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

解

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

\frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}} + C

解答ステップ

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

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

\int \frac{2}{3 x ^{5}} d x = - \frac{1}{6 x ^{4}}

= \frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}}

定数を解答に追加する

= \frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}} + C