integral from 1 to 3 of (ln(3x)-ln(x))

解

\int_{1}^{3} (ln (3 x) - ln (x)) d x

2 ln (3)

十進法表記

2.19722 \dots

解答ステップ

\int_{1}^{3} ln (3 x) - ln (x) 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}^{3} ln (3 x) d x - \int_{1}^{3} ln (x) d x

\int_{1}^{3} ln (3 x) d x = 5 ln (3) - 2

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

= 5 ln (3) - 2 - (3 ln (3) - 2)

簡素化

5 ln (3) - 2 - (3 ln (3) - 2) : 2 ln (3)

= 2 ln (3)