What is the integral of e^{4x} 1/5 ?

The integral of e^{4x} 1/5 is 1/20 e^{4x}+C

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integral of e^{4x} 1/5

\int e^{4 x} \frac{1}{5} d x

\frac{1}{20} e^{4 x} + C

Solution steps

\int e^{4 x} \frac{1}{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^{4 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{4} d u

= \frac{1}{5} \cdot \int e^{u} \frac{1}{4} 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}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{5} \cdot \frac{1}{4} e^{u}

Substitute back

u = 4 x

= \frac{1}{5} \cdot \frac{1}{4} e^{4 x}

Simplify

\frac{1}{5} \cdot \frac{1}{4} e^{4 x} : \frac{1}{20} e^{4 x}

= \frac{1}{20} e^{4 x}

Add a constant to the solution

= \frac{1}{20} e^{4 x} + C

\frac{d y}{d t} = (5 + sin (t)) \cdot (\frac{y}{5})

\int \frac{x + 11}{( x - 4 ) ( x + 1 )} d x

y = a x + b

x^{2} = y, x^{2} = - (y - 2)

\frac{\partial}{\partial x} (x + 3 y^{\frac{1}{3}})

What is the integral of e^{4x} 1/5 ?
The integral of e^{4x} 1/5 is 1/20 e^{4x}+C