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

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

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integral of (ln(x))/2

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

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

Solution steps

\int \frac{ln ( x )}{2} 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

= \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

d er i v a t i v e cos^{2} (3 x)

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x \to 1 + lim (ln (x))

\frac{d ^{2}}{d x ^{2}} (e^{5 e^{x}})

\int e^{7 x + 5} d x

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