Primitive of Sine of x over x has no Solution in Elementary Functions/Historical Note
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Historical Note on Primitive of $\dfrac {\sin x} x$ has no Solution in Elementary Functions
The proof that $\ds \int \dfrac {\sin x \rd x} x$ cannot be expressed with a finite number of elementary functions was first proved by Joseph Liouville.
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.29$: Liouville ($\text {1809}$ – $\text {1882}$)