What is the integral of 1/5 e^{5x-2} ?

The integral of 1/5 e^{5x-2} is 1/25 e^{5x-2}+C

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integral of 1/5 e^{5x-2}

\int \frac{1}{5} e^{5 x - 2} d x

\frac{1}{25} e^{5 x - 2} + C

Solution steps

\int \frac{1}{5} e^{5 x - 2} d x

Take the constant out:

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

= \frac{1}{5} \cdot \int e^{5 x - 2} d x

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

= \frac{1}{5} \cdot \int e^{u} \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{5} \cdot \frac{1}{5} e^{u}

Substitute back

u = 5 x - 2

= \frac{1}{5} \cdot \frac{1}{5} e^{5 x - 2}

Simplify

\frac{1}{5} \cdot \frac{1}{5} e^{5 x - 2} : \frac{1}{25} e^{5 x - 2}

= \frac{1}{25} e^{5 x - 2}

Add a constant to the solution

= \frac{1}{25} e^{5 x - 2} + C

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What is the integral of 1/5 e^{5x-2} ?
The integral of 1/5 e^{5x-2} is 1/25 e^{5x-2}+C