What is the integral of e^{-1.5x} ?

The integral of e^{-1.5x} is -0.66666…e^{-1.5x}+C

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integral of e^{-1.5x}

\int e^{- 1.5 x} d x

- 0.66666 \dots e^{- 1.5 x} + C

Solution steps

\int e^{- 1.5 x} d x

Apply u-substitution

: \int - \frac{1}{1.5} e^{u} d u

= \int - \frac{1}{1.5} e^{u} d u

Take the constant out:

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

= - \frac{1}{1.5} \cdot \int e^{u} d u

Simplify

= - 0.66666 \dots \cdot \int e^{u} d u

Use the common integral:

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

= - 0.66666 \dots e^{u}

Substitute back

u = - 1.5 x

= - 0.66666 \dots e^{- 1.5 x}

Add a constant to the solution

= - 0.66666 \dots e^{- 1.5 x} + C

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What is the integral of e^{-1.5x} ?
The integral of e^{-1.5x} is -0.66666…e^{-1.5x}+C