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Integration of a product doesn't evaluate?

Posted 2 years ago

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? enter image description here

POSTED BY: Minwoo Kim
9 Replies

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

The rules explain how to format your code properly. Posting code Images doesn't help other members to copy your code. Please EDIT your post and make sure code blocks start on a new paragraph and look framed and colored like this.

int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]

You can also embed notebook or attach notebook.

enter image description here

POSTED BY: Moderation Team
Posted 2 years ago

OK Thank you

POSTED BY: Minwoo Kim

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*)

?

POSTED BY: Mariusz Iwaniuk
Posted 2 years ago

Firstly, thank you for helping. Actually I want like thisenter image description here when I delete j=3 in your first expression, I could get it. But what is different between enter image description here and enter image description here

I think it is only different is shape of product sign. why former one get enter image description here and later one get enter image description here?

POSTED BY: Minwoo Kim

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:

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

POSTED BY: Mariusz Iwaniuk
Posted 2 years ago

Thank you so much.

POSTED BY: Minwoo Kim

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

POSTED BY: Gianluca Gorni
Posted 2 years ago

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 thisenter image description here

POSTED BY: Minwoo Kim

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]
POSTED BY: Gianluca Gorni
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