How do you integrate the function f(x)=sin(x)/x ?

Answer 1

Get the series expansion for sin x/x and then integrate term by term . Usually 5 terms is sufficient to get an answer accurate to 5 decimal places

Answer 2

Like at other answer, you develoment sin(x)/x in power serie and integrate trem by term. But if you want integrate over all real line, for example, can complex methods. Use Cauchy theorem with f(z)=e^(-iz)/z over the closed curve: segment [-R,-r] and segment [r,R], |z|=r and |z|=R both with Im z>=0 (0
....

Answer 3

∫((sin(x))/x) does not have a closed form.
Integrate numerically or integrate terms of the series to desired accuracy.