x+\sqrt {b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.32.43 \(\int \frac {\sqrt {-b+a^2 x^2} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}}{\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.32.44 \(\int \frac {a b c-b^2 x+a^2 x^2}{\sqrt {c+b x+a x^2} (c+b x^2)^2} \, dx\)
  3.32.45 \(\int \frac {(b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}}}{(-b^2+a x^2)^2} \, dx\)
  3.32.46 \(\int \frac {\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(d+c x)^2 \sqrt {b+a^2 x^4}} \, dx\)
  3.32.47 \(\int \frac {-b-a c+(1+c) x}{(-a+x) \sqrt [3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx\)
  3.32.48 \(\int \frac {-a-b c+(1+c) x}{\sqrt [3]{(-a+x) (-b+x)^2} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\)
  3.32.49 \(\int \frac {-b-a c+(1+c) x}{\sqrt [3]{(-a+x) (-b+x)^2} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.32.50 \(\int \frac {c_8+x c_9}{\sqrt {c_4+\sqrt {\frac {c_0+x c_1}{c_2+x c_3}} c_5} (c_6+x c_7)} \, dx\)
  3.32.51 \(\int \frac {(-b+x) (-a-b c+(1+c) x)}{((-a+x) (-b+x)^2)^{2/3} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\)
  3.32.52 \(\int \frac {(-b+x) (-b-a c+(1+c) x)}{((-a+x) (-b+x)^2)^{2/3} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.32.53 \(\int \frac {x^2-c x^2 (\frac {b+a x}{d+c x})^{3/2}}{a-b \sqrt {\frac {b+a x}{d+c x}}} \, dx\)
  3.32.54 \(\int \frac {(c_6+x c_7){}^2}{\sqrt {c_4+\sqrt {\frac {c_0+x c_1}{c_2+x c_3}} c_5}} \, dx\)