Integrating the Sine Integral: Solving the Challenging Integral of sinx/x

[Roni1985]

1. The problem statement, all variables and given/known

Homework Statement

$$\int \frac{sinx}{x}dx$$

Homework Equations

The Attempt at a Solution

Which method should work here? I tried integration by parts and it looks too much.
Is there a way to solve it without approximating it with the Taylor expansion of sinx ?

Thanks

 

[Dick]

That's the 'sine integral'. It's defined as a special function Si(x), you can't express it terms of a simple form using powers of x and trig functions. Approximating by taylor series is the way to go.

 

[Roni1985]

That's the 'sine integral'. It's defined as a special function, you can't express it terms of a simple form using powers of x and trig functions. Approximating by taylor series is the way to go.

I see. Thanks very much for the explanation.