Find the antiderivative of the function given by f(x)=(ln(2x-5))/(2x-5)?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to find the anti derivative of f(x) = (ln(2x-5)) / (2x-5).

This can be done using substitution

Int [ (ln(2x-5)) / (2x-5) dx]

let ln(2x - 5)  = t

=> dt/dx = 2/(2x - 5)

=> dt / 2 = dx/(2x - 5)

Int [ (ln(2x-5)) / (2x-5) dx]

=> Int [ t/2  dt]

=> t^2/4 + C

substitute t = ln (2x - 5)

=> [ln (2x - 5)]^2 / 4 + C

The anti derivative of f(x) = (ln(2x-5)) / (2x-5) is [ln (2x - 5)]^2 / 4 + C

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial