If f 3 x - 4 3 x + 4 = x + 2 ,   x ≠ - 4 3 , and ∫ f x d x = A log 1 - x + B x + C , then…

If f3x-43x+4=x+2, x≠-43, and ∫fxdx=Alog1-x+Bx+C , then the ordered pair A, B is equal to
  1. -83,-23
  2. -83,23
  3. 83,23
  4. 83,-23

Solution

Given f3x-43x+4=x+2, x≠-43

Let,  3x-43x+4=t

3x-4=3tx+4t

x=4t+43-3t+2

∴ft=10-2t3-3t

⇒fx=2x-103x-3

∫fxdx=∫2x-103x-3dx

=∫2x3x-3dx-10∫dx3x-3

=2x3-83lnx-1+C, where C is the constant of integration.

Asked in: JEE Main 2017 (09 Apr Online)

Practice more Indefinite Integration questions on Aicharya