What is the integral of 2e^{(-x)/3} ?

The integral of 2e^{(-x)/3} is -6e^{-x/3}+C

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integral of 2e^{(-x)/3}

integral

2 e^{\frac{- x}{3}}

- 6 e^{- \frac{x}{3}} + C

Solution steps

\int 2 e^{\frac{- x}{3}} d x

Take the constant out:

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

= 2 \cdot \int e^{\frac{- x}{3}} d x

Simplify

= 2 \cdot \int e^{- \frac{x}{3}} d x

Apply u-substitution

: \int - 3 e^{u} d u

= 2 \cdot \int - 3 e^{u} d u

Take the constant out:

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

= 2 (- 3 \cdot \int e^{u} d u)

Use the common integral:

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

= 2 (- 3 e^{u})

Substitute back

u = - \frac{x}{3}

= 2 (- 3 e^{- \frac{x}{3}})

Simplify

= - 6 e^{- \frac{x}{3}}

Add a constant to the solution

= - 6 e^{- \frac{x}{3}} + C

\frac{1}{x ^{3} y ^{2}}

(100 + 2 x)^{- 1}

x (2 x + 1)^{3}

(t - x)^{3} e^{x}

x (x + 2)^{\frac{1}{2}}

What is the integral of 2e^{(-x)/3} ?
The integral of 2e^{(-x)/3} is -6e^{-x/3}+C