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

\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

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