What is the integral of 2sqrt(x)*1/x ?

The integral of 2sqrt(x)*1/x is 4sqrt(x)+C

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integral of 2sqrt(x)*1/x

\int 2 x \cdot \frac{1}{x} d x

4 x + C

Solution steps

\int 2 x \frac{1}{x} d x

Take the constant out:

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

= 2 \cdot \int x \frac{1}{x} d x

Simplify

x \frac{1}{x} : \frac{1}{x}

= 2 \cdot \int \frac{1}{x} d x

Apply the Power Rule

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

Simplify

2 \cdot 2 x^{\frac{1}{2}} : 4 x

= 4 x

Add a constant to the solution

= 4 x + C

What is the integral of 2sqrt(x)*1/x ?
The integral of 2sqrt(x)*1/x is 4sqrt(x)+C