Question

Найти неопределенный интеграл ∫\frac{dx}{\sqrt{25-9x^{2}}}

Answer 1

$\int {\frac{1}{\sqrt{25-9x^2}}} \, dx = \int {\frac{1}{ \sqrt{5^2-(3x)^2} }} \, dx = \\ 3x=t\\ 3dx=dt \\ \int {\frac{dt}{3\sqrt{5^2-t^2}}} = \frac{1}{3} \cdot arcsin(\frac{t}{5})+C = \frac{1}{3} arcsin(\frac{3x}{5})+C$