integral of (5x+4)/(x^3)

解

\int \frac{5 x + 4}{x ^{3}} d x

- \frac{5}{x} - \frac{2}{x ^{2}} + C

解答ステップ

\int \frac{5 x + 4}{x ^{3}} d x

拡張

\frac{5 x + 4}{x ^{3}} : \frac{5}{x ^{2}} + \frac{4}{x ^{3}}

= \int \frac{5}{x ^{2}} + \frac{4}{x ^{3}} 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{5}{x ^{2}} d x + \int \frac{4}{x ^{3}} d x

\int \frac{5}{x ^{2}} d x = - \frac{5}{x}

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

= - \frac{5}{x} - \frac{2}{x ^{2}}

定数を解答に追加する

= - \frac{5}{x} - \frac{2}{x ^{2}} + C