3.3.1 \(\int \frac {(\sqrt {1-x}+\sqrt {1+x})^2}{x^2} \, dx\)
  3.3.2 \(\int \frac {(\sqrt {1-x}+\sqrt {1+x})^2}{x^3} \, dx\)
  3.3.3 \(\int \frac {x^3}{\sqrt {a+b x}+\sqrt {a+c x}} \, dx\)
  3.3.4 \(\int \frac {x^2}{\sqrt {a+b x}+\sqrt {a+c x}} \, dx\)
  3.3.5 \(\int \frac {x}{\sqrt {a+b x}+\sqrt {a+c x}} \, dx\)
  3.3.6 \(\int \frac {1}{\sqrt {a+b x}+\sqrt {a+c x}} \, dx\)
  3.3.7 \(\int \frac {1}{x (\sqrt {a+b x}+\sqrt {a+c x})} \, dx\)
  3.3.8 \(\int \frac {1}{x^2 (\sqrt {a+b x}+\sqrt {a+c x})} \, dx\)
  3.3.9 \(\int \frac {x^3}{(\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\)
  3.3.10 \(\int \frac {x^2}{(\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\)
  3.3.11 \(\int \frac {x}{(\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\)
  3.3.12 \(\int \frac {1}{(\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\)
  3.3.13 \(\int \frac {1}{x (\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\)
  3.3.14 \(\int \frac {1}{x^2 (\sqrt {a+b x}+\sqrt {a+c x})^2} \, dx\)
  3.3.15 \(\int \frac {x^4}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\)
  3.3.16 \(\int \frac {x^3}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\)
  3.3.17 \(\int \frac {x^2}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\)
  3.3.18 \(\int \frac {x}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\)
  3.3.19 \(\int \frac {1}{(\sqrt {a+b x}+\sqrt {a+c x})^3} \, dx\)
  3.3.20 \(\int \sqrt {1-x} (\sqrt {1-x}+\sqrt {1+x}) \, dx\)
  3.3.21 \(\int x^3 (-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x}) \, dx\)
  3.3.22 \(\int x^2 (-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x}) \, dx\)
  3.3.23 \(\int x (-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x}) \, dx\)
  3.3.24 \(\int (-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x}) \, dx\)
  3.3.25 \(\int \frac {(-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x})}{x} \, dx\)
  3.3.26 \(\int \frac {(-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x})}{x^2} \, dx\)
  3.3.27 \(\int \frac {(-\sqrt {1-x}-\sqrt {1+x}) (\sqrt {1-x}+\sqrt {1+x})}{x^3} \, dx\)
  3.3.28 \(\int \frac {\sqrt {1-x}+\sqrt {1+x}}{-\sqrt {1-x}+\sqrt {1+x}} \, dx\)
  3.3.29 \(\int \frac {-\sqrt {-1+x}+\sqrt {1+x}}{\sqrt {-1+x}+\sqrt {1+x}} \, dx\)
  3.3.30 \(\int (d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}})^3 \, dx\)
  3.3.31 \(\int (d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}})^2 \, dx\)
  3.3.32 \(\int (d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}}) \, dx\)
  3.3.33 \(\int \frac {1}{d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}}} \, dx\)
  3.3.34 \(\int \frac {1}{(d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}})^2} \, dx\)
  3.3.35 \(\int \frac {1}{(d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}})^3} \, dx\)
  3.3.36 \(\int (d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}})^{5/2} \, dx\)
  3.3.37 \(\int (d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}})^{3/2} \, dx\)
  3.3.38 \(\int \sqrt {d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}}} \, dx\)
  3.3.39 \(\int \frac {1}{\sqrt {d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}}}} \, dx\)
  3.3.40 \(\int \frac {1}{(d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}})^{3/2}} \, dx\)
  3.3.41 \(\int \frac {1}{(d+e x+f \sqrt {a+\frac {e^2 x^2}{f^2}})^{5/2}} \, dx\)
  3.3.42 \(\int \sqrt {x-\sqrt {-4+x^2}} \, dx\)
  3.3.43 \(\int \sqrt {a x+b \sqrt {c+\frac {a^2 x^2}{b^2}}} \, dx\)
  3.3.44 \(\int \sqrt {1+\sqrt {1-x^2}} \, dx\)
  3.3.45 \(\int \sqrt {1+\sqrt {1+x^2}} \, dx\)
  3.3.46 \(\int \sqrt {5+\sqrt {25+x^2}} \, dx\)
  3.3.47 \(\int \sqrt {a+b \sqrt {\frac {a^2}{b^2}+c x^2}} \, dx\)
  3.3.48 \(\int (d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}})^3 \, dx\)
  3.3.49 \(\int (d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}})^2 \, dx\)
  3.3.50 \(\int (d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}}) \, dx\)
  3.3.51 \(\int \frac {1}{d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}}} \, dx\)
  3.3.52 \(\int \frac {1}{(d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}})^2} \, dx\)
  3.3.53 \(\int \frac {1}{(d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}})^3} \, dx\)
