Try:

ClearAll["`*"]; Remove["`*"];

 HoldForm[Integrate[Product[1/(1/c[i]^2 - (u[i] + x[i])^2), {i, 1, n}],
     x]] == Integrate[
   Product[1/(1/c[i]^2 - (u[i] + x[i])^2), {i, 1, n}], x, 
   GeneratedParameters -> C]

Give you:

$\int \left(\prod _{i=1}^n \frac{1}{\frac{1}{c(i)^2}-(u(i)+x(i))^2}\right) \, dx=x \prod _{i=1}^n \frac{1}{\frac{1}{c(i)^2}-(u(i)+x(i))^2}+c_1$

Try first with a numerical value for j, for example j=1. What do you expect as an answer?

OK Thank you

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I expected the symbolic integration value. For example, if I do ∫xSin(x), I want to get -xCos(x) + Sin(x) expression. but now my Mathematica value represent integrate(xSin(x)) = ∫xSin(x). So it is not solving.

and it is not numerical solve so I cannot put the numbers in it. If I insert the number in j, I only get like this