Sinx x dxSolution I = integration ( 0 to in.pdf

Sinx / x dx
Solution
I = integration ( 0 to infinty ) e -sx cos(x) dx J = integration ( 0 to infinty ) e-sx
sin(x)dx use integration by parts - I = e-sx ( sin (x )) + s J J = - e-sx ( cos(x ))- s I by solving
the above equations - J = 1 / ( s2 +1 ) integration ( oto infinity ) integration ( 0 to infinity ) ( e-
sxsin(x)ds )dx = integration ( 0 to infinty ) sin(x) / x dx integration ( 0 to infinty ) 1 / s2 +1 ds =
integration ( 0 to infinty ) ( sin(x) / x ) dx pi / 2 = integration ( 0 to infinty ) sin(x) / x dx.

1. Sinx / x dx

Solution
I = integration ( 0 to infinty ) e -sx cos(x) dx J = integration ( 0 to infinty ) e-sx
sin(x)dx use integration by parts - I = e-sx ( sin (x )) + s J J = - e-sx ( cos(x ))- s I by solving
the above equations - J = 1 / ( s2 +1 ) integration ( oto infinity ) integration ( 0 to infinity ) ( e-
sxsin(x)ds )dx = integration ( 0 to infinty ) sin(x) / x dx integration ( 0 to infinty ) 1 / s2 +1 ds =
integration ( 0 to infinty ) ( sin(x) / x ) dx pi / 2 = integration ( 0 to infinty ) sin(x) / x dx