integral from 0 to ln(3) of e^x-e^{-4x}

解

\int_{0}^{l n (3)} e^{x} - e^{- 4 x} d x

\frac{142}{81}

十進法表記

1.75308 \dots

解答ステップ

\int_{0}^{l n (3)} e^{x} - e^{- 4 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}^{l n (3)} e^{x} d x - \int_{0}^{l n (3)} e^{- 4 x} d x

\int_{0}^{l n (3)} e^{x} d x = 2

\int_{0}^{l n (3)} e^{- 4 x} d x = \frac{20}{81}

= 2 - \frac{20}{81}

簡素化

2 - \frac{20}{81} : \frac{142}{81}

= \frac{142}{81}