3.25.1 \(\int \frac {(-b+a^2 x^2)^{3/2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x} \, dx\)
  3.25.2 \(\int \frac {(b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}}{-b^2+a x^2} \, dx\)
  3.25.3 \(\int \frac {d+c x^4}{x \sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.25.4 \(\int \frac {(-b+a^2 x^2)^{3/2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x^2} \, dx\)
  3.25.5 \(\int \frac {b-x}{\sqrt [3]{(-a+x) (-b+x)^2} (a^2-b^2 d-2 (a-b d) x+(1-d) x^2)} \, dx\)
  3.25.6 \(\int \frac {-b+x}{\sqrt [3]{(-a+x) (-b+x)^2} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\)
  3.25.7 \(\int \frac {b^2+a x^2}{(-b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.25.8 \(\int \frac {1}{\sqrt [3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx\)
  3.25.9 \(\int \frac {\sqrt {x^2+\sqrt {1+x^4}}}{1+a x} \, dx\)
  3.25.10 \(\int \frac {-b+x}{\sqrt [3]{(-a+x) (-b+x)^2} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.25.11 \(\int \frac {(b^2+a x^2)^2}{(-b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\)
  3.25.12 \(\int \frac {\sqrt {1+x^4}}{(1+x)^3 \sqrt {x^2+\sqrt {1+x^4}}} \, dx\)
  3.25.13 \(\int \frac {x^2}{\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}} \, dx\)
  3.25.14 \(\int \frac {x^2}{\sqrt {1+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.25.15 \(\int \sqrt [3]{\frac {x}{-1-a x+3 x^2+3 a x^3-3 x^4-3 a x^5+x^6+a x^7}} \, dx\)
  3.25.16 \(\int \frac {\sqrt {-b+a^2 x^2} \sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}{\sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.25.17 \(\int \frac {\sqrt [6]{a x+\sqrt {-b+a^2 x^2}}}{x^3 \sqrt {-b+a^2 x^2}} \, dx\)
  3.25.18 \(\int \frac {1}{\sqrt [4]{a x+\sqrt {-b+a^2 x^2}} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.25.19 \(\int \frac {1}{\sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.25.20 \(\int \sqrt [4]{\frac {1+a x-4 x^2-4 a x^3+6 x^4+6 a x^5-4 x^6-4 a x^7+x^8+a x^9}{-c+b x}} \, dx\)
  3.25.21 \(\int \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.25.22 \(\int \frac {\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x (-b+a^2 x^2)^{3/2}} \, dx\)
  3.25.23 \(\int \frac {(-d+c x) \sqrt {a x+\sqrt {b^2+a^2 x^2}}}{d+c x} \, dx\)
  3.25.24 \(\int \frac {\sqrt [3]{\frac {x}{-1-a x+3 x^2+3 a x^3-3 x^4-3 a x^5+x^6+a x^7}}}{x^3} \, dx\)
  3.25.25 \(\int \frac {\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x^2 (-b+a^2 x^2)^{3/2}} \, dx\)
  3.25.26 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.25.27 \(\int \frac {\sqrt {-b+a^2 x^2}}{\sqrt [3]{a x+\sqrt {-b+a^2 x^2}} \sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\)
  3.25.28 \(\int \frac {(b+a x^4) \sqrt {-b-c x^2+a x^4}}{(-b+a x^4)^2} \, dx\)
  3.25.29 \(\int \frac {-a-b c+(1+c) x}{((-a+x) (-b+x)^2)^{2/3} (a-b d+(-1+d) x)} \, dx\)
  3.25.30 \(\int \frac {-a-b c+(1+c) x}{(-b+x) \sqrt [3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx\)
  3.25.31 \(\int \frac {(d+c x^2) (a x+\sqrt {-b+a^2 x^2})^{5/4}}{x (-b+a^2 x^2)^{5/2}} \, dx\)
  3.25.32 \(\int \frac {\sqrt [6]{\frac {1-b x}{c+x}} (1+d x^2)}{(1+b x) (1+c x)} \, dx\)
  3.25.33 \(\int \frac {\sqrt {-b+a^2 x^2} (a x+\sqrt {-b+a^2 x^2})^{3/4}}{(c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}})^{2/3}} \, dx\)
  3.25.34 \(\int \frac {\sqrt {-b+a^2 x^2}}{(c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}})^{2/3}} \, dx\)
  3.25.35 \(\int (b+a^2 x^2)^{3/2} \sqrt {a x+\sqrt {b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\)
  3.25.36 \(\int \frac {\sqrt {-b+a^2 x^2} \sqrt [3]{c+\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}}{\sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\)
  3.25.37 \(\int \frac {(b^2+a x^2)^2 \sqrt {b+\sqrt {b^2+a x^2}}}{(-b^2+a x^2)^2} \, dx\)
  3.25.38 \(\int \frac {-b-a c+(1+c) x}{(-a+x) \sqrt [3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx\)
  3.25.39 \(\int \frac {-a-b c+(1+c) x}{\sqrt [3]{(-a+x) (-b+x)^2} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\)
  3.25.40 \(\int \frac {-b-a c+(1+c) x}{\sqrt [3]{(-a+x) (-b+x)^2} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.25.41 \(\int \frac {(-b+x) (-a-b c+(1+c) x)}{((-a+x) (-b+x)^2)^{2/3} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\)
  3.25.42 \(\int \frac {(-b+x) (-b-a c+(1+c) x)}{((-a+x) (-b+x)^2)^{2/3} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\)
  3.25.43 \(\int \frac {x^2-c x^2 (\frac {b+a x}{d+c x})^{3/2}}{a-b \sqrt {\frac {b+a x}{d+c x}}} \, dx\)