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

The integral of (5a)/(sqrt(x)) is 10asqrt(x)+C

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integral of (5a)/(sqrt(x))

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

10 a x + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

5 a \cdot 2 x^{\frac{1}{2}} : 10 a x

= 10 a x

Add a constant to the solution

= 10 a x + C

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What is the integral of (5a)/(sqrt(x)) ?
The integral of (5a)/(sqrt(x)) is 10asqrt(x)+C