integral from 1 to 3 of ((x^2+2)/x)

解

\int_{1}^{3} (\frac{x ^{2} + 2}{x}) d x

4 + 2 ln (3)

十進法表記

6.19722 \dots

解答ステップ

\int_{1}^{3} \frac{x ^{2} + 2}{x} d x

拡張

\frac{x ^{2} + 2}{x} : x + \frac{2}{x}

= \int_{1}^{3} x + \frac{2}{x} 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_{1}^{3} x d x + \int_{1}^{3} \frac{2}{x} d x

\int_{1}^{3} x d x = 4

\int_{1}^{3} \frac{2}{x} d x = 2 ln (3)

= 4 + 2 ln (3)