How to find indefinite integrals for the rational trigonometric functions of the form
$\qquad\Lambda^{pq}_m = \int \frac{\cos^p x\sin^q x}{(a+b\sin x +c\cos x)^m} dx$
where $(p,q,m)>0$ using Mathematica?
Any suggestions for preventing the results from being given in terms of AppellF1
, but rather to obtain them as simpler summation functions for the ranges
$\qquad 0 \leq p \leq 5$, $0 \leq q \leq 1$ and $3 \leq m \leq 9$.
For example:
ClearAll[x, a, b, c, p, q, m];Integrate[1/(a + b Cos[x] + c Sin[x])^m, x]
yields an output in terms of AppellF1
Any suggestions for preventing the results from being given in terms of AppellF1
it always helps to show the Mathematica code you used to obtain this result you claim to contain AppellF1 as I can't get Mathematica to give any result using the image you posted. So may be you typed something else, but without seeing what you typed, one can only guess. This is what I typedClearAll[x,a,b,c,p,q]; int=(Cos[x]^p Sin[x]^q)/(a+b Sin[x]+c Cos[x])^m; Assuming[p>0&&q>0&&m>0,Integrate[int,x]]
$\endgroup$ – Nasser Dec 27 '17 at 16:56