Consider the following integral:
Integrate[(Sin[x] + Cos[x])^a Sin[x]^b Cos[x]^c, x]
On my system Mathematica 11 just returns the input back, which suggests that this integral does not appear in the database.
However, if we add definite boundaries to the integral:
Integrate[(Sin[x] + Cos[x])^a Sin[x]^b Cos[x]^c, {x, 0, Pi/2}]
all of a sudden the integral evaluates to a bunch of hypergeometric functions.
How can this be? If Mathematica does not know the indefinite integral, how can it obtain the definite one? Is it possible to still somehow extract the indefinite integral from Mathematica?
b
andc
nonnegative integers? $\endgroup$b,c
are complex numbers. But if something non-trivial can be said about the integer case, I would be very interested in that as well! $\endgroup$b=0
MMA 11.2 spit enormous expression withAppellF1
function $\endgroup$