What is the integral of 0.33e^{-0.33y} ?

The integral of 0.33e^{-0.33y} is -1e^{-0.33y}+C

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integral of 0.33e^{-0.33y}

\int 0.33 e^{- 0.33 y} d y

- 1 e^{- 0.33 y} + C

Solution steps

\int 0.33 e^{- 0.33 y} d y

Take the constant out:

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

= 0.33 \cdot \int e^{- 0.33 y} d y

Apply u-substitution

: \int - \frac{1}{0.33} e^{u} d u

= 0.33 \cdot \int - \frac{1}{0.33} e^{u} d u

Take the constant out:

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

= 0.33 (- \frac{1}{0.33} \cdot \int e^{u} d u)

Simplify

= 0.33 (- 3.03030 \dots \cdot \int e^{u} d u)

Use the common integral:

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

= 0.33 (- 3.03030 \dots e^{u})

Substitute back

u = - 0.33 y

= 0.33 (- 3.03030 \dots e^{- 0.33 y})

Simplify

= - 1 e^{- 0.33 y}

Add a constant to the solution

= - 1 e^{- 0.33 y} + C

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What is the integral of 0.33e^{-0.33y} ?
The integral of 0.33e^{-0.33y} is -1e^{-0.33y}+C