Задача 71089 integrate 3/(6x ^ 2 + 4x + 7) dx...
Условие
86
Решение
★
6x^2+4x+7=6*(x^2+2x+1-1+(7/6))=6*((x+1)^2+(1/6))
∫ 3dx/(6x^2+4x+7)=(3/6) ∫ dx/((x+1)^2+(1/6))=(1/2)*1/(sqrt(1/6))arctg (x+1)/(sqrt(1/6))+C=
=(sqrt(6)/2)arctg(sqrt(6)*(x+1))+C