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

解

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

3 (ln (5) - ln (2)) + \frac{9}{10}

十進法表記

3.64887 \dots

解答ステップ

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

拡張

\frac{3 x + 3}{x ^{2}} : \frac{3}{x} + \frac{3}{x ^{2}}

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

\int_{2}^{5} \frac{3}{x} d x = 3 (ln (5) - ln (2))

\int_{2}^{5} \frac{3}{x ^{2}} d x = \frac{9}{10}

= 3 (ln (5) - ln (2)) + \frac{9}{10}