What is the integral of-1/2 ln(x) ?

The integral of-1/2 ln(x) is -1/2 (xln(x)-x)+C

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integral of-1/2 ln(x)

\int - \frac{1}{2} ln (x) d x

- \frac{1}{2} (x ln (x) - x) + C

Solution steps

\int - \frac{1}{2} ln (x) d x

Take the constant out:

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

= - \frac{1}{2} \cdot \int ln (x) d x

Apply Integration By Parts

: x ln (x) - \int 1 d x

= - \frac{1}{2} (x ln (x) - \int 1 d x)

\int 1 d x = x

= - \frac{1}{2} (x ln (x) - x)

Add a constant to the solution

= - \frac{1}{2} (x ln (x) - x) + C

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What is the integral of-1/2 ln(x) ?
The integral of-1/2 ln(x) is -1/2 (xln(x)-x)+C