3.31.1 \(\int \genfrac {}{}{}{}{\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\) [3001]
  3.31.2 \(\int \genfrac {}{}{}{}{\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\) [3002]
  3.31.3 \(\int \genfrac {}{}{}{}{\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\) [3003]
  3.31.4 \(\int \genfrac {}{}{}{}{\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\) [3004]
  3.31.5 \(\int \genfrac {}{}{}{}{(1+(-2+k) x) (1-2 k x+k^2 x^2)}{\sqrt [3]{(1-x) x (1-k x)} (b-4 b k x+(-1+6 b k^2) x^2+(2-4 b k^3) x^3+(-1+b k^4) x^4)} \, dx\) [3005]
  3.31.6 \(\int \genfrac {}{}{}{}{\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\) [3006]
  3.31.7 \(\int \genfrac {}{}{}{}{\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\) [3007]
  3.31.8 \(\int \genfrac {}{}{}{}{(a-2 b+x) (a^2-2 a x+x^2)}{\sqrt [3]{(-a+x) (-b+x)} (-b^2+a^4 d+2 (b-2 a^3 d) x+(-1+6 a^2 d) x^2-4 a d x^3+d x^4)} \, dx\) [3008]
  3.31.9 \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^4) \sqrt {x+\sqrt {1+x^2}}} \, dx\) [3009]
  3.31.10 \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^4) \sqrt {x+\sqrt {1+x^2}}} \, dx\) [3010]
  3.31.11 \(\int \genfrac {}{}{}{}{\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}}{x-\sqrt {b+a x}} \, dx\) [3011]
  3.31.12 \(\int \genfrac {}{}{}{}{1+x}{(1-a x) \sqrt [4]{\genfrac {}{}{}{}{1-b x}{c+x}}} \, dx\) [3012]
  3.31.13 \(\int \genfrac {}{}{}{}{x^5 (-7 b+9 a x^2)}{\sqrt [4]{-b x^3+a x^5} (1-b x^7+a x^9)} \, dx\) [3013]
  3.31.14 \(\int \genfrac {}{}{}{}{b+a x^4}{\sqrt {-b+a x^4} (-b+c^2 x^2+a x^4)} \, dx\) [3014]
  3.31.15 \(\int \genfrac {}{}{}{}{x (-a+x) (a b-2 b x+x^2)}{\sqrt [3]{x (-a+x) (-b+x)^2} (-b^2+2 b x+(-1+a^2 d) x^2-2 a d x^3+d x^4)} \, dx\) [3015]
  3.31.16 \(\int \genfrac {}{}{}{}{b+a x}{(-b+a x) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\) [3016]
  3.31.17 \(\int \genfrac {}{}{}{}{\sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{-b+a^2 x^4} \, dx\) [3017]
  3.31.18 \(\int \genfrac {}{}{}{}{\sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{-b+a^2 x^4} \, dx\) [3018]
  3.31.19 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{(-a+x) (-b+x)^2} (b-a d+(-1+d) x)} \, dx\) [3019]
  3.31.20 \(\int \genfrac {}{}{}{}{(-4-3 x+2 x^2) (1+x-x^2+x^4) \sqrt [3]{\genfrac {}{}{}{}{1+x-x^2+2 x^4}{1+x-x^2+3 x^4}}}{x^5 (-1-x+x^2+x^4)} \, dx\) [3020]
  3.31.21 \(\int \genfrac {}{}{}{}{-b+a x}{(b+a x) \sqrt [3]{-b^2 x^2+a^3 x^3}} \, dx\) [3021]
  3.31.22 \(\int \genfrac {}{}{}{}{(-q+p x^4) \sqrt {q+p x^4}}{c x^4+b x^2 (q+p x^4)+a (q+p x^4)^2} \, dx\) [3022]
  3.31.23 \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\sqrt {1+x^2} (1-x^4)} \, dx\) [3023]
  3.31.24 \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\sqrt {1+x^2} (1-x^4)} \, dx\) [3024]
