What is the integral of ln(2x-5) ?

The integral of ln(2x-5) is xln(2x-5)-x+5/2-5/2 ln|2x-5|+C

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integral of ln(2x-5)

\int ln (2 x - 5) d x

x ln (2 x - 5) - x + \frac{5}{2} - \frac{5}{2} ln ∣ 2 x - 5 ∣ + C

Solution steps

\int ln (2 x - 5) d x

Apply Integration By Parts

: x ln (2 x - 5) - \int \frac{2 x}{2 x - 5} d x

= x ln (2 x - 5) - \int \frac{2 x}{2 x - 5} d x

\int \frac{2 x}{2 x - 5} d x = x - \frac{5}{2} + \frac{5}{2} ln ∣ 2 x - 5 ∣

= x ln (2 x - 5) - (x - \frac{5}{2} + \frac{5}{2} ln ∣ 2 x - 5 ∣)

Simplify

= x ln (2 x - 5) - x + \frac{5}{2} - \frac{5}{2} ln ∣ 2 x - 5 ∣

Add a constant to the solution

= x ln (2 x - 5) - x + \frac{5}{2} - \frac{5}{2} ln ∣ 2 x - 5 ∣ + C

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What is the integral of ln(2x-5) ?
The integral of ln(2x-5) is xln(2x-5)-x+5/2-5/2 ln|2x-5|+C