integral of 3/x-2/(x^2)

解

\int \frac{3}{x} - \frac{2}{x ^{2}} d x

3 ln ∣ x ∣ + \frac{2}{x} + C

解答ステップ

\int \frac{3}{x} - \frac{2}{x ^{2}} 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{3}{x} d x - \int \frac{2}{x ^{2}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ - (- \frac{2}{x})

簡素化

= 3 ln ∣ x ∣ + \frac{2}{x}

定数を解答に追加する

= 3 ln ∣ x ∣ + \frac{2}{x} + C