  3.31.25 \(\int \genfrac {}{}{}{}{1-x^3+x^6}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\) [3025]
  3.31.26 \(\int \genfrac {}{}{}{}{1+x^3+x^6}{\sqrt [3]{x^2+x^4} (-1+x^6)} \, dx\) [3026]
  3.31.27 \(\int \genfrac {}{}{}{}{\sqrt {-b+a^2 x^2} \sqrt {a x+\sqrt {-b+a^2 x^2}}}{\sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [3027]
  3.31.28 \(\int \genfrac {}{}{}{}{(-1+a x^8) (1+a x^8)^{3/4}}{1+x^8+a^2 x^{16}} \, dx\) [3028]
  3.31.29 \(\int \genfrac {}{}{}{}{-b+a x}{(b+a x) \sqrt [3]{b^2 x^2+a^3 x^3}} \, dx\) [3029]
  3.31.30 \(\int \genfrac {}{}{}{}{1}{(-1+x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\) [3030]
  3.31.31 \(\int \genfrac {}{}{}{}{(c+b x+a x^2)^{3/2}}{1-x \sqrt {c+b x+a x^2}} \, dx\) [3031]
  3.31.32 \(\int \genfrac {}{}{}{}{(-b+x)^2}{((-a+x) (-b+x)^2)^{2/3} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\) [3032]
  3.31.33 \(\int \genfrac {}{}{}{}{b+a x}{(-b+a x) \sqrt [3]{-b^2 x^2+a^3 x^3}} \, dx\) [3033]
  3.31.34 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{a x+\sqrt {-b+a^2 x^2}} \sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [3034]
  3.31.35 \(\int \genfrac {}{}{}{}{x^4}{\sqrt [4]{-b+a x^4} (-b+2 a x^4+x^8)} \, dx\) [3035]
  3.31.36 \(\int \genfrac {}{}{}{}{(d+c x^2) (a x+\sqrt {-b+a^2 x^2})^{3/4}}{(-b+a^2 x^2)^{5/2}} \, dx\) [3036]
  3.31.37 \(\int \genfrac {}{}{}{}{x^2}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\) [3037]
  3.31.38 \(\int \genfrac {}{}{}{}{x^2}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\) [3038]
  3.31.39 \(\int \genfrac {}{}{}{}{-1+x^4}{(1+x^4) \sqrt [4]{-x^2+x^6}} \, dx\) [3039]
  3.31.40 \(\int \genfrac {}{}{}{}{(-b+a x^4)^{3/4}}{-b+2 a x^4+x^8} \, dx\) [3040]
  3.31.41 \(\int \genfrac {}{}{}{}{\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^{5/2}} \, dx\) [3041]
  3.31.42 \(\int \genfrac {}{}{}{}{\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x^2)^{5/2}} \, dx\) [3042]
  3.31.43 \(\int \genfrac {}{}{}{}{x^2 \sqrt {b+a x}}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\) [3043]
  3.31.44 \(\int \genfrac {}{}{}{}{x^2 \sqrt {b+a x}}{x^2-\sqrt {b+a x} \sqrt {c+\sqrt {b+a x}}} \, dx\) [3044]
  3.31.45 \(\int \sqrt {b+a^2 x^2} \sqrt {a x+\sqrt {b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\) [3045]
  3.31.46 \(\int \genfrac {}{}{}{}{x^4}{\sqrt [4]{b+a x^4} (b+2 a x^4+2 x^8)} \, dx\) [3046]
  3.31.47 \(\int \genfrac {}{}{}{}{x^4 (-q+p x^4) \sqrt {q+p x^4}}{b x^8+a (q+p x^4)^4} \, dx\) [3047]
  3.31.48 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{1-3 x+3 x^3-9 x^4+3 x^6-9 x^7+x^9-3 x^{10}}} \, dx\) [3048]
  3.31.49 \(\int \genfrac {}{}{}{}{(b+a x^4)^{3/4}}{b+2 a x^4+2 x^8} \, dx\) [3049]
  3.31.50 \(\int \genfrac {}{}{}{}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(d+c x) \sqrt {b+a^2 x^4}} \, dx\) [3050]
