integral from 2 to 6 of (x-4)/(x+1)

解

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

5 ln (3) - 5 ln (7) + 4

十進法表記

- 0.23648 \dots

解答ステップ

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

拡張

\frac{x - 4}{x + 1} : \frac{x}{x + 1} - \frac{4}{x + 1}

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

\int_{2}^{6} \frac{x}{x + 1} d x = 4 - ln (7) + ln (3)

\int_{2}^{6} \frac{4}{x + 1} d x = 4 (ln (7) - ln (3))

= 4 - ln (7) + ln (3) - 4 (ln (7) - ln (3))

簡素化

4 - ln (7) + ln (3) - 4 (ln (7) - ln (3)) : 5 ln (3) - 5 ln (7) + 4

= 5 ln (3) - 5 ln (7) + 4