integral from 1 to 5 of 4/x-4/(x^2)

解

\int_{1}^{5} \frac{4}{x} - \frac{4}{x ^{2}} d x

4 ln (5) - \frac{16}{5}

十進法表記

3.23775 \dots

解答ステップ

\int_{1}^{5} \frac{4}{x} - \frac{4}{x ^{2}} 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}^{5} \frac{4}{x} d x - \int_{1}^{5} \frac{4}{x ^{2}} d x

\int_{1}^{5} \frac{4}{x} d x = 4 ln (5)

\int_{1}^{5} \frac{4}{x ^{2}} d x = \frac{16}{5}

= 4 ln (5) - \frac{16}{5}