integral from 2 to 4 of x/(x+2)

解

\int_{2}^{4} \frac{x}{x + 2} d x

2 - 2 ln (\frac{3}{2})

十進法表記

1.18906 \dots

解答ステップ

\int_{2}^{4} \frac{x}{x + 2} d x

u置換積分法を適用する

= \int_{4}^{6} \frac{u - 2}{u} d u

拡張

\frac{u - 2}{u} : 1 - \frac{2}{u}

= \int_{4}^{6} 1 - \frac{2}{u} d u

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_{4}^{6} 1 d u - \int_{4}^{6} \frac{2}{u} d u

\int_{4}^{6} 1 d u = 2

\int_{4}^{6} \frac{2}{u} d u = 2 ln (\frac{3}{2})

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