What is the integral from 1 to 3 of (5/x-e^{-x}) ?

The integral from 1 to 3 of (5/x-e^{-x}) is 5ln(3)-1/e+1/(e^3)

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integral from 1 to 3 of (5/x-e^{-x})

\int_{1}^{3} (\frac{5}{x} - e^{- x}) d x

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

Decimal

5.17496 \dots

Solution steps

\int_{1}^{3} \frac{5}{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}^{3} \frac{5}{x} d x - \int_{1}^{3} e^{- x} d x

\int_{1}^{3} \frac{5}{x} d x = 5 ln (3)

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

= 5 ln (3) - (\frac{1}{e} - \frac{1}{e ^{3}})

Simplify

= 5 ln (3) - \frac{1}{e} + \frac{1}{e ^{3}}

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What is the integral from 1 to 3 of (5/x-e^{-x}) ?
The integral from 1 to 3 of (5/x-e^{-x}) is 5ln(3)-1/e+1/(e^3)