  We present a conspicuous number of indefinite integrals involving Heun
functions and their products obtained by means of the Lagrangian formulation of
a general homogeneous linear ordinary differential equation. As a by-product we
also derive new indefinite integrals involving the Gauss hypergeometric
function and products of hypergeometric functions with elliptic functions of
the first kind. All integrals we obtained cannot be computed using Maple and
Mathematica.
