What is the integral of (2-5e^{-x})/(e^{-x)} ?

The integral of (2-5e^{-x})/(e^{-x)} is 2e^x-5x+C

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integral of (2-5e^{-x})/(e^{-x)}

\int \frac{2 - 5 e ^{- x}}{e ^{- x}} d x

2 e^{x} - 5 x + C

Solution steps

\int \frac{2 - 5 e ^{- x}}{e ^{- x}} d x

Expand

\frac{2 - 5 e ^{- x}}{e ^{- x}} : \frac{2}{e ^{- x}} - \frac{5 e ^{- x}}{e ^{- 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{5 e ^{- x}}{e ^{- x}} d x

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

\int \frac{5 e ^{- x}}{e ^{- x}} d x = 5 x

= 2 e^{x} - 5 x

Add a constant to the solution

= 2 e^{x} - 5 x + C

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What is the integral of (2-5e^{-x})/(e^{-x)} ?
The integral of (2-5e^{-x})/(e^{-x)} is 2e^x-5x+C