tính nguyên hàm : căn bậc 2( (2/x) -1 )

Đáp án: $\sqrt{\dfrac{2-x}{x}}x+\arcsin \left(x-1\right)+C$

Giải thích các bước giải:

$\int\sqrt{\dfrac2x-1}dx$

$=\sqrt{\dfrac{2-x}{x}}x-\int \:-\dfrac{1}{x^{\dfrac{1}{2}}\sqrt{-x+2}}dx$

$=\sqrt{\dfrac{2-x}{x}}x+\int \dfrac{1}{\sqrt{-x^2+2x}}dx$

$=\sqrt{\dfrac{2-x}{x}}x+\int \dfrac{1}{\sqrt{-x^2+2x-1+1}}dx$

$=\sqrt{\dfrac{2-x}{x}}x+\int \dfrac{1}{\sqrt{-\left(x-1\right)^2+1}}dx$

$=\sqrt{\dfrac{2-x}{x}}x+\int \dfrac{1}{\sqrt{1-\left(x-1\right)^2}}dx$

$=\sqrt{\dfrac{2-x}{x}}x+\arcsin \left(x-1\right)+C$