Question

Найти интеграл
dx/(5*x^2-9)

Answer 1

$int frac{dx}{5x^2-9}=frac{1}{5}intfrac{dx}{x^2-frac{9}{5}}=frac{1}{5}cdot frac{1}{2cdot frac{3}{sqrt5}}cdot lnBig |frac{x- frac{3}{sqrt5} }{x+ frac{3}{sqrt5}}Big |+C=\\=frac{1}{6sqrt5}cdot lnBig |frac{sqrt5x-3}{sqrt5x+3}Big |+C$