What is the integral of 1080e^{-0.9x} ?

The integral of 1080e^{-0.9x} is -1199.99999…e^{-0.9x}+C

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integral of 1080e^{-0.9x}

\int 1080 e^{- 0.9 x} d x

- 1199.99999 \dots e^{- 0.9 x} + C

Solution steps

\int 1080 e^{- 0.9 x} d x

Take the constant out:

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

= 1080 \cdot \int e^{- 0.9 x} d x

Apply u-substitution

: \int - \frac{1}{0.9} e^{u} d u

= 1080 \cdot \int - \frac{1}{0.9} e^{u} d u

Take the constant out:

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

= 1080 (- \frac{1}{0.9} \cdot \int e^{u} d u)

Simplify

= 1080 (- 1.11111 \dots \cdot \int e^{u} d u)

Use the common integral:

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

= 1080 (- 1.11111 \dots e^{u})

Substitute back

u = - 0.9 x

= 1080 (- 1.11111 \dots e^{- 0.9 x})

Simplify

= - 1199.99999 \dots e^{- 0.9 x}

Add a constant to the solution

= - 1199.99999 \dots e^{- 0.9 x} + C

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What is the integral of 1080e^{-0.9x} ?
The integral of 1080e^{-0.9x} is -1199.99999…e^{-0.9x}+C