What is the integral of-e^{-2y}+1 ?

The integral of-e^{-2y}+1 is 1/2 e^{-2y}+y+C

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integral of-e^{-2y}+1

\int - e^{- 2 y} + 1 d y

\frac{1}{2} e^{- 2 y} + y + C

Solution steps

\int - e^{- 2 y} + 1 d y

Apply the Sum Rule:

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

= - \int e^{- 2 y} d y + \int 1 d y

\int e^{- 2 y} d y = - \frac{1}{2} e^{- 2 y}

\int 1 d y = y

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

Simplify

= \frac{1}{2} e^{- 2 y} + y

Add a constant to the solution

= \frac{1}{2} e^{- 2 y} + y + C

y = \frac{x}{x - 5}, (- 1, a)

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u^{\frac{1}{2}}

What is the integral of-e^{-2y}+1 ?
The integral of-e^{-2y}+1 is 1/2 e^{-2y}+y+C