What is the integral of (1-ye^{-x}) ?

The integral of (1-ye^{-x}) is x+ye^{-x}+C

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integral of (1-ye^{-x})

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

x + y e^{- x} + C

Solution steps

\int 1 - y 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 d x - \int y e^{- x} d x

\int 1 d x = x

\int y e^{- x} d x = - y e^{- x}

= x - (- y e^{- x})

Simplify

= x + y e^{- x}

Add a constant to the solution

= x + y e^{- x} + C

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What is the integral of (1-ye^{-x}) ?
The integral of (1-ye^{-x}) is x+ye^{-x}+C