integral from 1 to 4 of ln(3x)-ln(x)

解

\int_{1}^{4} ln (3 x) - ln (x) d x

ln (6912) - 8 ln (2)

十進法表記

3.29583 \dots

解答ステップ

\int_{1}^{4} 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}^{4} ln (3 x) d x - \int_{1}^{4} ln (x) d x

\int_{1}^{4} ln (3 x) d x = ln (6912) - 3

\int_{1}^{4} ln (x) d x = 8 ln (2) - 3

= ln (6912) - 3 - (8 ln (2) - 3)

簡素化

= ln (6912) - 8 ln (2)