  3.3.54 \(\int (d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}})^{5/2} \, dx\)
  3.3.55 \(\int (d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}})^{3/2} \, dx\)
  3.3.56 \(\int \sqrt {d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}}} \, dx\)
  3.3.57 \(\int \frac {1}{\sqrt {d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}}}} \, dx\)
  3.3.58 \(\int \frac {1}{(d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}})^{3/2}} \, dx\)
  3.3.59 \(\int \frac {1}{(d+e x+f \sqrt {a+b x+\frac {e^2 x^2}{f^2}})^{5/2}} \, dx\)
  3.3.60 \(\int (a+x^2)^2 (x+\sqrt {a+x^2})^n \, dx\)
  3.3.61 \(\int (a+x^2) (x+\sqrt {a+x^2})^n \, dx\)
  3.3.62 \(\int (x+\sqrt {a+x^2})^n \, dx\)
  3.3.63 \(\int (a+x^2)^2 (x-\sqrt {a+x^2})^n \, dx\)
  3.3.64 \(\int (a+x^2) (x-\sqrt {a+x^2})^n \, dx\)
  3.3.65 \(\int (x-\sqrt {a+x^2})^n \, dx\)
  3.3.66 \(\int (a+x^2)^{5/2} (x+\sqrt {a+x^2})^n \, dx\)
  3.3.67 \(\int (a+x^2)^{3/2} (x+\sqrt {a+x^2})^n \, dx\)
  3.3.68 \(\int \sqrt {a+x^2} (x+\sqrt {a+x^2})^n \, dx\)
  3.3.69 \(\int \frac {(x+\sqrt {a+x^2})^n}{\sqrt {a+x^2}} \, dx\)
  3.3.70 \(\int (a+x^2)^{5/2} (x-\sqrt {a+x^2})^n \, dx\)
  3.3.71 \(\int (a+x^2)^{3/2} (x-\sqrt {a+x^2})^n \, dx\)
  3.3.72 \(\int \sqrt {a+x^2} (x-\sqrt {a+x^2})^n \, dx\)
  3.3.73 \(\int \frac {(x-\sqrt {a+x^2})^n}{\sqrt {a+x^2}} \, dx\)
  3.3.74 \(\int (a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2})^2 (d+e x+f \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}})^n \, dx\)
  3.3.75 \(\int (a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}) (d+e x+f \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}})^n \, dx\)
  3.3.76 \(\int (d+e x+f \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}})^n \, dx\)
  3.3.77 \(\int (d+e x+f \sqrt {\frac {a f^2+e x (2 d+e x)}{f^2}})^n \, dx\)
  3.3.78 \(\int (a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2})^{3/2} (d+e x+f \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}})^n \, dx\)
  3.3.79 \(\int \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}} (d+e x+f \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}})^n \, dx\)
  3.3.80 \(\int \frac {(d+e x+f \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}})^n}{\sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}}} \, dx\)
  3.3.81 \(\int \frac {(d+e x+f \sqrt {\frac {a f^2+e x (2 d+e x)}{f^2}})^n}{\sqrt {\frac {a f^2+e x (2 d+e x)}{f^2}}} \, dx\)
  3.3.82 \(\int \sqrt {a g+\frac {2 d e g x}{f^2}+\frac {e^2 g x^2}{f^2}} (d+e x+f \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}})^n \, dx\)
  3.3.83 \(\int \frac {(d+e x+f \sqrt {a+\frac {2 d e x}{f^2}+\frac {e^2 x^2}{f^2}})^n}{\sqrt {a g+\frac {2 d e g x}{f^2}+\frac {e^2 g x^2}{f^2}}} \, dx\)
  3.3.84 \(\int \frac {(d+e x+f \sqrt {\frac {a f^2+e x (2 d+e x)}{f^2}})^n}{\sqrt {\frac {a f^2 g+e g x (2 d+e x)}{f^2}}} \, dx\)
  3.3.85 \(\int \frac {e-2 f x^2}{e^2+4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\)
  3.3.86 \(\int \frac {e-2 f x^2}{e^2-4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\)
  3.3.87 \(\int \frac {e-4 f x^3}{e^2+4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\)
  3.3.88 \(\int \frac {e-4 f x^3}{e^2-4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\)
  3.3.89 \(\int \frac {e-2 f (-1+n) x^n}{e^2+4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
  3.3.90 \(\int \frac {e-2 f (-1+n) x^n}{e^2-4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
  3.3.91 \(\int \frac {x}{e^2+4 e f x^2+4 d f x^4+4 f^2 x^4} \, dx\)
  3.3.92 \(\int \frac {x}{e^2+4 e f x^2-4 d f x^4+4 f^2 x^4} \, dx\)
  3.3.93 \(\int \frac {x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^6} \, dx\)
  3.3.94 \(\int \frac {x^2 (3 e+2 f x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^6} \, dx\)
  3.3.95 \(\int \frac {x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^{2+2 m}} \, dx\)
  3.3.96 \(\int \frac {x^m (e (1+m)+2 f (-1+m) x^2)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^{2+2 m}} \, dx\)
  3.3.97 \(\int \frac {x (2 e-2 f x^3)}{e^2+4 e f x^3+4 d f x^4+4 f^2 x^6} \, dx\)
  3.3.98 \(\int \frac {x (2 e-2 f x^3)}{e^2+4 e f x^3-4 d f x^4+4 f^2 x^6} \, dx\)
  3.3.99 \(\int \frac {x^2}{e^2+4 e f x^3+4 d f x^6+4 f^2 x^6} \, dx\)
  3.3.100 \(\int \frac {x^2}{e^2+4 e f x^3-4 d f x^6+4 f^2 x^6} \, dx\)