What is the integral of e^{-(5x)/3} ?

The integral of e^{-(5x)/3} is -3/5 e^{-(5x)/3}+C

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integral of e^{-(5x)/3}

\int e^{- \frac{5 x}{3}} d x

- \frac{3}{5} e^{- \frac{5 x}{3}} + C

Solution steps

\int e^{- \frac{5 x}{3}} d x

Apply u-substitution

: \int - \frac{3}{5} e^{u} d u

= \int - \frac{3}{5} e^{u} d u

Take the constant out:

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

= - \frac{3}{5} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{3}{5} e^{u}

Substitute back

u = - \frac{5 x}{3}

= - \frac{3}{5} e^{- \frac{5 x}{3}}

Add a constant to the solution

= - \frac{3}{5} e^{- \frac{5 x}{3}} + C

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What is the integral of e^{-(5x)/3} ?
The integral of e^{-(5x)/3} is -3/5 e^{-(5x)/3}+C