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Popular >

integral of 2+e^{-x}

Solution

\int 2 + e^{- x} d x

Solution

2 x - e^{- x} + C

Solution steps

\int 2 + e^{- x} d x

Apply u-substitution

: \int - 2 - e^{u} d u

= \int - 2 - e^{u} 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 2 d u - \int e^{u} d u

\int 2 d u = 2 u

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

= - 2 u - e^{u}

Substitute back

u = - x

= - 2 (- x) - e^{- x}

Simplify

= 2 x - e^{- x}

Add a constant to the solution

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

Graph

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\int cosh^{5} (x) d x

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\int sin (2 x) d sin (x) d x

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\int sec^{2} (x) \cdot (1 + tan (x)) d x

integral of 0.5e^{0.1x}

\int 0.5 e^{0.1 x} d x

Frequently Asked Questions (FAQ)

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