Динара
Сообщение
#4523 8.6.2007, 9:57
Помогите, пожалуйста, найти интеграл
int dx/(x * (1 + x^2)^(1/2))
Lion
Сообщение
#4526 8.6.2007, 10:19
int dx/(x * (1 + x^2)^(1/2)) = | t = 1/x; x = 1/t; dx = -1/t^2 dt | =
= int -1/t^2 dt/(1/t * (1 + 1/t^2)^(1/2)) = -int dt/(t * (1 + 1/t^2)^(1/2)) =
= -int dt/((1 + 1/t^2) * t^2)^(1/2) = -int dt/(t^2 + 1)^(1/2) =
= -ln |t + (t^2 + 1)^(1/2)| + C = | t = 1/x | =
= -ln |1/x + (1/x^2 + 1)^(1/2)| + C = -ln |1/x + (x^2 + 1)^(1/2)/x| + C =
= -ln |(1 + (x^2 + 1)^(1/2))/x| + C