Question

Решить интеграл ∫ $frac{x^2}{x^2+16} dx$

Answer 1

$intlimits^._. { frac{x^{2} }{ x^{2}+16}} , dx = intlimits^._. { frac{x^{2}+16-16 }{ x^{2}+16}} , dx = intlimits^._. {(1-16* frac{1 }{ x^{2}+16})} , dx = \ = intlimits^._. , dx -16 intlimits^._. { frac{1 }{ x^{2}+ 4^{2}}} , dx =x-16* frac{1}{4} *arctg( frac{x}{4})=x-4*arctg( frac{x}{4})$