3.2 Integrals 101 to 200

\(\int \genfrac {}{}{}{}{1}{\sqrt {\sqrt {x}+x}} \, dx\) [101]
\(\int \sqrt {\sqrt {x}+x} \, dx\) [102]
\(\int \sqrt {-x} (\sqrt {-x}+x) \, dx\) [103]
\(\int \genfrac {}{}{}{}{5+\sqrt [4]{x}}{-6+x} \, dx\) [104]
\(\int \genfrac {}{}{}{}{1}{4+\sqrt {4-x}-x} \, dx\) [105]
\(\int \genfrac {}{}{}{}{1}{1+x-\sqrt {2+x}} \, dx\) [106]
\(\int \genfrac {}{}{}{}{1}{4+x+\sqrt {1+x}} \, dx\) [107]
\(\int \genfrac {}{}{}{}{1}{x-\sqrt {1+x}} \, dx\) [108]
\(\int \genfrac {}{}{}{}{1}{x-\sqrt {2+x}} \, dx\) [109]
\(\int \genfrac {}{}{}{}{1}{-\sqrt {1-x}+x} \, dx\) [110]
\(\int \sqrt {1+\sqrt {x}+x} \, dx\) [111]
\(\int \sqrt {1+x+\sqrt {1+x}} \, dx\) [112]
\(\int \sqrt {\sqrt {-1+x}+x} \, dx\) [113]
\(\int \sqrt {2 x+\sqrt {-1+2 x}} \, dx\) [114]
\(\int \sqrt {3 x+\sqrt {-7+8 x}} \, dx\) [115]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x+\sqrt {1+x}}} \, dx\) [116]
\(\int \genfrac {}{}{}{}{1+x}{4+x+\sqrt {-9+6 x}} \, dx\) [117]
\(\int \genfrac {}{}{}{}{12-x}{4+x+\sqrt {-9+6 x}} \, dx\) [118]
\(\int \genfrac {}{}{}{}{-1+x^3}{\sqrt {x} (1+x^2)} \, dx\) [119]
\(\int \genfrac {}{}{}{}{1}{2 \sqrt {-1+x} \sqrt {-\sqrt {-1+x}+x}} \, dx\) [120]
\(\int \genfrac {}{}{}{}{1+x^{7/2}}{1-x^2} \, dx\) [121]
\(\int \genfrac {}{}{}{}{4+2 x}{\sqrt [3]{-1+2 x}+\sqrt {-1+2 x}} \, dx\) [122]
\(\int \genfrac {}{}{}{}{1}{\sqrt {-1+x} \sqrt {-\sqrt {-1+x}+x}} \, dx\) [123]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+x+\sqrt {-1+2 x}}} \, dx\) [124]
\(\int \genfrac {}{}{}{}{q+p x}{\sqrt {b+a x} (f+\sqrt {b+a x})} \, dx\) [125]
\(\int \sqrt {1-\sqrt {x}-x} \, dx\) [126]
\(\int \genfrac {}{}{}{}{9+6 \sqrt {x}+x}{4 \sqrt {x}+x} \, dx\) [127]
\(\int \genfrac {}{}{}{}{6-8 x^{7/2}}{5-9 \sqrt {x}} \, dx\) [128]
\(\int \genfrac {}{}{}{}{\sqrt {1+x} (1+x^3)}{1+x^2} \, dx\) [129]
\(\int \genfrac {}{}{}{}{\sqrt {-1-\sqrt {x}+x}}{(-1+x) \sqrt {x}} \, dx\) [130]
\(\int \genfrac {}{}{}{}{1+2 \sqrt {1+x}}{x \sqrt {1+x} \sqrt {x+\sqrt {1+x}}} \, dx\) [131]
\(\int \genfrac {}{}{}{}{(2 \sqrt {3-x}+\genfrac {}{}{}{}{3}{\sqrt {1+x}})^2}{x} \, dx\) [132]
\(\int \genfrac {}{}{}{}{-1+x+x^2}{1+x+\sqrt {1+x^2}} \, dx\) [133]
\(\int \genfrac {}{}{}{}{2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx\) [134]
\(\int (a+c \sqrt {x}+b x^{2/3})^2 \, dx\) [135]
\(\int (a+c \sqrt {x}+b x^{2/3})^3 \, dx\) [136]
