\(\int\frac{\text{d}x}{\sqrt{1-x}}=\)
\(\dfrac{C}{\sqrt{1-x}}\). \(C\sqrt{1-x}\). \(-2\sqrt{1-x}+C\). \(\dfrac{2}{\sqrt{1-x}}+C\). Hướng dẫn giải:Điều kiện \(x< 1\), khi đó:
\(\int\frac{\text{d}x}{\sqrt{1-x}}=\int\left(1-x\right)^{-\frac{1}{2}}\text{d}x=-\int\left(1-x\right)^{-\frac{1}{2}}\text{d}\left(1-x\right)\)
\(=-\dfrac{1}{-\frac{1}{2}+1}\left(1-x\right)^{-\frac{1}{2}+1}+C\)
\(=-2\left(1-x\right)^{\frac{1}{2}}+C\)
\(=-2\sqrt{\left(1-x\right)}+C\).