integral of (x^3-4+5/(x^6))

解

\int (x^{3} - 4 + \frac{5}{x ^{6}}) d x

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

解答ステップ

\int x^{3} - 4 + \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 x^{3} d x - \int 4 d x + \int \frac{5}{x ^{6}} d x

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

\int 4 d x = 4 x

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

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

定数を解答に追加する

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