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

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

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integral of (e^{5x})

\int (e^{5 x}) d x

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

Solution steps

\int e^{5 x} d x

Apply u-substitution

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

= \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 \int e^{u} d u

Use the common integral:

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

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

Substitute back

u = 5 x

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

Add a constant to the solution

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

\int x + 3 - 3 d x

x + y y^{^{'}} = 0

y = x^{3} + 7 x^{2} - 4

\frac{d y}{d t} = 4 t - 0.1 y t

x^{2} - 5 x + 1