how do I integrate this function?

Question

sin(x)/x

Answer 1

This function will not integrate into any normal functions and in fact mathematicians had to invent a new function.
It is defined via this integral.
si(x) = ∫sin(x)/x dx
This is also commonly called SinIntegral.
Below is a link for more information.

Answer 2

What you have is an integral with no closed form solution. You can use integration by parts and you'' end up with :

integral = -cos(x)/x +integral(cos(x)/x^2 dx)

Then you can integrate by parts again and agains and again. Esstneitally, you never get e closed form solution just a sequence of sin(x) or cos(x) over x to some increasing large power.