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

解

\int (\frac{3}{t} - \frac{2}{t ^{2}}) d t

3 ln ∣ t ∣ + \frac{2}{t} + C

解答ステップ

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

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}{t} d t - \int \frac{2}{t ^{2}} d t

\int \frac{3}{t} d t = 3 ln ∣ t ∣

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

= 3 ln ∣ t ∣ - (- \frac{2}{t})

簡素化

= 3 ln ∣ t ∣ + \frac{2}{t}

定数を解答に追加する

= 3 ln ∣ t ∣ + \frac{2}{t} + C