integral of-7x-3+2/(x-1)

解

\int - 7 x - 3 + \frac{2}{x - 1} d x

- \frac{7 x ^{2}}{2} - 3 x + 2 ln ∣ x - 1 ∣ + C

解答ステップ

\int - 7 x - 3 + \frac{2}{x - 1} 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 7 x d x - \int 3 d x + \int \frac{2}{x - 1} d x

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 3 d x = 3 x

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

= - \frac{7 x ^{2}}{2} - 3 x + 2 ln ∣ x - 1 ∣

定数を解答に追加する

= - \frac{7 x ^{2}}{2} - 3 x + 2 ln ∣ x - 1 ∣ + C