What is the integral from 1 to 4 of (2/x-e^{-x}) ?

The integral from 1 to 4 of (2/x-e^{-x}) is 4ln(2)-1/e+1/(e^4)

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integral from 1 to 4 of (2/x-e^{-x})

\int_{1}^{4} (\frac{2}{x} - e^{- x}) d x

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

Decimal Notation

2.42302 \dots

Solution steps

\int_{1}^{4} \frac{2}{x} - e^{- x} d x

Apply the Sum Rule:

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

= \int_{1}^{4} \frac{2}{x} d x - \int_{1}^{4} e^{- x} d x

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

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

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

Simplify

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

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What is the integral from 1 to 4 of (2/x-e^{-x}) ?
The integral from 1 to 4 of (2/x-e^{-x}) is 4ln(2)-1/e+1/(e^4)