int dx/(x^2 * (x^2 + 7)^(1/2))
(IMG:style_emoticons/default/smile.gif) напишите, пожалуйста, как решать этот интеграл? (IMG:style_emoticons/default/unsure.gif)

int dx/(x^2 * (x^2 + 7)^(1/2)) = | x = 1/t; t = 1/x; dx = -1/t^2 dt | =
= -int (1/t^2)/(1/t^2 * (1/t^2 + 7)^(1/2)) dt = -int dt/(1/t^2 + 7)^(1/2) =
= -int t dt/(7 * t^2 + 1)^(1/2) = -1/2 * int d(t^2)/(7 * t^2 + 1)^(1/2) = | t^2 = u | =
= -1/2 * int du/(7 * u + 1)^(1/2) = -1/2 * int (7 * u + 1)^(-1/2) du =
= -1/2 * 1/7 * 1/(-1/2 + 1) * (7 * u + 1)^(-1/2 + 1) + C =
= -1/7 * (7 * u + 1)^(1/2) + C = | u = t^2 | = -1/7 * (7 * t^2 + 1)^(1/2) + C =
= | t = 1/x | = -1/7 * (7/x^2 + 1)^(1/2) + C = -1/7 * (x^2 + 7)^(1/2)/x + C