integral from 2 to 4 of 5/x-(10)/(x^2)

解

\int_{2}^{4} \frac{5}{x} - \frac{10}{x ^{2}} d x

5 ln (2) - \frac{5}{2}

十進法表記

0.96573 \dots

解答ステップ

\int_{2}^{4} \frac{5}{x} - \frac{10}{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_{2}^{4} \frac{5}{x} d x - \int_{2}^{4} \frac{10}{x ^{2}} d x

\int_{2}^{4} \frac{5}{x} d x = 5 ln (2)

\int_{2}^{4} \frac{10}{x ^{2}} d x = \frac{5}{2}

= 5 ln (2) - \frac{5}{2}