Question

Решите интеграл пожалуйста

Answer 1

$\int\limits^3_{-1}\, \frac{dx}{2-5x}=-\frac{1}{5}\int \limits^3_{-1}\,\frac{-5\, dx}{2-5x}=-\frac{1}{5}\int\limits^3_{-1}\, \frac{d(2-5x)}{2-5x}=-\frac{1}{5}\cdot ln|2-5x|\, \Big |_{-1}^3=\\\\\\=-\frac{1}{5}\cdot (ln13-ln7)=-\frac{1}{5}\cdot ln\frac{13}{7}=\frac{1}{5}\cdot ln\frac{7}{13}$