tính tích phân

N

nguyenbahiep1

bài này có thể đặt................................................................

[laTEX]1- x = \frac{1}{t}[/laTEX]
 
N

nguyenbahiep1

[laTEX]I = \int_{0}^{1}\frac{dx}{(1-x)\sqrt{(x-1)(3x+1)}} \\ \\ 1-x = \frac{1}{t} \Rightarrow dx = \frac{dt}{t^2} \\ \\ I = \int_{0}^{1}\frac{-dt}{t^2.\frac{1}{t}.\sqrt{(\frac{1}{t}-1)(\frac{3}{t}+1)}} \\ \\ I = \int_{0}^{1}\frac{-dt}{\sqrt{3-2t-t^2}} \\ \\ I = \int_{0}^{1}\frac{-dt}{\sqrt{4 - (t+1)^2}} \\ \\ t+1 = 2sinu[/laTEX]
 
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