# Math Help - Indefinite Integral

1. ## Indefinite Integral

What is ∫(sin(√(x))/x)dx?

2. Originally Posted by th%$&873 What is ∫(sin(√(x))/x)dx? This integral is unsolvable (no finite forms). 3. Originally Posted by th%$&873
What is ∫(sin(√(x))/x)dx?
The best we can do is to let $u = \sqrt{x} \implies 2u~du = dx$, so
$\int \frac{sin(\sqrt{x})}{x}~dx = \int \frac{sin(u)}{u^2} \cdot 2u~du = 2 \int \frac{sin(u)}{u}~du$

This integral (at least) sometimes goes by the name of "Si." (So as a function of x it is $Si(x)$.) There is no closed-form solution to this integral.

-Dan

4. Originally Posted by topsquark
This integral (at least) sometimes goes by the name of "Si."
The $\text{Si}$ function is defined as follows:

${\text{Si}}\,(x) = \int_0^x {\frac{{\sin u}}
{u}\,du} .$

As a definite integral, may be it could have more sense.

5. Thanks, everyone.