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Popular Calculus >

integral of-e^{-x}+1

Solution

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

Solution

e^{- x} + x + C

Solution steps

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

Apply u-substitution

= \int e^{u} - 1 d u

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^{u} d u - \int 1 d u

\int e^{u} d u = e^{u}

\int 1 d u = u

= e^{u} - u

Substitute back

u = - x

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

Simplify

= e^{- x} + x

Add a constant to the solution

= e^{- x} + x + C

Graph

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Frequently Asked Questions (FAQ)

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