Indefinite Integral

• Dec 10th 2007, 07:13 AM
th%$&873 Indefinite Integral What is ∫(sin(√(x))/x)dx? • Dec 10th 2007, 08:19 AM curvature Quote: Originally Posted by th%$&873
What is ∫(sin(√(x))/x)dx?

This integral is unsolvable (no finite forms).
• Dec 10th 2007, 08:30 AM
topsquark
Quote:

Originally Posted by th%$&873 What is ∫(sin(√(x))/x)dx? The best we can do is to let$\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)$.) There is no closed-form solution to this integral. -Dan • Dec 10th 2007, 10:19 AM Krizalid Quote: Originally Posted by topsquark This integral (at least) sometimes goes by the name of "Si." The$\displaystyle \text{Si}$function is defined as follows:$\displaystyle {\text{Si}}\,(x) = \int_0^x {\frac{{\sin u}}
{u}\,du} .$As a definite integral, may be it could have more sense. • Dec 13th 2007, 12:00 PM th%$&873
Thanks, everyone.