3.10 Integrals 901 to 1000

3.10.1 \(\int \sqrt {x-x^2} F(x) \, dx\) [901]
3.10.2 \(\int \genfrac {}{}{}{}{F(x)}{\sqrt {x-x^2}} \, dx\) [902]
3.10.3 \(\int \sqrt {1-x} \sqrt {x} F(x) \, dx\) [903]
3.10.4 \(\int \genfrac {}{}{}{}{F(x)}{\sqrt {1-x} \sqrt {x}} \, dx\) [904]
3.10.5 \(\int F(\genfrac {}{}{}{}{a+b x}{x}) \, dx\) [905]
3.10.6 \(\int F(\genfrac {}{}{}{}{a+b x^2}{x^2}) \, dx\) [906]
3.10.7 \(\int F(\genfrac {}{}{}{}{x}{a+b x}) \, dx\) [907]
3.10.8 \(\int F(\genfrac {}{}{}{}{x^2}{a+b x^2}) \, dx\) [908]
3.10.9 \(\int F(\genfrac {}{}{}{}{x^2}{(a+b x)^2}) \, dx\) [909]
3.10.10 \(\int F(\genfrac {}{}{}{}{x^4}{(a+b x^2)^2}) \, dx\) [910]
3.10.11 \(\int \genfrac {}{}{}{}{\sqrt {b x^2+\sqrt {a+b^2 x^4}}}{\sqrt {a+b^2 x^4}} \, dx\) [911]
3.10.12 \(\int \genfrac {}{}{}{}{\sqrt {-b x^2+\sqrt {a+b^2 x^4}}}{\sqrt {a+b^2 x^4}} \, dx\) [912]
3.10.13 \(\int \genfrac {}{}{}{}{\sqrt {2 x^2+\sqrt {3+4 x^4}}}{(c+d x) \sqrt {3+4 x^4}} \, dx\) [913]
3.10.14 \(\int \genfrac {}{}{}{}{\sqrt {2 x^2+\sqrt {3+4 x^4}}}{(c+d x)^2 \sqrt {3+4 x^4}} \, dx\) [914]
3.10.15 \(\int \genfrac {}{}{}{}{-4+x}{(1+\sqrt [3]{x}) \sqrt {x}} \, dx\) [915]
3.10.16 \(\int \genfrac {}{}{}{}{1+\sqrt {x}}{x^{5/6}+x^{7/6}} \, dx\) [916]
3.10.17 \(\int \genfrac {}{}{}{}{1+\sqrt {x}}{(1+\sqrt [3]{x}) \sqrt {x}} \, dx\) [917]
3.10.18 \(\int \genfrac {}{}{}{}{\sqrt {2+\genfrac {}{}{}{}{b}{x^2}}}{b+2 x^2} \, dx\) [918]
3.10.19 \(\int \genfrac {}{}{}{}{\sqrt {2-\genfrac {}{}{}{}{b}{x^2}}}{-b+2 x^2} \, dx\) [919]
3.10.20 \(\int \genfrac {}{}{}{}{\sqrt {a+\genfrac {}{}{}{}{c}{x^2}}}{d+e x} \, dx\) [920]
3.10.21 \(\int \genfrac {}{}{}{}{\sqrt {a+\genfrac {}{}{}{}{c}{x^2}+\genfrac {}{}{}{}{b}{x}}}{d+e x} \, dx\) [921]
3.10.22 \(\int \genfrac {}{}{}{}{\sqrt [6]{x}+\sqrt [5]{x^3}}{\sqrt {x}} \, dx\) [922]
3.10.23 \(\int \genfrac {}{}{}{}{2+x}{\sqrt {4 x-x^2}} \, dx\) [923]
3.10.24 \(\int \genfrac {}{}{}{}{3+x}{\sqrt [3]{6 x+x^2}} \, dx\) [924]
3.10.25 \(\int \genfrac {}{}{}{}{4+x}{(6 x-x^2)^{3/2}} \, dx\) [925]
3.10.26 \(\int \genfrac {}{}{}{}{1}{(1+x) \sqrt {2 x+x^2}} \, dx\) [926]
3.10.27 \(\int \genfrac {}{}{}{}{1}{(1+2 x) \sqrt {x+x^2}} \, dx\) [927]
3.10.28 \(\int \genfrac {}{}{}{}{-1+x}{\sqrt {2 x-x^2}} \, dx\) [928]
3.10.29 \(\int \genfrac {}{}{}{}{\sqrt {x-x^2}}{1+x} \, dx\) [929]
3.10.30 \(\int \sqrt {\sqrt [4]{x}+x} \, dx\) [930]
3.10.31 \(\int \sqrt {x+x^{3/2}} \, dx\) [931]
3.10.32 \(\int x \sqrt {x+x^{3/2}} \, dx\) [932]
3.10.33 \(\int (1-x^2) \sqrt {\genfrac {}{}{}{}{1}{2-x^2}} \, dx\) [933]
