Question

Ребят, решите интеграл

Answer 1

$\int { \frac{1}{3+2x^{2}} } \, dx = \int { \frac{1}{3(1+ \frac{2x^{2}}{3} )} } \, dx= \frac{1}{3} \int { \frac{1}{1+ \frac{2x^{2}}{3}} } \, dx= \frac{1}{3} \int { \frac{1}{1+ ( \frac{ \sqrt{2} x}{ \sqrt{3} } )^{2}} } \, dx= \\ = \frac{ \sqrt{3} }{3 \sqrt{2} } \int { \frac{1}{1+ ( \frac{ \sqrt{2} x}{ \sqrt{3} } )^{2}} } \, d(\frac{ \sqrt{2} x}{ \sqrt{3} })= \frac{ \sqrt{6} }{6} arctg(\frac{ \sqrt{6} x}{ 3 })+C$