Special Trigonometric Integrals
There are a select few functions specifically defined to be the antiderivatives of common integrands.
Several are listed below:
`\displaystyle \mathrm{Si}(x)=\int_0^x \frac{\sin t}t\,\mathrm dt=\int_0^x \mathrm{sinc}\,t\,\mathrm dt`
`\displaystyle \mathrm{si}(x)=-\int_x^\infty \frac{\sin t}t\,\mathrm dt`
In the first function above, the `\mathrm{sinc}(x)` function is known as the "cardinal sine function".
Note that, by definition, `\mathrm{Si}(x)-\mathrm{si}(x)=\int_0^\infty \frac{\sin t}t\,\mathrm dt=\frac\pi2`, known as the Dirichlet integral.
TODO: Links above and below!
`\displaystyle \mathrm{Ci}(x)=-\int_x^\infty \frac{\cos t}t\,\mathrm dt=\gamma+\ln x+\int_0^x \frac{\cos t-1}t\,\mathrm dt`
`\displaystyle \mathrm{Cin}(x)=\int_0^x \frac{1-\cos t}t\,\mathrm dt=\gamma+\ln x-\mathrm{Ci}(x)`
In the two definitions above, `\gamma` represents the Euler-Mascheroni constant.
TODO: Add hyperbolics, sin(x^2) family (Fresnel), and broaden scope or add another page with exponential integral, erf, and erfi, and Gaussian integral / Gaussian function