Using function of a function rule in integration.....?

Question

find the indefinite integral (primitive function) of
∫ 1/(2(4x-5)^3 dx
please go through step by step cos im not getting the correct answer.... thanks

yes, there is a ) after the 3

thats not giving me the right answer... i know what ur trying to do, but its not that.... sorry

Answer 1

There's a ")" missing in your question - i'll assume it's after the 3.

first take the 1/2 out of the integral, to be left to multiply the answer.
we now need to integrate 1/(4x-5)^3
set u = 4x-5
du = 4 dx, ie., dx can be rewritten as (1/4) du
so we can rewrite this as
1/2 * (1/4) integral(du/u^3)
which is relatively straightforward.

Answer 2

Reading this as it is (4x - 5) that is cubed as shown in question (ie the 2 is not cubed):-
I = (1/2) ∫ 1 / (4 - 5x)³ dx
let u = 4 - 5x
du = - 5 dx
- du/5 = dx
I = (- 1/10) ∫ u^(-3). du
I = (1/10).u^(-2) + C
I = 1 / (10.(4 - 5x)² ) + C