What is the integral of 1/(5sqrt(x)) ?

The integral of 1/(5sqrt(x)) is 2/5 sqrt(x)+C

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integral of 1/(5sqrt(x))

\int \frac{1}{5 x} d x

\frac{2}{5} x + C

Solution steps

\int \frac{1}{5 x} 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 \frac{1}{x} d x

Apply the Power Rule

: 2 x^{\frac{1}{2}}

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

Simplify

\frac{1}{5} \cdot 2 x^{\frac{1}{2}} : \frac{2}{5} x

= \frac{2}{5} x

Add a constant to the solution

= \frac{2}{5} x + C

\frac{d}{d x} (\frac{1 + cos ( 2 x )}{1 - cos ( 2 x )})

\int x sin (\frac{1}{7} x) d x

\int 40 x^{\frac{3}{2}} - 60 x^{2} d x

\frac{4}{t ^{2}}

\frac{s}{s ^{2} + s + 3}

What is the integral of 1/(5sqrt(x)) ?
The integral of 1/(5sqrt(x)) is 2/5 sqrt(x)+C