Integration of a product doesn't evaluate?

[kimminwoo190 (Minwoo Kim)]

I tried to integrate the function with symbolic expression. Mathematica only output the original form of expression.
How can I get the solved symbolic integral form of expression?

[gianlucagorni]

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

[kimminwoo190 (Minwoo Kim)]

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

[mariuszi28cg (Mariusz Iwaniuk)]

Maybe you want:

    j = 3; Integrate[Product[1/(1/c[i]^2 - (u[i] + x[i])^2), {i, 1, j}], x]

Or:

    j = 3; Integrate[Product[1/(1/c[i]^2 - (u[i] + x[i])^2), {i, 1, j}], x[1], x[2], x[3]]
           (*if j=3 integration a function with respect to three variables,then we need x[1] ,x[2] ,x[3]  *)

    j = 3; Integrate[Product[1/(1/c[i]^2 - (u[i] + x[i])^2), {i, 1, j}], Sequence @@ Table[x[i], {i, 1, j}]] 
           (*More automatic*)

?

[kimminwoo190 (Minwoo Kim)]

Firstly, thank you for helping.
Actually I want like this

when I delete j=3 in your first expression, I could get it.
But what is different between

and

I think it is only different is shape of product sign. why former one get

and later one get

?

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[mariuszi28cg (Mariusz Iwaniuk)]

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

[kimminwoo190 (Minwoo Kim)]

Thank you so much.

[kimminwoo190 (Minwoo Kim)]

OK Thank you

[gianlucagorni]

Maybe you should check your syntax, because I get the expected result:

In[246]:= Integrate[x Sin[x], x]

Out[246]= -x Cos[x] + Sin[x]

As for your symbolic integration, Mathematica finds the symbol x inside your function, so it assumes that the function depends on x. In Mathematica syntax, Subscript[x, i] is a function of x and i, it is not a symbol distinct from x. Try integrating with respect to y:

Integrate[Subscript[x, i], x]
Integrate[Subscript[x, i], y]