The Risch Algorithm is a computer algebra method of
finding an indefinite integral. The basic idea behind
it is to transform each trigonometric expression in the
function to be integrated into an equivalent logarithmic
or exponential expression. Because all the sin's,
cosine's, tan's and hyperbolic trigonometric functions
are expressed using only two basic transcendental
functions, it is easier to simplify and combine these
expressions. The Risch Algorithm will produce a correct
result for any integrable function, and will tell you if
no such algebraic function exists.