integral of 3/(x^4)-2/x

解

\int \frac{3}{x ^{4}} - \frac{2}{x} d x

- \frac{1}{x ^{3}} - 2 ln ∣ x ∣ + C

解答ステップ

\int \frac{3}{x ^{4}} - \frac{2}{x} 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 ^{4}} d x - \int \frac{2}{x} d x

\int \frac{3}{x ^{4}} d x = - \frac{1}{x ^{3}}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= - \frac{1}{x ^{3}} - 2 ln ∣ x ∣

定数を解答に追加する

= - \frac{1}{x ^{3}} - 2 ln ∣ x ∣ + C