What is the integral of sqrt(5x) ?

The integral of sqrt(5x) is sqrt(5) 2/3 x^{3/2}+C

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integral of sqrt(5x)

\int 5 x d x

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

Solution steps

\int 5 x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int 5 x d x

Take the constant out:

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

= 5 \cdot \int x d x

Apply the Power Rule

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

= 5 \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 5 \frac{2}{3} x^{\frac{3}{2}} + C

\frac{d}{d x} (x y^{3} - x^{2})

f (x) = 2 (x^{3} - x)^{4}

\frac{\partial}{\partial y} (sin^{2} (x y))

y^{^{'}} + \frac{4 y}{x} = - \frac{3}{x}, y (1) = - 2

\int - 2 cos (\frac{x}{2}) d x

What is the integral of sqrt(5x) ?
The integral of sqrt(5x) is sqrt(5) 2/3 x^{3/2}+C