integral from 3 to 7 of 6+2ln(t+8)

解

\int_{3}^{7} 6 + 2 ln (t + 8) d t

16 + 30 ln (15) - 22 ln (11)

十進法表記

44.48781 \dots

解答ステップ

\int_{3}^{7} 6 + 2 ln (t + 8) d t

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_{3}^{7} 6 d t + \int_{3}^{7} 2 ln (t + 8) d t

\int_{3}^{7} 6 d t = 24

\int_{3}^{7} 2 ln (t + 8) d t = 2 (15 ln (15) - 4 - 11 ln (11))

= 24 + 2 (15 ln (15) - 4 - 11 ln (11))

簡素化

24 + 2 (15 ln (15) - 4 - 11 ln (11)) : 16 + 30 ln (15) - 22 ln (11)

= 16 + 30 ln (15) - 22 ln (11)