3.3 Integrals 201 to 300

\(\int \sqrt {1+x} \, dx\) [201]
\(\int \genfrac {}{}{}{}{\sqrt {1-x^2}}{\sqrt {1-x}} \, dx\) [202]
\(\int (1-\sqrt [4]{x}) \, dx\) [203]
\(\int \genfrac {}{}{}{}{1-\sqrt {x}}{1+\sqrt [4]{x}} \, dx\) [204]
\(\int \genfrac {}{}{}{}{\sqrt {2+3 x}}{\sqrt {1+x}} \, dx\) [205]
\(\int \genfrac {}{}{}{}{\sqrt {1-x} \sqrt {2+3 x}}{\sqrt {1-x^2}} \, dx\) [206]
\(\int \genfrac {}{}{}{}{(1+x)^3}{x (1-x^2)^{3/2}} \, dx\) [207]
\(\int \genfrac {}{}{}{}{(1+x)^{3/2}}{(1-x)^{3/2} x} \, dx\) [208]
\(\int \genfrac {}{}{}{}{(1+a x)^3}{x (1-a^2 x^2)^{3/2}} \, dx\) [209]
\(\int \genfrac {}{}{}{}{(1+a x)^{3/2}}{x (1-a x)^{3/2}} \, dx\) [210]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1-x^2}} \, dx\) [211]
\(\int \genfrac {}{}{}{}{\sqrt {1+x^2}}{\sqrt {1-x^4}} \, dx\) [212]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+x^2}} \, dx\) [213]
\(\int \genfrac {}{}{}{}{\sqrt {1-x^2}}{\sqrt {1-x^4}} \, dx\) [214]
\(\int \sqrt {1-x^2} \, dx\) [215]
\(\int \genfrac {}{}{}{}{\sqrt {1-x^4}}{\sqrt {1+x^2}} \, dx\) [216]
\(\int \sqrt {1+x^2} \, dx\) [217]
\(\int \genfrac {}{}{}{}{\sqrt {1-x^4}}{\sqrt {1-x^2}} \, dx\) [218]
\(\int (\genfrac {}{}{}{}{a+b+c x^2}{d})^m \, dx\) [219]
\(\int \genfrac {}{}{}{}{1}{x-\sqrt {1+x^2}} \, dx\) [220]
\(\int \genfrac {}{}{}{}{1}{x-\sqrt {1-x^2}} \, dx\) [221]
\(\int \genfrac {}{}{}{}{1}{x-\sqrt {1+2 x^2}} \, dx\) [222]
\(\int \genfrac {}{}{}{}{2 x-x^3+x^2 \sqrt {2-x^2}}{-2+2 x^2} \, dx\) [223]
\(\int \genfrac {}{}{}{}{x \sqrt {2-x^2}}{x-\sqrt {2-x^2}} \, dx\) [224]
\(\int \genfrac {}{}{}{}{x}{-x+\sqrt {2 x-x^2}} \, dx\) [225]
\(\int \genfrac {}{}{}{}{x+\sqrt {2 x-x^2}}{2-2 x} \, dx\) [226]
\(\int \genfrac {}{}{}{}{\sqrt {2-x} \sqrt {x}+x}{2-2 x} \, dx\) [227]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{\sqrt {2-x}-\sqrt {x}} \, dx\) [228]
\(\int \genfrac {}{}{}{}{1}{((1+x) (-1+x^2))^{2/3}} \, dx\) [229]
\(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt {x (1+x^2)}} \, dx\) [230]
\(\int \genfrac {}{}{}{}{-1+x^2}{(1+x^2) \sqrt {x+x^3}} \, dx\) [231]
\(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{(-1+x^2)^2}{x (1+x^2)}}}{1+x^2} \, dx\) [232]
\(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{(-1+x^2)^2}{x+x^3}}}{1+x^2} \, dx\) [233]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+\genfrac {}{}{}{}{b}{x^2}} \sqrt {c+d x^2}} \, dx\) [234]
\(\int \genfrac {}{}{}{}{\sqrt {-2 x^2+x^4}}{(1-x^2) (2+x^2)} \, dx\) [235]
\(\int (1+\genfrac {}{}{}{}{2 x}{1+x^2})^{5/2} \, dx\) [236]
\(\int (1+\genfrac {}{}{}{}{2 x}{1+x^2})^{3/2} \, dx\) [237]
