What is the integral of ln(2x-3) ?

The integral of ln(2x-3) is xln(2x-3)-x+3/2-3/2 ln|2x-3|+C

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integral of ln(2x-3)

\int ln (2 x - 3) d x

x ln (2 x - 3) - x + \frac{3}{2} - \frac{3}{2} ln ∣ 2 x - 3 ∣ + C

Solution steps

\int ln (2 x - 3) d x

Apply Integration By Parts

= x ln (2 x - 3) - \int \frac{2 x}{2 x - 3} d x

\int \frac{2 x}{2 x - 3} d x = x - \frac{3}{2} + \frac{3}{2} ln ∣ 2 x - 3 ∣

= x ln (2 x - 3) - (x - \frac{3}{2} + \frac{3}{2} ln ∣ 2 x - 3 ∣)

Simplify

= x ln (2 x - 3) - x + \frac{3}{2} - \frac{3}{2} ln ∣ 2 x - 3 ∣

Add a constant to the solution

= x ln (2 x - 3) - x + \frac{3}{2} - \frac{3}{2} ln ∣ 2 x - 3 ∣ + C

What is the integral of ln(2x-3) ?
The integral of ln(2x-3) is xln(2x-3)-x+3/2-3/2 ln|2x-3|+C