integral from 2 to 3 of (xe^{3x}-2ln(x))

解

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

\frac{8 e ^{9} - 5 e ^{6}}{9} - 2 (3 ln (3) - 1 - 2 ln (2))

十進法表記

6976.79507 \dots

解答ステップ

\int_{2}^{3} x e^{3 x} - 2 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_{2}^{3} x e^{3 x} d x - \int_{2}^{3} 2 ln (x) d x

\int_{2}^{3} x e^{3 x} d x = \frac{8 e ^{9} - 5 e ^{6}}{9}

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

= \frac{8 e ^{9} - 5 e ^{6}}{9} - 2 (3 ln (3) - 1 - 2 ln (2))