integral of (x^4-6/(x^4))

解

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

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

解答ステップ

\int x^{4} - \frac{6}{x ^{4}} 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^{4} d x - \int \frac{6}{x ^{4}} d x

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

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

= \frac{x ^{5}}{5} - (- \frac{2}{x ^{3}})

簡素化

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

定数を解答に追加する

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