View source for Pseudo-elliptic integral

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Let $R(\cdot ,\cdot)$ be a rational function of two variables and $f(z)$ a polynomial of degree three or four, without multiple roots. A pseudo-elliptic integral is an integral of the form
\begin{equation*}
\int R(z,\sqrt{f(z)})\,dz,
\end{equation*}
which can be expressed elementarily, that is, by algebraic functions in $z$ or in the logarithms of such functions. For example,
\begin{equation*}
\int \frac{z^3\,dz}{\sqrt{z^4-1}}
\end{equation*}
is a pseudo-elliptic integral. See [[Elliptic integral|Elliptic integral]].