What is the integral of 3*e^{-3y+6} ?

The integral of 3*e^{-3y+6} is -e^{-3y+6}+C

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integral of 3*e^{-3y+6}

\int 3 \cdot e^{- 3 y + 6} d y

- e^{- 3 y + 6} + C

Solution steps

\int 3 e^{- 3 y + 6} d y

Take the constant out:

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

= 3 \cdot \int e^{- 3 y + 6} d y

Apply u-substitution

: \int - \frac{1}{3} e^{u} d u

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

Take the constant out:

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

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

Use the common integral:

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

= 3 (- \frac{1}{3} e^{u})

Substitute back

u = - 3 y + 6

= 3 (- \frac{1}{3} e^{- 3 y + 6})

Simplify

3 (- \frac{1}{3} e^{- 3 y + 6}) : - e^{- 3 y + 6}

= - e^{- 3 y + 6}

Add a constant to the solution

= - e^{- 3 y + 6} + C

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What is the integral of 3*e^{-3y+6} ?
The integral of 3*e^{-3y+6} is -e^{-3y+6}+C