how to extract a function from an integral?

[m.mohamed]

Dear all,

If I have an integral like this:



and I intend to extract the function p(x) from this integration, how can I do such a conversion?

 

[_Eduardo_]

Dear all,

If I have an integral like this:

View attachment 140289

and I intend to extract the function p(x) from this integration, how can I do such a conversion?

\[\displaystyle\int_{0}^{\infty}g(x)\text{d}x = \text{constant} \;\; \forall \; g(x)\]

Please, write the equation properly.

 

[m.mohamed]

Please, write the equation properly.

the equation is true. For instance, if i have p(x) as undefined function such like a curve of square function or any other undefined curve. We can call the denominator and the numerator with another function like g(x).
For instance, if g(x)=tan(x) which equals to sin(x)/cos(x) but in my equation i know the function in the denominator and also the function f(x) , but i do not know which function in the numerator. consequently i am trying to find p(x).

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or also you can find the equation which I want to solve


where I desire to find the second part of the numerator which is psi(w)