\(\int \sqrt {1+\genfrac {}{}{}{}{2 x}{1+x^2}} \, dx\) [238]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1+\genfrac {}{}{}{}{2 x}{1+x^2}}} \, dx\) [239]
\(\int \genfrac {}{}{}{}{1}{(1+\genfrac {}{}{}{}{2 x}{1+x^2})^{3/2}} \, dx\) [240]
\(\int \genfrac {}{}{}{}{\sqrt {1+\genfrac {}{}{}{}{2 x}{1+x^2}}}{1+x^2} \, dx\) [241]
\(\int \genfrac {}{}{}{}{A+B x^2+C x^4}{\sqrt {c+\genfrac {}{}{}{}{d}{x^2}} \sqrt {a+b x^2}} \, dx\) [242]
\(\int \sqrt {x-x^2} F(x) \, dx\) [243]
\(\int \genfrac {}{}{}{}{F(x)}{\sqrt {x-x^2}} \, dx\) [244]
\(\int \sqrt {1-x} \sqrt {x} F(x) \, dx\) [245]
\(\int \genfrac {}{}{}{}{F(x)}{\sqrt {1-x} \sqrt {x}} \, dx\) [246]
\(\int F(\genfrac {}{}{}{}{a+b x}{x}) \, dx\) [247]
\(\int F(\genfrac {}{}{}{}{a+b x^2}{x^2}) \, dx\) [248]
\(\int F(\genfrac {}{}{}{}{x}{a+b x}) \, dx\) [249]
\(\int F(\genfrac {}{}{}{}{x^2}{a+b x^2}) \, dx\) [250]
\(\int F(\genfrac {}{}{}{}{x^2}{(a+b x)^2}) \, dx\) [251]
\(\int F(\genfrac {}{}{}{}{x^4}{(a+b x^2)^2}) \, dx\) [252]
\(\int \genfrac {}{}{}{}{\sqrt {b x^2+\sqrt {a+b^2 x^4}}}{\sqrt {a+b^2 x^4}} \, dx\) [253]
\(\int \genfrac {}{}{}{}{\sqrt {-b x^2+\sqrt {a+b^2 x^4}}}{\sqrt {a+b^2 x^4}} \, dx\) [254]
\(\int \genfrac {}{}{}{}{\sqrt {2 x^2+\sqrt {3+4 x^4}}}{(c+d x) \sqrt {3+4 x^4}} \, dx\) [255]
\(\int \genfrac {}{}{}{}{\sqrt {2 x^2+\sqrt {3+4 x^4}}}{(c+d x)^2 \sqrt {3+4 x^4}} \, dx\) [256]
\(\int \genfrac {}{}{}{}{(a+b x^2) (a e+5 b e x^2)}{c+d x^2 (a+b x^2)^4} \, dx\) [257]
\(\int \genfrac {}{}{}{}{(a+b x^2) (a e+5 b e x^2)}{c+a^4 d x^2+4 a^3 b d x^4+6 a^2 b^2 d x^6+4 a b^3 d x^8+b^4 d x^{10}} \, dx\) [258]
\(\int \genfrac {}{}{}{}{a^2 e+6 a b e x^2+5 b^2 e x^4}{c+d x^2 (a+b x^2)^4} \, dx\) [259]
\(\int \genfrac {}{}{}{}{x (a+b x^2) (a e+3 b e x^2)}{c+d x^4 (a+b x^2)^4} \, dx\) [260]
\(\int \genfrac {}{}{}{}{x (a+b x^2) (a e+3 b e x^2)}{c+a^4 d x^4+4 a^3 b d x^6+6 a^2 b^2 d x^8+4 a b^3 d x^{10}+b^4 d x^{12}} \, dx\) [261]
\(\int \genfrac {}{}{}{}{a^2 e x+4 a b e x^3+3 b^2 e x^5}{c+d x^4 (a+b x^2)^4} \, dx\) [262]
\(\int \genfrac {}{}{}{}{(a+b x^2) (a e+5 b e x^2)}{c-d x^2 (a+b x^2)^4} \, dx\) [263]
\(\int \genfrac {}{}{}{}{(a+b x^2) (a e+5 b e x^2)}{c-a^4 d x^2-4 a^3 b d x^4-6 a^2 b^2 d x^6-4 a b^3 d x^8-b^4 d x^{10}} \, dx\) [264]
\(\int \genfrac {}{}{}{}{a^2 e+6 a b e x^2+5 b^2 e x^4}{c-d x^2 (a+b x^2)^4} \, dx\) [265]
\(\int \genfrac {}{}{}{}{x (a+b x^2) (a e+3 b e x^2)}{c-d x^4 (a+b x^2)^4} \, dx\) [266]
\(\int \genfrac {}{}{}{}{x (a+b x^2) (a e+3 b e x^2)}{c-a^4 d x^4-4 a^3 b d x^6-6 a^2 b^2 d x^8-4 a b^3 d x^{10}-b^4 d x^{12}} \, dx\) [267]
