integral from 1 to 4 of (9/x-e^{-x})

Lösung

\int_{1}^{4} (\frac{9}{x} - e^{- x}) d x

18 ln (2) - \frac{1}{e} + \frac{1}{e ^{4}}

Dezimale

12.12708 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{9}{x} - e^{- x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{4} \frac{9}{x} d x - \int_{1}^{4} e^{- x} d x

\int_{1}^{4} \frac{9}{x} d x = 18 ln (2)

\int_{1}^{4} e^{- x} d x = \frac{1}{e} - \frac{1}{e ^{4}}

= 18 ln (2) - (\frac{1}{e} - \frac{1}{e ^{4}})

Vereinfache

= 18 ln (2) - \frac{1}{e} + \frac{1}{e ^{4}}