integral of (2/(x^3)+3/(x^3)+5)

解

\int (\frac{2}{x ^{3}} + \frac{3}{x ^{3}} + 5) d x

- \frac{1}{x ^{2}} - \frac{3}{2 x ^{2}} + 5 x + C

解答ステップ

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

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

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

\int 5 d x = 5 x

= - \frac{1}{x ^{2}} - \frac{3}{2 x ^{2}} + 5 x

定数を解答に追加する

= - \frac{1}{x ^{2}} - \frac{3}{2 x ^{2}} + 5 x + C