What is the integral of ln(f)(x) ?

The integral of ln(f)(x) is 1/2 x^2ln(f)+C

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integral of ln(f)(x)

\int ln (f) (x) d x

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

Solution steps

\int ln (f) x d x

Take the constant out:

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

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

Apply the Power Rule

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

= ln (f) \frac{x ^{2}}{2}

Simplify

ln (f) \frac{x ^{2}}{2} : \frac{1}{2} x^{2} ln (f)

= \frac{1}{2} x^{2} ln (f)

Add a constant to the solution

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

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