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

解

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

- 3 ln (3) + \frac{26}{3}

十進法表記

5.37082 \dots

解答ステップ

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

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

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

\int_{1}^{3} 2 x d x = 8

= \frac{2}{3} - 3 ln (3) + 8

分数を組み合わせる

8 + \frac{2}{3} : \frac{26}{3}

= - 3 ln (3) + \frac{26}{3}