Помогите, пожалуйста, найти интеграл
int (1 + x^2)^(1/2)/x^2 dx
int (1 + x^2)^(1/2)/x^2 dx = int (1 + x^2)^(1/2) d(-1/x) =
= -int (1 + x^2)^(1/2) d(1/x) = -1/x * (1 + x^2)^(1/2) + int 1/x d((1 + x^2)^(1/2)) =
= -1/x * (1 + x^2)^(1/2) + int 1/x * 1/2 * (1 + x^2)^(-1/2) * 2 * x dx =
= -1/x * (1 + x^2)^(1/2) + int (1 + x^2)^(-1/2) dx =
= -1/x * (1 + x^2)^(1/2) + int 1/(1 + x^2)^(1/2) dx =
= -1/x * (1 + x^2)^(1/2) + ln |x + (x^2 + 1)^(1/2)| + C
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