Question

найти интеграл dx/(2+3x^2)

Answer 1

$intfrac{dx}{2+3x^2}=int frac{dx}{(sqrt2)^2+(sqrt3x)^2}=frac{1}{sqrt2}cdot frac{1}{sqrt3}arctgfrac{sqrt3x}{sqrt2}+C=frac{1}{sqrt6}arctgfrac{sqrt3x}{sqrt2}+C$