integral from 4 to 7 of 3+2ln(t+5)

解

\int_{4}^{7} 3 + 2 ln (t + 5) d t

2 ln (\frac{16777216}{729}) + 3

十進法表記

23.08771 \dots

解答ステップ

\int_{4}^{7} 3 + 2 ln (t + 5) 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_{4}^{7} 3 d t + \int_{4}^{7} 2 ln (t + 5) d t

\int_{4}^{7} 3 d t = 9

\int_{4}^{7} 2 ln (t + 5) d t = 2 (ln (\frac{16777216}{729}) - 3)

= 9 + 2 (ln (\frac{16777216}{729}) - 3)

簡素化

9 + 2 (ln (\frac{16777216}{729}) - 3) : 2 ln (\frac{16777216}{729}) + 3

= 2 ln (\frac{16777216}{729}) + 3