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

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

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integral of 5/(sqrt(x))

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

10 x + C

Solution steps

\int \frac{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 \frac{1}{x} d x

Apply the Power Rule

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

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

Simplify

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

= 10 x

Add a constant to the solution

= 10 x + C

y^{2} + (x^{2} \frac{d y}{d x}) = (x y) \frac{d y}{d x}

\frac{d}{d x} (\frac{x ( 2 - x )}{e ^{x}})

\int (\frac{1}{ln ( x )}) d x

\int x^{2} (x - 5) 7 - x d x

\frac{d}{d w} (t e^{(\frac{w}{t})})

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