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

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

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integral of-2e^{-x}

integral

- 2 e^{- x}

2 e^{- x} + C

Solution steps

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

Take the constant out:

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

= - 2 \cdot \int e^{- x} d x

Apply u-substitution

: \int - e^{u} d u

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

Take the constant out:

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

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

Use the common integral:

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

= - 2 (- e^{u})

Substitute back

u = - x

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

Simplify

= 2 e^{- x}

Add a constant to the solution

= 2 e^{- x} + C

e^{2} x + 1

e^{\frac{- 2 r}{a}}

\frac{( 1 + x )}{( 1 - x ) ^{2}}

\frac{1}{( x ^{2} + a )}

\frac{1}{( cos ^{2} ( x ) ( 1 - tan ( x ) ) ^{2} )}