integral of (5-2x^2)/(y^2)

解

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

- \frac{5 - 2 x ^{2}}{y} + C

解答ステップ

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

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= (5 - 2 x^{2}) \cdot \int \frac{1}{y ^{2}} d y

\int \frac{1}{y ^{2}} d y = - \frac{1}{y}

= (5 - 2 x^{2}) (- \frac{1}{y})

簡素化

(5 - 2 x^{2}) (- \frac{1}{y}) : - \frac{5 - 2 x ^{2}}{y}

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

定数を解答に追加する

= - \frac{5 - 2 x ^{2}}{y} + C