Mastering Indefinite Integration: Tips for Solving (sin(x))/x Without Tricks

[voomdama]

I am trying to integrate (sin(x))/x It's an indefinite integral I can't think of any tricks to work this out

 

[Zurtex]

I am trying to integrate (sin(x))/x It's an indefinite integral I can't think of any tricks to work this out

It has no elementry solution.

There is a function however called SinIntegral(x) that is defined by this very integral: http://mathworld.wolfram.com/SineIntegral.html

 

[rock.freak667]

The most I can guess is to write out sin(x) as the infinite series and divide by x and integrate

$$sinx=\sum_{n=0} ^\infty \frac{(-1)^n x^{2n+1}}{(2n+1)!}$$

then $\frac{sinx}{x}$ will become

$$\sum_{n=0} ^\infty \frac{(-1)^n x^{2n}}{(2n+1)!}$$

Integrate this w.r.t.x and you'll get the infinite series representation of it