What is the integral of (6x)/(sqrt(x)) ?

The integral of (6x)/(sqrt(x)) is 4x^{3/2}+C

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integral of (6x)/(sqrt(x))

\int \frac{6 x}{x} d x

4 x^{\frac{3}{2}} + C

Solution steps

\int \frac{6 x}{x} d x

Take the constant out:

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

= 6 \cdot \int \frac{x}{x} d x

Simplify

\frac{x}{x} : x

= 6 \cdot \int x d x

Apply the Power Rule

: \frac{2}{3} x^{\frac{3}{2}}

= 6 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

6 \cdot \frac{2}{3} x^{\frac{3}{2}} : 4 x^{\frac{3}{2}}

= 4 x^{\frac{3}{2}}

Add a constant to the solution

= 4 x^{\frac{3}{2}} + C

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What is the integral of (6x)/(sqrt(x)) ?
The integral of (6x)/(sqrt(x)) is 4x^{3/2}+C