What is the integral of log_{2}(x-4) ?

The integral of log_{2}(x-4) is xlog_{2}(x-4)-1/(ln(2))(x-4+4ln|x-4|)+C

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integral of log_{2}(x-4)

\int lo g_{2} (x - 4) d x

x lo g_{2} (x - 4) - \frac{1}{ln ( 2 )} (x - 4 + 4 ln ∣ x - 4 ∣) + C

Solution steps

\int lo g_{2} (x - 4) d x

Apply Integration By Parts

: x lo g_{2} (x - 4) - \int \frac{x}{ln ( 2 ) ( x - 4 )} d x

= x lo g_{2} (x - 4) - \int \frac{x}{ln ( 2 ) ( x - 4 )} d x

\int \frac{x}{ln ( 2 ) ( x - 4 )} d x = \frac{1}{ln ( 2 )} (x - 4 + 4 ln ∣ x - 4 ∣)

= x lo g_{2} (x - 4) - \frac{1}{ln ( 2 )} (x - 4 + 4 ln ∣ x - 4 ∣)

Add a constant to the solution

= x lo g_{2} (x - 4) - \frac{1}{ln ( 2 )} (x - 4 + 4 ln ∣ x - 4 ∣) + C

\frac{4 x ^{2} + 8 x + 4}{x}

x \to 0 lim (\frac{( x ^{3} )}{x ^{2}})

\frac{d}{d x} (\frac{7 e ^{x} x ^{\frac{5}{2}}}{2} + e^{x} x^{\frac{7}{2}})

\frac{\partial}{\partial x} (x y^{3})

arccos (e^{7 x})

What is the integral of log_{2}(x-4) ?
The integral of log_{2}(x-4) is xlog_{2}(x-4)-1/(ln(2))(x-4+4ln|x-4|)+C