3.10.34 \(\int \sqrt {x^2+x^3-x^4} \, dx\) [934]
3.10.35 \(\int \genfrac {}{}{}{}{1}{\sqrt {(a^2+x^2)^3}} \, dx\) [935]
3.10.36 \(\int \genfrac {}{}{}{}{\sqrt {x}}{1+\sqrt {x}+x} \, dx\) [936]
3.10.37 \(\int \genfrac {}{}{}{}{x}{1+\sqrt {x}+x} \, dx\) [937]
3.10.38 \(\int \genfrac {}{}{}{}{1}{\sqrt {x} (1+\sqrt {x}+x)^{7/2}} \, dx\) [938]
3.10.39 \(\int \genfrac {}{}{}{}{-1+x}{1+\sqrt {1+x^2}} \, dx\) [939]
3.10.40 \(\int \genfrac {}{}{}{}{1}{(1+x)^{2/3} (-1+x^2)^{2/3}} \, dx\) [940]
3.10.41 \(\int ((1-x^6)^{2/3}+\genfrac {}{}{}{}{(1-x^6)^{2/3}}{x^6}) \, dx\) [941]
3.10.42 \(\int \genfrac {}{}{}{}{x^{-1+m} (2 a m+b (2 m-n) x^n)}{2 (a+b x^n)^{3/2}} \, dx\) [942]
3.10.43 \(\int \genfrac {}{}{}{}{x-2 x^3}{\sqrt {2+3 x}} \, dx\) [943]
3.10.44 \(\int \genfrac {}{}{}{}{1}{\sqrt [4]{1+x}+\sqrt {1+x}} \, dx\) [944]
3.10.45 \(\int \genfrac {}{}{}{}{1+2 x}{\sqrt {x+x^2}} \, dx\) [945]
3.10.46 \(\int \genfrac {}{}{}{}{1}{2 \sqrt {x} (1+x)} \, dx\) [946]
3.10.47 \(\int \genfrac {}{}{}{}{1}{x \sqrt {6 x-x^2}} \, dx\) [947]
3.10.48 \(\int (1+\sqrt {x}) \sqrt {x} \, dx\) [948]
3.10.49 \(\int \genfrac {}{}{}{}{1-\sqrt {x}}{\sqrt [3]{x}} \, dx\) [949]
3.10.50 \(\int \genfrac {}{}{}{}{\sqrt {x}}{1+\sqrt [3]{x}} \, dx\) [950]
3.10.51 \(\int \genfrac {}{}{}{}{\sqrt [3]{1+\sqrt {x}}}{x} \, dx\) [951]
3.10.52 \(\int (1-\sqrt {x}) \, dx\) [952]
3.10.53 \(\int (1-\sqrt [4]{x}) \, dx\) [953]
3.10.54 \(\int \genfrac {}{}{}{}{1-\sqrt {x}}{1+\sqrt [4]{x}} \, dx\) [954]
3.10.55 \(\int \genfrac {}{}{}{}{1}{\sqrt {(a+b x) (c+d x)}} \, dx\) [955]
3.10.56 \(\int \genfrac {}{}{}{}{1}{\sqrt {(a+b x) (c-d x)}} \, dx\) [956]
3.10.57 \(\int \genfrac {}{}{}{}{1}{\sqrt {x} (1-x^2)} \, dx\) [957]
3.10.58 \(\int \genfrac {}{}{}{}{\sqrt {x}}{x-x^3} \, dx\) [958]
3.10.59 \(\int \genfrac {}{}{}{}{x}{2-\sqrt {3}+(1+\sqrt {3}) x+x^2} \, dx\) [959]
3.10.60 \(\int \sqrt {x^2+x^3} \, dx\) [960]
3.10.61 \(\int \genfrac {}{}{}{}{1}{(1+x) \sqrt {2 x+x^2}} \, dx\) [961]
3.10.62 \(\int \sqrt {1-\sqrt {x}-x} \sqrt {x} \, dx\) [962]
3.10.63 \(\int \sqrt [3]{1+\sqrt {-3+x}} \, dx\) [963]
3.10.64 \(\int \genfrac {}{}{}{}{1}{\sqrt {3+\sqrt {-1+2 x}}} \, dx\) [964]
3.10.65 \(\int \genfrac {}{}{}{}{\sqrt {1-x}}{1+\sqrt {x}} \, dx\) [965]
3.10.66 \(\int \genfrac {}{}{}{}{\sqrt {1-x}}{1-\sqrt {x}} \, dx\) [966]
3.10.67 \(\int \genfrac {}{}{}{}{x}{x-\sqrt {1+x^2}} \, dx\) [967]
3.10.68 \(\int \genfrac {}{}{}{}{x}{x-\sqrt {1-x^2}} \, dx\) [968]