\(\int \genfrac {}{}{}{}{a^2 e x+4 a b e x^3+3 b^2 e x^5}{c-d x^4 (a+b x^2)^4} \, dx\) [268]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} (a e+4 b e x^2)}{c+d x^2 (a+b x^2)^3} \, dx\) [269]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} (a e+4 b e x^2)}{c+a^3 d x^2+3 a^2 b d x^4+3 a b^2 d x^6+b^3 d x^8} \, dx\) [270]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} (a e+4 b e x^2)}{c-d x^2 (a+b x^2)^3} \, dx\) [271]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} (a e+4 b e x^2)}{c-a^3 d x^2-3 a^2 b d x^4-3 a b^2 d x^6-b^3 d x^8} \, dx\) [272]
\(\int \genfrac {}{}{}{}{x^2 \sqrt {a+b x^2} (a e+2 b e x^2)}{c+d x^6 (a+b x^2)^3} \, dx\) [273]
\(\int \genfrac {}{}{}{}{x^2 \sqrt {a+b x^2} (a e+2 b e x^2)}{c+a^3 d x^6+3 a^2 b d x^8+3 a b^2 d x^{10}+b^3 d x^{12}} \, dx\) [274]
\(\int \genfrac {}{}{}{}{x^2 \sqrt {a+b x^2} (a e+2 b e x^2)}{c-d x^6 (a+b x^2)^3} \, dx\) [275]
\(\int \genfrac {}{}{}{}{x^2 \sqrt {a+b x^2} (a e+2 b e x^2)}{c-a^3 d x^6-3 a^2 b d x^8-3 a b^2 d x^{10}-b^3 d x^{12}} \, dx\) [276]
\(\int \genfrac {}{}{}{}{2-5 x^3}{\sqrt {1-x^3} (1+x^2 (1-x^3))} \, dx\) [277]
\(\int \genfrac {}{}{}{}{2-5 x^3}{\sqrt {1-x^3} (1+x^2-x^5)} \, dx\) [278]
\(\int \genfrac {}{}{}{}{-4+x}{(1+\sqrt [3]{x}) \sqrt {x}} \, dx\) [279]
\(\int \genfrac {}{}{}{}{1+\sqrt {x}}{x^{5/6}+x^{7/6}} \, dx\) [280]
\(\int \genfrac {}{}{}{}{1+\sqrt {x}}{(1+\sqrt [3]{x}) \sqrt {x}} \, dx\) [281]
\(\int \genfrac {}{}{}{}{\sqrt {2+\genfrac {}{}{}{}{b}{x^2}}}{b+2 x^2} \, dx\) [282]
\(\int \genfrac {}{}{}{}{\sqrt {2-\genfrac {}{}{}{}{b}{x^2}}}{-b+2 x^2} \, dx\) [283]
\(\int \genfrac {}{}{}{}{\sqrt {a+\genfrac {}{}{}{}{c}{x^2}}}{d+e x} \, dx\) [284]
\(\int \genfrac {}{}{}{}{\sqrt {a+\genfrac {}{}{}{}{c}{x^2}+\genfrac {}{}{}{}{b}{x}}}{d+e x} \, dx\) [285]
\(\int \genfrac {}{}{}{}{\sqrt [6]{x}+\sqrt [5]{x^3}}{\sqrt {x}} \, dx\) [286]
\(\int \genfrac {}{}{}{}{2+x}{\sqrt {4 x-x^2}} \, dx\) [287]
\(\int \genfrac {}{}{}{}{3+x}{\sqrt [3]{6 x+x^2}} \, dx\) [288]
\(\int \genfrac {}{}{}{}{4+x}{(6 x-x^2)^{3/2}} \, dx\) [289]
\(\int \genfrac {}{}{}{}{1}{(1+x) \sqrt {2 x+x^2}} \, dx\) [290]
\(\int \genfrac {}{}{}{}{1}{(1+2 x) \sqrt {x+x^2}} \, dx\) [291]
\(\int \genfrac {}{}{}{}{-1+x}{\sqrt {2 x-x^2}} \, dx\) [292]
\(\int \genfrac {}{}{}{}{\sqrt {x-x^2}}{1+x} \, dx\) [293]
\(\int \sqrt {\sqrt [4]{x}+x} \, dx\) [294]
\(\int \sqrt {x+x^{3/2}} \, dx\) [295]
\(\int x \sqrt {x+x^{3/2}} \, dx\) [296]
\(\int (1-x^2) \sqrt {\genfrac {}{}{}{}{1}{2-x^2}} \, dx\) [297]
\(\int \sqrt {x^2+x^3-x^4} \, dx\) [298]
\(\int \genfrac {}{}{}{}{1}{\sqrt {(a^2+x^2)^3}} \, dx\) [299]
\(\int \genfrac {}{}{}{}{\sqrt {x}}{1+\sqrt {x}+x} \, dx\) [300]