  3.31.51 \(\int \genfrac {}{}{}{}{\sqrt {a x^2+\sqrt {b+a^2 x^4}}}{(d+c x) \sqrt {b+a^2 x^4}} \, dx\) [3051]
  3.31.52 \(\int \genfrac {}{}{}{}{1}{\sqrt {c+b x+a x^2} (c^3+a^3 b^3 x^3)} \, dx\) [3052]
  3.31.53 \(\int \genfrac {}{}{}{}{(-d+c x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\) [3053]
  3.31.54 \(\int \genfrac {}{}{}{}{(-d+c x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\) [3054]
  3.31.55 \(\int \sqrt {\genfrac {}{}{}{}{-1+a x-2 x^2+2 a x^3-x^4+a x^5}{1+a x-2 x^2-2 a x^3+x^4+a x^5}} \, dx\) [3055]
  3.31.56 \(\int \genfrac {}{}{}{}{1+x}{(-3+x^2) \sqrt [3]{1+x^2}} \, dx\) [3056]
  3.31.57 \(\int \genfrac {}{}{}{}{1-x^4}{(1+x^4) \sqrt [4]{-x^3+x^5}} \, dx\) [3057]
  3.31.58 \(\int \genfrac {}{}{}{}{-1+x^8}{\sqrt [4]{-x^2+x^6} (1+x^8)} \, dx\) [3058]
  3.31.59 \(\int \genfrac {}{}{}{}{-1+x^8}{\sqrt [4]{-x^2+x^6} (1+x^8)} \, dx\) [3059]
  3.31.60 \(\int \genfrac {}{}{}{}{\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}{\sqrt [4]{c+\sqrt [3]{a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [3060]
  3.31.61 \(\int \genfrac {}{}{}{}{b^2+a x}{(-b^2+a x) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\) [3061]
  3.31.62 \(\int \genfrac {}{}{}{}{(-b+a x^4)^{3/4}}{b-2 a x^4+2 x^8} \, dx\) [3062]
  3.31.63 \(\int \genfrac {}{}{}{}{-d+c x^2}{(d+c x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\) [3063]
  3.31.64 \(\int \genfrac {}{}{}{}{-d+c x^2}{(d+c x^2) \sqrt {a x^2+\sqrt {b+a^2 x^4}}} \, dx\) [3064]
  3.31.65 \(\int \genfrac {}{}{}{}{x^4}{\sqrt [4]{-b+a x^4} (b-2 a x^4+2 x^8)} \, dx\) [3065]
  3.31.66 \(\int \genfrac {}{}{}{}{x^3 (-5 b+6 a x)}{\sqrt [4]{-b x+a x^2} (c-b x^5+a x^6)} \, dx\) [3066]
  3.31.67 \(\int \genfrac {}{}{}{}{-a+x}{\sqrt [3]{(-a+x) (-b+x)^2} (-b^2+a^2 d+2 (b-a d) x+(-1+d) x^2)} \, dx\) [3067]
  3.31.68 \(\int \genfrac {}{}{}{}{b-a x^4+2 x^8}{\sqrt [4]{b+a x^4} (-b-2 a x^4+x^8)} \, dx\) [3068]
  3.31.69 \(\int \genfrac {}{}{}{}{\sqrt {-b+a^2 x^2}}{\sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [3069]
  3.31.70 \(\int \genfrac {}{}{}{}{1+x}{\sqrt [3]{27+189 x+522 x^2+784 x^3+825 x^4+679 x^5+338 x^6+84 x^7+8 x^8}} \, dx\) [3070]
  3.31.71 \(\int \genfrac {}{}{}{}{-1+k^2 x^4}{\sqrt {(1-x^2) (1-k^2 x^2)} (1+k^2 x^4)} \, dx\) [3071]
  3.31.72 \(\int \genfrac {}{}{}{}{1+2 x}{\sqrt [3]{-1+x^2} (3+x^2)} \, dx\) [3072]
  3.31.73 \(\int \genfrac {}{}{}{}{x}{\sqrt {1-\sqrt {1-\sqrt {1-\genfrac {}{}{}{}{1}{x}}}}} \, dx\) [3073]
  3.31.74 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x^2+x^6} (1-x^4+x^8)}{x^4 (1+x^4)} \, dx\) [3074]
  3.31.75 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x^2+x^6} (1-x^4+x^8)}{x^4 (1+x^4)} \, dx\) [3075]
