integral of ((x^7-4x^5+11)/(x^5))

解

\int (\frac{x ^{7} - 4 x ^{5} + 11}{x ^{5}}) d x

\frac{x ^{3}}{3} - 4 x - \frac{11}{4 x ^{4}} + C

解答ステップ

\int \frac{x ^{7} - 4 x ^{5} + 11}{x ^{5}} d x

拡張

\frac{x ^{7} - 4 x ^{5} + 11}{x ^{5}} : x^{2} - 4 + \frac{11}{x ^{5}}

= \int x^{2} - 4 + \frac{11}{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 x^{2} d x - \int 4 d x + \int \frac{11}{x ^{5}} d x

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

\int 4 d x = 4 x

\int \frac{11}{x ^{5}} d x = - \frac{11}{4 x ^{4}}

= \frac{x ^{3}}{3} - 4 x - \frac{11}{4 x ^{4}}

定数を解答に追加する

= \frac{x ^{3}}{3} - 4 x - \frac{11}{4 x ^{4}} + C