integral from 1 to 2 of 3/x+5/(x^2)

解

\int_{1}^{2} \frac{3}{x} + \frac{5}{x ^{2}} d x

3 ln (2) + \frac{5}{2}

十進法表記

4.57944 \dots

解答ステップ

\int_{1}^{2} \frac{3}{x} + \frac{5}{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}^{2} \frac{3}{x} d x + \int_{1}^{2} \frac{5}{x ^{2}} d x

\int_{1}^{2} \frac{3}{x} d x = 3 ln (2)

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

= 3 ln (2) + \frac{5}{2}