What is the integral of In(sqrt(x)) ?

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

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integral of In(sqrt(x))

\int I n (x) d x

I n \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int I n x d x

Take the constant out:

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

= I n \cdot \int x d x

Apply the Power Rule

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

= I n \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= I n \frac{2}{3} x^{\frac{3}{2}} + C

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