Question

найти интеграл ∫36dx/3+4x^2

Answer 1

$int dfrac{36dx}{3+4x^2} = frac{36}{3} int dfrac{dx}{1+( frac{2}{ sqrt3 } x)^2} = frac{36}{3} cdotfrac{sqrt3}{2} int dfrac{d( frac{2}{ sqrt3 } x)}{1+( frac{2}{ sqrt3 } x)^2} =\ = 6sqrt3 arctg( frac{2}{ sqrt3 } x)+C.$