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

Simplify

= (- \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)

Simplify

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

Add a constant to the solution

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

f (x) = x^{2} 1 - x^{2}

f (x) = x^{3} - 3 x + 5

f (x) = \frac{cos ( x ) + 4}{1 - sin ( x )}

\int \frac{1}{C ^{2}} d C

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