Improper integral with variable

[DIrtyPio]

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.

 

[CompuChip]

Note that they are basically asking you to calculate F(0).

 

[Dick]

And can you think of a way to write a simple expression for F'(t)? Use that to find F(t).

 

[DIrtyPio]

Sorry, indeed I figured out how should I find the other integral, but actually I'm having problems integrateing F'(t).

 

[Dick]

Sorry to hear that. Maybe if you show what kind of problems, someone could help.