Date/Time: 2010-05-28 10:39 (UTC)Posted by: [identity profile] unibasil.livejournal.com
Неопределённый интеграл:
∫(n/x^n)dx = n*∫x^(-n)dx = n (x^(-n+1))/(-n+1) + с

т.е. для n=2:

2
2*∫x^(-2) = 2*((2^(-1)/(-1) - (1^(-1)/(-1)) = 2*(-½ - (-1)) = 2 * ½ = 1
1

n=3:

2
3*∫x^(-3) = 2*((2^(-2)/(-2) - (1^(-2)/(-2)) = 2*(2 - 1) = 2 * (- ¼ /2 + ½) =
1

= 2 * ⅜ = ¾

Как-то так... За безошибочность вычислений не ручаюсь – торопился... ;)
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