Question

Найти интеграл пж... ​

Answer 1

$\int \dfrac{dx}{x\sqrt{4x-5x^2}}=\Big[\; x=\dfrac{1}{t}\ ,\ dx=-\dfrac{dt}{t^2}\; \Big]=\int \dfrac{-dt}{t^2\cdot \frac{1}{t}\cdot \sqrt{\frac{4}{t}-\frac{5}{t^2}}}=\\\\\\=-\int \dfrac{dt}{\sqrt{4t-5}}=-2\cdot \dfrac{1}{4}\, \sqrt{4t-5}+C=-\dfrac{1}{2}\cdot \sqrt{\dfrac{4}{x}-5}+C=-\dfrac{1}{2}\cdot \sqrt{\dfrac{4-5x}{x}}+C$