integral from 1 to 2 of (3/x-e^{-x})

Lösung

\int_{1}^{2} (\frac{3}{x} - e^{- x}) d x

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

Dezimale

1.84689 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{3}{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}^{2} \frac{3}{x} d x - \int_{1}^{2} e^{- x} d x

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

\int_{1}^{2} e^{- x} d x = \frac{1}{e} - \frac{1}{e ^{2}}

= 3 ln (2) - (\frac{1}{e} - \frac{1}{e ^{2}})

Vereinfache

= 3 ln (2) - \frac{1}{e} + \frac{1}{e ^{2}}

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

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