\(\int \genfrac {}{}{}{}{-1+x^2}{\sqrt {a-b+\genfrac {}{}{}{}{b}{x^2}} x^3} \, dx\) [137]
\(\int \genfrac {}{}{}{}{-1+x^2}{\sqrt {a+b (-1+\genfrac {}{}{}{}{1}{x^2})} x^3} \, dx\) [138]
\(\int \genfrac {}{}{}{}{1+x}{(4+x^2) \sqrt {9+x^2}} \, dx\) [139]
\(\int x (1+\sqrt {1-x} \sqrt {1+x}) \, dx\) [140]
\(\int x (1+\genfrac {}{}{}{}{1}{\sqrt {2+x} \sqrt {3+x}}) \, dx\) [141]
\(\int \genfrac {}{}{}{}{x-\sqrt {x^6}}{x (1-x^4)} \, dx\) [142]
\(\int \genfrac {}{}{}{}{1-\genfrac {}{}{}{}{\sqrt {x^6}}{x}}{1-x^4} \, dx\) [143]
\(\int \genfrac {}{}{}{}{x-\sqrt {x^6}}{x-x^5} \, dx\) [144]
\(\int \genfrac {}{}{}{}{x}{x+\sqrt {x^6}} \, dx\) [145]
\(\int \genfrac {}{}{}{}{\sqrt {x}-\sqrt {x^3}}{x-x^3} \, dx\) [146]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x}+\sqrt {x^3}} \, dx\) [147]
\(\int \genfrac {}{}{}{}{1}{\sqrt {-1+x}+\sqrt {(-1+x)^3}} \, dx\) [148]
\(\int (-\genfrac {}{}{}{}{3}{(4+5 x)^2}-\genfrac {}{}{}{}{5+4 x}{(4+5 x)^2 \sqrt {1-x^2}}) \, dx\) [149]
\(\int \genfrac {}{}{}{}{-5-4 x-3 \sqrt {1-x^2}}{(4+5 x)^2 \sqrt {1-x^2}} \, dx\) [150]
\(\int \genfrac {}{}{}{}{1}{(-5-4 x) \sqrt {1-x^2}+3 (1-x^2)} \, dx\) [151]
\(\int \genfrac {}{}{}{}{1}{3-3 x^2-5 \sqrt {1-x^2}-4 x \sqrt {1-x^2}} \, dx\) [152]
\(\int \genfrac {}{}{}{}{-1+\sqrt {1-x^2}}{\sqrt {1-x^2} (2+x-2 \sqrt {1-x^2})^2} \, dx\) [153]
\(\int \genfrac {}{}{}{}{a+b x^{-1+n}}{c x+d x^n} \, dx\) [154]
\(\int \genfrac {}{}{}{}{\sqrt {-1+4 x^2}}{x+\sqrt {-1+4 x^2}} \, dx\) [155]
\(\int \genfrac {}{}{}{}{a+b x+c x^2}{(d+e x)^3 \sqrt {-1+x^2}} \, dx\) [156]
\(\int \genfrac {}{}{}{}{(1-c^2 x^2)^3 (1+4 c^2 x^2)}{\sqrt {-1+c x} \sqrt {1+c x}} \, dx\) [157]
\(\int \genfrac {}{}{}{}{(1-c^2 x^2)^2 (1+4 c^2 x^2)}{\sqrt {-1+c x} \sqrt {1+c x}} \, dx\) [158]
\(\int \genfrac {}{}{}{}{(1-c^2 x^2) (1+4 c^2 x^2)}{\sqrt {-1+c x} \sqrt {1+c x}} \, dx\) [159]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x}} \, dx\) [160]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)} \, dx\) [161]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)^2} \, dx\) [162]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)^3} \, dx\) [163]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)^4} \, dx\) [164]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)^5} \, dx\) [165]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)^6} \, dx\) [166]
