integral of (7x^2+5x^{-2})

解

\int (7 x^{2} + 5 x^{- 2}) d x

\frac{7 x ^{3}}{3} - \frac{5}{x} + C

解答ステップ

\int 7 x^{2} + 5 x^{- 2} d x

5 x^{- 2} = \frac{5}{x ^{2}}

= \int 7 x^{2} + \frac{5}{x ^{2}} 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 7 x^{2} d x + \int \frac{5}{x ^{2}} d x

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

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

= \frac{7 x ^{3}}{3} - \frac{5}{x}

定数を解答に追加する

= \frac{7 x ^{3}}{3} - \frac{5}{x} + C