integral from 0 to 0.5 of 2x+3-xe^{3x}

解

\int_{0}^{0.5} 2 x + 3 - x e^{3 x} d x

1.38990 \dots

解答ステップ

\int_{0}^{0.5} 2 x + 3 - x e^{3 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_{0}^{0.5} 2 x d x + \int_{0}^{0.5} 3 d x - \int_{0}^{0.5} x e^{3 x} d x

\int_{0}^{0.5} 2 x d x = 0.25

\int_{0}^{0.5} 3 d x = 1.5

\int_{0}^{0.5} x e^{3 x} d x = 0.36009 \dots

= 0.25 + 1.5 - 0.36009 \dots

簡素化

= 1.38990 \dots