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

The integral of (e^{5x})/5 is 1/25 e^{5x}+C

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

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

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

Solution steps

\int \frac{e ^{5 x}}{5} 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} 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

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

Simplify

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

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

Add a constant to the solution

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

\int_{0}^{1} \frac{2 x}{( x ^{2} + 3 ) ^{2}} d x

f (x) = \frac{- 9 x ^{2}}{2} + 7 x + 2

\frac{\partial}{\partial y} (arctan (x^{4} y^{3}))

5 (t - 1)

\frac{d}{d x} (\frac{A}{B + C e ^{x}})

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