  3.31.76 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x^2+x^6} (1+x^4+x^8)}{x^4 (1+x^4)} \, dx\) [3076]
  3.31.77 \(\int \genfrac {}{}{}{}{\sqrt [4]{-x^2+x^6} (1+x^4+x^8)}{x^4 (1+x^4)} \, dx\) [3077]
  3.31.78 \(\int \genfrac {}{}{}{}{\sqrt [3]{b^2 x^2+a^3 x^3}}{-b+a x} \, dx\) [3078]
  3.31.79 \(\int \genfrac {}{}{}{}{\sqrt {-b+a^2 x^2}}{\sqrt {a x+\sqrt {-b+a^2 x^2}} \sqrt {c+\sqrt {a x+\sqrt {-b+a^2 x^2}}}} \, dx\) [3079]
  3.31.80 \(\int \genfrac {}{}{}{}{(-3+x^2) (1-2 x^2+x^4+x^6)}{x^{10} \sqrt [4]{\genfrac {}{}{}{}{-a+a x^2+b x^3}{-c+c x^2+d x^3}}} \, dx\) [3080]
  3.31.81 \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^4} \, dx\) [3081]
  3.31.82 \(\int \genfrac {}{}{}{}{(1+x^4) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^4} \, dx\) [3082]
  3.31.83 \(\int \sqrt {b+a^2 x^2} \sqrt {c+\sqrt {a x+\sqrt {b+a^2 x^2}}} \, dx\) [3083]
  3.31.84 \(\int \genfrac {}{}{}{}{\sqrt {(-81+27 x+135 x^2-150 x^3+65 x^4-13 x^5+x^6)^3}}{-1+x} \, dx\) [3084]
  3.31.85 \(\int \genfrac {}{}{}{}{(1+x^2+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)^2} \, dx\) [3085]
  3.31.86 \(\int \genfrac {}{}{}{}{(1+x^2+x^4)^2 \sqrt {x^2+\sqrt {1+x^4}}}{\sqrt {1+x^4} (-1+x^2+x^4)^2} \, dx\) [3086]
  3.31.87 \(\int \genfrac {}{}{}{}{(-q+p x^4) \sqrt {q+p x^4}}{x^2 (a q+b x^2+a p x^4)} \, dx\) [3087]
  3.31.88 \(\int \genfrac {}{}{}{}{\sqrt [3]{b^2 x^2+a^3 x^3}}{b+a x} \, dx\) [3088]
  3.31.89 \(\int \genfrac {}{}{}{}{(-b+a^2 x^2)^{3/2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x} \, dx\) [3089]
  3.31.90 \(\int \genfrac {}{}{}{}{(b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}}{-b^2+a x^2} \, dx\) [3090]
  3.31.91 \(\int \genfrac {}{}{}{}{d+c x^4}{x \sqrt {-b+a^2 x^2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}} \, dx\) [3091]
  3.31.92 \(\int \genfrac {}{}{}{}{(-b+a^2 x^2)^{3/2} \sqrt [4]{a x+\sqrt {-b+a^2 x^2}}}{x^2} \, dx\) [3092]
  3.31.93 \(\int \genfrac {}{}{}{}{b-x}{\sqrt [3]{(-a+x) (-b+x)^2} (a^2-b^2 d-2 (a-b d) x+(1-d) x^2)} \, dx\) [3093]
  3.31.94 \(\int \genfrac {}{}{}{}{-b+x}{\sqrt [3]{(-a+x) (-b+x)^2} (-a^2+b^2 d+2 (a-b d) x+(-1+d) x^2)} \, dx\) [3094]
  3.31.95 \(\int \genfrac {}{}{}{}{b^2+a x^2}{(-b^2+a x^2) \sqrt {b+\sqrt {b^2+a x^2}}} \, dx\) [3095]
  3.31.96 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{(-a+x) (-b+x)^2} (a-b d+(-1+d) x)} \, dx\) [3096]
  3.31.97 \(\int \genfrac {}{}{}{}{\sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\) [3097]
  3.31.98 \(\int \genfrac {}{}{}{}{\sqrt {b+a^2 x^4} \sqrt {a x^2+\sqrt {b+a^2 x^4}}}{d+c x^2} \, dx\) [3098]
  3.31.99 \(\int \genfrac {}{}{}{}{\sqrt {x^2+\sqrt {1+x^4}}}{1+a x} \, dx\) [3099]
  3.31.100 \(\int \genfrac {}{}{}{}{1}{\sqrt {c_4+\sqrt {\genfrac {}{}{}{}{c_0+x c_1}{c_2+x c_3}} c_5} (c_6+x c_7)} \, dx\) [3100]