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

The integral of (2/(e^{-x)}-1/(2x)) is 2e^x-1/2 ln|x|+C

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

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

2 e^{x} - \frac{1}{2} ln ∣ x ∣ + C

Solution steps

\int \frac{2}{e ^{- x}} - \frac{1}{2 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 \frac{2}{e ^{- x}} d x - \int \frac{1}{2 x} d x

\int \frac{2}{e ^{- x}} d x = 2 e^{x}

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

= 2 e^{x} - \frac{1}{2} ln ∣ x ∣

Add a constant to the solution

= 2 e^{x} - \frac{1}{2} ln ∣ x ∣ + C

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