integral from 2 to 4 of (x^3-2)-ln(x+1)

解

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

58 + 3 ln (3) - 5 ln (5)

十進法表記

53.24864 \dots

解答ステップ

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

\int_{2}^{4} x^{3} d x = 60

\int_{2}^{4} 2 d x = 4

\int_{2}^{4} ln (x + 1) d x = 5 ln (5) - 2 - 3 ln (3)

= 60 - 4 - (5 ln (5) - 2 - 3 ln (3))

簡素化

= 58 + 3 ln (3) - 5 ln (5)