\(\int \genfrac {}{}{}{}{(1-c^2 x^2)^{5/2} (1+4 c^2 x^2)}{\sqrt {-1+c x} \sqrt {1+c x}} \, dx\) [167]
\(\int \genfrac {}{}{}{}{(1-c^2 x^2)^{3/2} (1+4 c^2 x^2)}{\sqrt {-1+c x} \sqrt {1+c x}} \, dx\) [168]
\(\int \genfrac {}{}{}{}{\sqrt {1-c^2 x^2} (1+4 c^2 x^2)}{\sqrt {-1+c x} \sqrt {1+c x}} \, dx\) [169]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} \sqrt {1-c^2 x^2}} \, dx\) [170]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)^{3/2}} \, dx\) [171]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)^{5/2}} \, dx\) [172]
\(\int \genfrac {}{}{}{}{1+4 c^2 x^2}{\sqrt {-1+c x} \sqrt {1+c x} (1-c^2 x^2)^{7/2}} \, dx\) [173]
\(\int \genfrac {}{}{}{}{1+2 x^8}{x (1+x^8)^{3/2}} \, dx\) [174]
\(\int \genfrac {}{}{}{}{\sqrt {1+x^8} (1+2 x^8)}{x+2 x^9+x^{17}} \, dx\) [175]
\(\int (1-9 x^2+\genfrac {}{}{}{}{x}{\sqrt {1-9 x^2}}) \, dx\) [176]
\(\int \genfrac {}{}{}{}{x+(1-9 x^2)^{3/2}}{\sqrt {1-9 x^2}} \, dx\) [177]
\(\int \genfrac {}{}{}{}{(-3+2 \sqrt {x}) (-3 \sqrt {x}+x)^{2/3}}{\sqrt {x}} \, dx\) [178]
\(\int \genfrac {}{}{}{}{9-9 \sqrt {x}+2 x}{\sqrt [3]{-3 \sqrt {x}+x}} \, dx\) [179]
\(\int \genfrac {}{}{}{}{1}{\sqrt {4-9 x^2}} \, dx\) [180]
\(\int \genfrac {}{}{}{}{1}{\sqrt {2-3 x} \sqrt {2+3 x}} \, dx\) [181]
\(\int \genfrac {}{}{}{}{1}{\sqrt {(2-3 x) (2+3 x)}} \, dx\) [182]
\(\int \genfrac {}{}{}{}{1}{\sqrt {15-2 x-x^2}} \, dx\) [183]
\(\int \genfrac {}{}{}{}{1}{\sqrt {3-x} \sqrt {5+x}} \, dx\) [184]
\(\int \genfrac {}{}{}{}{1}{\sqrt {(3-x) (5+x)}} \, dx\) [185]
\(\int \genfrac {}{}{}{}{1}{\sqrt {-15-8 x-x^2}} \, dx\) [186]
\(\int \genfrac {}{}{}{}{1}{\sqrt {-3-x} \sqrt {5+x}} \, dx\) [187]
\(\int \genfrac {}{}{}{}{1}{\sqrt {(-3-x) (5+x)}} \, dx\) [188]
\(\int (1-\sqrt {x}) \, dx\) [189]
\(\int \genfrac {}{}{}{}{1-x}{1+\sqrt {x}} \, dx\) [190]
\(\int \sqrt {\genfrac {}{}{}{}{1}{1-x^2}} \, dx\) [191]
\(\int \sqrt {\genfrac {}{}{}{}{1+x^2}{1-x^4}} \, dx\) [192]
\(\int \sqrt {\genfrac {}{}{}{}{1}{-1+x^2}} \, dx\) [193]
\(\int \sqrt {\genfrac {}{}{}{}{1+x^2}{-1+x^4}} \, dx\) [194]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1-x}} \, dx\) [195]
\(\int \genfrac {}{}{}{}{\sqrt {1+x}}{\sqrt {1-x^2}} \, dx\) [196]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+x}} \, dx\) [197]
\(\int \genfrac {}{}{}{}{\sqrt {1-x}}{\sqrt {1-x^2}} \, dx\) [198]
\(\int \sqrt {1-x} \, dx\) [199]
\(\int \genfrac {}{}{}{}{\sqrt {1-x^2}}{\sqrt {1+x}} \, dx\) [200]