What is the integral of 5/(2sqrt(x)) ?

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

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integral of 5/(2sqrt(x))

\int \frac{5}{2 x} d x

5 x + C

Solution steps

\int \frac{5}{2 x} d x

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

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

= 5 x

Add a constant to the solution

= 5 x + C

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