integral of (3/x-5/(x^6))

解

\int (\frac{3}{x} - \frac{5}{x ^{6}}) d x

3 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

解答ステップ

\int \frac{3}{x} - \frac{5}{x ^{6}} 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{5}{x ^{6}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{5}{x ^{6}} d x = - \frac{1}{x ^{5}}

= 3 ln ∣ x ∣ - (- \frac{1}{x ^{5}})

簡素化

= 3 ln ∣ x ∣ + \frac{1}{x ^{5}}

定数を解答に追加する

= 3 ln ∣ x ∣ + \frac{1}{x ^{5}} + C