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

解

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

- \frac{1}{x} + \frac{2}{x} + 5 x + C

解答ステップ

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

総和規則を適用する:

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

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

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

\int \frac{1}{x x} d x = - \frac{2}{x}

\int 5 d x = 5 x

= - \frac{1}{x} - (- \frac{2}{x}) + 5 x

簡素化

= - \frac{1}{x} + \frac{2}{x} + 5 x

定数を解答に追加する

= - \frac{1}{x} + \frac{2}{x} + 5 x + C