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

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

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integral of e^{-2x}

integral

e^{- 2 x}

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

Solution steps

\int e^{- 2 x} d x

Apply u-substitution

: \int - \frac{1}{2} e^{u} d u

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

= - \frac{1}{2} e^{u}

Substitute back

u = - 2 x

= - \frac{1}{2} e^{- 2 x}

Add a constant to the solution

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

f (x) = 2 x^{3} + 4 x

(- 1, 7), (3, - 3)

f (x) = 8 x^{2} + 11 x, at x = 7

3 x - 4 y = 7

(4, - 43)