integral of (4x^6+3x^5-8)/(x^5)

解

\int \frac{4 x ^{6} + 3 x ^{5} - 8}{x ^{5}} d x

2 x^{2} + 3 x + \frac{2}{x ^{4}} + C

解答ステップ

\int \frac{4 x ^{6} + 3 x ^{5} - 8}{x ^{5}} d x

拡張

\frac{4 x ^{6} + 3 x ^{5} - 8}{x ^{5}} : 4 x + 3 - \frac{8}{x ^{5}}

= \int 4 x + 3 - \frac{8}{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 4 x d x + \int 3 d x - \int \frac{8}{x ^{5}} d x

\int 4 x d x = 2 x^{2}

\int 3 d x = 3 x

\int \frac{8}{x ^{5}} d x = - \frac{2}{x ^{4}}

= 2 x^{2} + 3 x - (- \frac{2}{x ^{4}})

簡素化

= 2 x^{2} + 3 x + \frac{2}{x ^{4}}

定数を解答に追加する

= 2 x^{2} + 3 x + \frac{2}{x ^{4}} + C