Thread: Indefinite Integral
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Old December 10th, 2007, 10:30 AM
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Originally Posted by th%$&873 View Post
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
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