Could you please help me out to solve this integration problem?

Questions
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1

Hi, the problem is given below,

Clear[x, a, b, c];
Integrate[(x - a)^2 (x - c)^2, {x, b, c}] /. {a -> Subscript[x, i], 
   b -> Subscript[x, i - 1], 
   c -> Subscript[x, i + 1]} // TraditionalForm

the answer for this problem is:

ans.png

…

the problem is: I need this answer in the form of ‘h’
where

3286hvalues.png
3286hvalues.png141×257 888 Bytes

Could you please help me out?

2

{a → Subscript[x, i], b → Subscript[x, i - 1], c → Subscript[x, i+ 1]}

The above means a is x and b is x-h and c is x+h. Then why not just write

Clear[x, a, b, c];
r = Integrate[(x - a)^2 (x - c)^2, {x, b, c}];
r /. {a -> x, b -> x - h, c -> x + h} // Simplify

which gives

(16 h^5)/15
3

Thanks a lot Mr Nasser

its nice to see this approach but unfortunately, i’m not able to solve my problem with this.

Regards