What is the integral of 2e^{-1.5x} ?

The integral of 2e^{-1.5x} is -1.33333…e^{-1.5x}+C

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integral of 2e^{-1.5x}

\int 2 e^{- 1.5 x} d x

- 1.33333 \dots e^{- 1.5 x} + C

Solution steps

\int 2 e^{- 1.5 x} d x

Take the constant out:

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

= 2 \cdot \int e^{- 1.5 x} d x

Apply u-substitution

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

= 2 \cdot \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

= 2 (- \frac{1}{1.5} \cdot \int e^{u} d u)

Simplify

= 2 (- 0.66666 \dots \cdot \int e^{u} d u)

Use the common integral:

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

= 2 (- 0.66666 \dots e^{u})

Substitute back

u = - 1.5 x

= 2 (- 0.66666 \dots e^{- 1.5 x})

Simplify

= - 1.33333 \dots e^{- 1.5 x}

Add a constant to the solution

= - 1.33333 \dots e^{- 1.5 x} + C

\frac{d}{d x} (\frac{e ^{x}}{x - 1})

\frac{d}{d x} (cos^{5} (3 x))

\int sin (\frac{x}{3}) cos (\frac{2 x}{3}) d x

\int x (e^{x}) d x

f (x) = \frac{2}{x - 1}, at x = - 2

What is the integral of 2e^{-1.5x} ?
The integral of 2e^{-1.5x} is -1.33333…e^{-1.5x}+C