Question

Нужно найти неопределенный интеграл.​

Answer 1

$int frac{dx}{sqrt{2x+3-x^2}}=Big [; 2x+3-x^2=-(x^2-2x-3)=-Big ((x-1)^2-1-3Big )=\\\=4-(x-1)^2; Big ]=int frac{dx}{sqrt{4-(x-1)^2}}=Big [; d(x-1)=(x-1)', dx=dx; Big ]=\\\=int frac{d(x-1)}{sqrt{4-(x-1)^2}}=Big [; int frac{dt}{sqrt{4-t^2}}=arcsinfrac{t}{2}+C; Big ]=arcsinfrac{x-1}{2}+C$