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Popular >

integral of 30e^{-x}

Solution

\int 30 e^{- x} d x

Solution

- 30 e^{- x} + C

Solution steps

\int 30 e^{- x} d x

Take the constant out:

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

= 30 \cdot \int e^{- x} d x

Apply u-substitution

: \int - e^{u} d u

= 30 \cdot \int - e^{u} d u

Take the constant out:

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

= 30 (- \int e^{u} d u)

Use the common integral:

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

= 30 (- e^{u})

Substitute back

u = - x

= 30 (- e^{- x})

Simplify

= - 30 e^{- x}

Add a constant to the solution

= - 30 e^{- x} + C

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Frequently Asked Questions (FAQ)

What is the integral of 30e^{-x} ?
The integral of 30e^{-x} is -30e^{-x}+C