What is ∫(sin(√(x))/x)dx?

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- Dec 10th 2007, 07:13 AMth%$&873Indefinite Integral
What is ∫(sin(√(x))/x)

*d*x? - Dec 10th 2007, 08:19 AMcurvature
- Dec 10th 2007, 08:30 AMtopsquark
The best we can do is to let $\displaystyle u = \sqrt{x} \implies 2u~du = dx$, so

$\displaystyle \int \frac{sin(\sqrt{x})}{x}~dx = \int \frac{sin(u)}{u^2} \cdot 2u~du = 2 \int \frac{sin(u)}{u}~du$

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

-Dan - Dec 10th 2007, 10:19 AMKrizalid
- Dec 13th 2007, 12:00 PMth%$&873
Thanks, everyone.