Improper integral with variable

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The discussion revolves around calculating the improper integral F(t) defined as the integral from 0 to infinity of (e^(-tx) sin(2x)/x) dx. Participants are tasked with finding S sin(2x)/x dx and specifically calculating F(0). There is also a focus on deriving a simple expression for F'(t) to facilitate finding F(t). One user expresses difficulty in integrating F'(t) and seeks assistance with the specific problems encountered. The conversation highlights the challenges of improper integrals and the need for collaborative problem-solving in calculus.
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With the help of F:[0-> infinity) F(t)= S( (e^(-tx)) sin(2x)/x )dx
find the S sin(2x)/x dx . The integral goes from 0 to infinity.
 
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Note that they are basically asking you to calculate F(0).
 
And can you think of a way to write a simple expression for F'(t)? Use that to find F(t).
 
Sorry, indeed I figured out how should I find the other integral, but actually I'm having problems integrateing F'(t).
 
Sorry to hear that. Maybe if you show what kind of problems, someone could help.
 

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