What is the integral of (ln(x))/4 ?

The integral of (ln(x))/4 is 1/4 (xln(x)-x)+C

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integral of (ln(x))/4

\int \frac{ln ( x )}{4} d x

\frac{1}{4} (x ln (x) - x) + C

Solution steps

\int \frac{ln ( x )}{4} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int ln (x) d x

Apply Integration By Parts

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

= \frac{1}{4} (x ln (x) - \int 1 d x)

\int 1 d x = x

= \frac{1}{4} (x ln (x) - x)

Add a constant to the solution

= \frac{1}{4} (x ln (x) - x) + C

\int x (x + 1)^{\frac{1}{2}} d x

\frac{\partial}{\partial x} (y^{0.75} x^{0.25})

f (x) = 9 e^{5} x + e^{- x^{2}}, at x = 1

\frac{d y}{d x} = 6 x^{2} y^{2}

x \to 2 - lim (4 - x^{2})

What is the integral of (ln(x))/4 ?
The integral of (ln(x))/4 is 1/4 (xln(x)-x)+C