What is the integral of 3/(sqrt(x)) ?

The integral of 3/(sqrt(x)) is 6sqrt(x)+C

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integral of 3/(sqrt(x))

\int \frac{3}{x} d x

6 x + C

Solution steps

\int \frac{3}{x} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{x} d x

Apply the Power Rule

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

= 3 \cdot 2 x^{\frac{1}{2}}

Simplify

3 \cdot 2 x^{\frac{1}{2}} : 6 x

= 6 x

Add a constant to the solution

= 6 x + C

ln (\frac{4 x - 4}{5 x + 9})

x y^{^{'}} - 3 y = 6

\frac{\partial}{\partial x} (e^{x^{2} + 2 y})

y = 10 x, y = x^{2}

3 x^{2} + 24 x - y^{2} + 2 y = - 44