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Popular >

integral of e^{-x}+2

Solution

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

Solution

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

Solution steps

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

Apply u-substitution

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

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

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

\int 2 d u = 2 u

= - e^{u} - 2 u

Substitute back

u = - x

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

Simplify

= - e^{- x} + 2 x

Add a constant to the solution

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

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\int 5 x^{15} e^{- x^{8}} d x

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\int \frac{1}{x ( ln ( x ) ) ^{6}} d x

Frequently Asked Questions (FAQ)

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