Tính ∫dx/√1−x A. C/√1−x. B. −2√1−x+C. C. 2/√1−x+C. D. C√1−x

Question

Tính \(\int \frac{dx}{\sqrt{1-x} }  \)
 

A. \(\frac{C}{\sqrt{1-x} } . \)

B. \(-2\sqrt{1-x} +C. \)

C. \(\frac{2}{\sqrt{1-x} } +C. \)

D. \(C\sqrt{1-x} . \)

Answer 1

Chọn B

Đặt \( t=\sqrt{1-x} .\)
\(\Rightarrow t^{2} =1-x. \)
\(\Rightarrow 2tdt=-dx\Rightarrow -2tdt=dx. \)
Ta có:\(\int \frac{dx}{\sqrt{1-x} }  =\int \frac{-2tdt}{t}  \)

           \(=-2\int dt =-2t+C=-2\sqrt{1-x} +C.\)

Vậy \(\int \frac{dx}{\sqrt{1-x} }  =-2\sqrt{1-x} +C\)