What is the integral of 3e^{-(2x+7)} ?

The integral of 3e^{-(2x+7)} is -3/2 e^{-2x-7}+C

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integral of 3e^{-(2x+7)}

\int 3 e^{- (2 x + 7)} d x

- \frac{3}{2} e^{- 2 x - 7} + C

Solution steps

\int 3 e^{- (2 x + 7)} d x

Take the constant out:

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

= 3 \cdot \int e^{- (2 x + 7)} d x

Apply u-substitution

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

= 3 \cdot \int e^{- u} \frac{1}{2} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int e^{- u} d u

Apply u-substitution

: \int - e^{v} d v

= 3 \cdot \frac{1}{2} \cdot \int - e^{v} d v

Take the constant out:

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

= 3 \cdot \frac{1}{2} (- \int e^{v} d v)

Use the common integral:

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

= 3 \cdot \frac{1}{2} (- e^{v})

Substitute back

= 3 \cdot \frac{1}{2} (- e^{- (2 x + 7)})

Simplify

3 \cdot \frac{1}{2} (- e^{- (2 x + 7)}) : - \frac{3}{2} e^{- 2 x - 7}

= - \frac{3}{2} e^{- 2 x - 7}

Add a constant to the solution

= - \frac{3}{2} e^{- 2 x - 7} + C

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What is the integral of 3e^{-(2x+7)} ?
The integral of 3e^{-(2x+7)} is -3/2 e^{-2x-7}+C