What is the integral of e^{(-4x)/3} ?

The integral of e^{(-4x)/3} is -3/4 e^{-(4x)/3}+C

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integral of e^{(-4x)/3}

\int e^{\frac{- 4 x}{3}} d x

- \frac{3}{4} e^{- \frac{4 x}{3}} + C

Solution steps

\int e^{\frac{- 4 x}{3}} d x

Simplify

= \int e^{- \frac{4 x}{3}} d x

Apply u-substitution

: \int - \frac{3}{4} e^{u} d u

= \int - \frac{3}{4} e^{u} d u

Take the constant out:

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

= - \frac{3}{4} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{3}{4} e^{u}

Substitute back

u = - \frac{4 x}{3}

= - \frac{3}{4} e^{- \frac{4 x}{3}}

Add a constant to the solution

= - \frac{3}{4} e^{- \frac{4 x}{3}} + C

x \to 0 lim (e^{x} - 1 - x)

n = 0 \sum \infty (\frac{2}{5})^{n}

\frac{d x}{d t} = \frac{t}{x e ^{t + 2 x}}

y^{^{'}} + sin (x) y = sin (x), y (0) = π

(87) (8 - 4)

What is the integral of e^{(-4x)/3} ?
The integral of e^{(-4x)/3} is -3/4 e^{-(4x)/3}+C