Question

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

Answer 1

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