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Popular >

integral of 1+e^{-x}

Solution

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

Solution

x - e^{- x} + C

Solution steps

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

\int 1 d x = x

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

= x - e^{- x}

Add a constant to the solution

= x - e^{- x} + C

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n = 0 \sum \infty (\frac{5}{16})^{n}

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Frequently Asked Questions (FAQ)

What is the integral of 1+e^{-x} ?
The integral of 1+e^{-x} is x-e^{-x}+C