3.10.69 \(\int \genfrac {}{}{}{}{x}{x-\sqrt {1+2 x^2}} \, dx\) [969]
3.10.70 \(\int \sqrt {x} \sqrt {\sqrt {x}+x} \, dx\) [970]
3.10.71 \(\int \genfrac {}{}{}{}{1+\sqrt [3]{x}}{1+\sqrt {x}} \, dx\) [971]
3.10.72 \(\int \genfrac {}{}{}{}{1+\sqrt [3]{x}}{1+\sqrt [4]{x}} \, dx\) [972]
3.10.73 \(\int \genfrac {}{}{}{}{x^2}{-1+x^2+\sqrt {1-x^2}} \, dx\) [973]
3.10.74 \(\int \sqrt {\genfrac {}{}{}{}{1+x}{x}} \, dx\) [974]
3.10.75 \(\int \sqrt {\genfrac {}{}{}{}{1-x}{x}} \, dx\) [975]
3.10.76 \(\int \sqrt {\genfrac {}{}{}{}{-1+x}{x}} \, dx\) [976]
3.10.77 \(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{1+x}{x}}}{x} \, dx\) [977]
3.10.78 \(\int \sqrt {\genfrac {}{}{}{}{x}{1+x}} \, dx\) [978]
3.10.79 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{-1-x}{x}}} \, dx\) [979]
3.10.80 \(\int \sqrt {(4-x) x} \, dx\) [980]
3.10.81 \(\int \genfrac {}{}{}{}{1}{\sqrt {(1-x) x}} \, dx\) [981]
3.10.82 \(\int \genfrac {}{}{}{}{x}{(x (2+x))^{3/2}} \, dx\) [982]
3.10.83 \(\int \genfrac {}{}{}{}{\sqrt {1+\genfrac {}{}{}{}{1}{x}}}{1-x^2} \, dx\) [983]
3.10.84 \(\int \genfrac {}{}{}{}{1}{1+\sqrt {5}-x^2+\sqrt {5} x^2} \, dx\) [984]
3.10.85 \(\int \genfrac {}{}{}{}{1}{\sqrt {a x+b x^2}} \, dx\) [985]
3.10.86 \(\int \genfrac {}{}{}{}{1}{\sqrt {x (a+b x)}} \, dx\) [986]
3.10.87 \(\int \genfrac {}{}{}{}{1}{\sqrt {(b+\genfrac {}{}{}{}{a}{x}) x^2}} \, dx\) [987]
3.10.88 \(\int \genfrac {}{}{}{}{1}{\sqrt {(\genfrac {}{}{}{}{a}{x^2}+\genfrac {}{}{}{}{b}{x}) x^3}} \, dx\) [988]
3.10.89 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a x^2+b x^3}{x}}} \, dx\) [989]
3.10.90 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a x^3+b x^4}{x^2}}} \, dx\) [990]
3.10.91 \(\int \genfrac {}{}{}{}{1}{\sqrt {a c x+b c x^2}} \, dx\) [991]
3.10.92 \(\int \genfrac {}{}{}{}{1}{\sqrt {c (a x+b x^2)}} \, dx\) [992]
3.10.93 \(\int \genfrac {}{}{}{}{1}{\sqrt {c x (a+b x)}} \, dx\) [993]
3.10.94 \(\int \genfrac {}{}{}{}{1}{\sqrt {c (b+\genfrac {}{}{}{}{a}{x}) x^2}} \, dx\) [994]
3.10.95 \(\int \sqrt {1-x^2+x \sqrt {-1+x^2}} \, dx\) [995]
3.10.96 \(\int \genfrac {}{}{}{}{\sqrt {-x+\sqrt {x} \sqrt {1+x}}}{\sqrt {1+x}} \, dx\) [996]
3.10.97 \(\int -\genfrac {}{}{}{}{x+2 \sqrt {1+x^2}}{x+x^3+\sqrt {1+x^2}} \, dx\) [997]
3.10.98 \(\int \genfrac {}{}{}{}{1+2 x}{(1+x^2) \sqrt {2+2 x+x^2}} \, dx\) [998]
3.10.99 \(\int \genfrac {}{}{}{}{1}{(1+x^4) \sqrt {-x^2+\sqrt {1+x^4}}} \, dx\) [999]
3.10.100 \(\int \genfrac {}{}{}{}{1}{(a+b x^4) \sqrt {c x^2+d \sqrt {a+b x^4}}} \, dx\) [1000]