integral from 1 to 2 of (6xy^2-4 x/y)

解

\int_{1}^{2} (6 x y^{2} - 4 \frac{x}{y}) d y

- 4 x ln (2) + 14 x

解答ステップ

\int_{1}^{2} 6 x y^{2} - 4 \cdot \frac{x}{y} d y

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_{1}^{2} 4 \cdot \frac{x}{y} d y + \int_{1}^{2} 6 x y^{2} d y

\int_{1}^{2} 4 \cdot \frac{x}{y} d y = 4 x ln (2)

\int_{1}^{2} 6 x y^{2} d y = 14 x

= - 4 x ln (2) + 14 x