Question

помогите найти интеграл. dx/3x^2-25

Answer 1

$\int \frac{dx}{3x^2-25}=\int \frac{dx}{(\sqrt3x)^2-5^2}=\frac{1}{\sqrt3} \cdot \frac{1}{2\cdot 5}\cdot ln\Big |\frac{\sqrt3x-5}{\sqrt3x+5}\Big |+C=\\\\=\frac{1}{10\sqrt3}\cdot ln\Big |\frac{\sqrt3x-5}{\sqrt3x+5}\Big |+C$