integral of 1/((x-5)^2)-1

解答

\int \frac{1}{( x - 5 ) ^{2}} - 1 d x

- \frac{1}{x - 5} - x + C

求解步骤

\int \frac{1}{( x - 5 ) ^{2}} - 1 d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{( x - 5 ) ^{2}} d x - \int 1 d x

\int \frac{1}{( x - 5 ) ^{2}} d x = - \frac{1}{x - 5}

\int 1 d x = x

= - \frac{1}{x - 5} - x

解答补常数

= - \frac{1}{x - 5} - x + C

d er i v a t i v e \frac{1}{2 x}

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