What is the integral of e^{-(2x)/5} ?

The integral of e^{-(2x)/5} is -5/2 e^{-(2x)/5}+C

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integral of e^{-(2x)/5}

\int e^{- \frac{2 x}{5}} d x

- \frac{5}{2} e^{- \frac{2 x}{5}} + C

Solution steps

\int e^{- \frac{2 x}{5}} d x

Apply u-substitution

: \int - \frac{5}{2} e^{u} d u

= \int - \frac{5}{2} e^{u} d u

Take the constant out:

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

= - \frac{5}{2} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{5}{2} e^{u}

Substitute back

u = - \frac{2 x}{5}

= - \frac{5}{2} e^{- \frac{2 x}{5}}

Add a constant to the solution

= - \frac{5}{2} e^{- \frac{2 x}{5}} + C

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What is the integral of e^{-(2x)/5} ?
The integral of e^{-(2x)/5} is -5/2 e^{-(2x)/5}+C