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Hi all,
I am working on the following integral
##
\int_0^{2\pi}\frac{1+\cos[\alpha x]}{1+\sin x}dx
##
where ##\alpha## is odd integer. Unless I set the ##\alpha## to a number then I can find the integral with mathematica easily. For general case with symbolic ##\alpha##, I cannot find the integral like this kind from any table and mathematica won't give the result as well. I am trying to apply the following relation to simplify the integrand
##
\cos[\alpha x] = 2\cos x \cos[(\alpha-1)x] - \cos[(\alpha-2)x]
##
it doesn't help to compute the integral. Any idea is welcomed. Thanks.
I am working on the following integral
##
\int_0^{2\pi}\frac{1+\cos[\alpha x]}{1+\sin x}dx
##
where ##\alpha## is odd integer. Unless I set the ##\alpha## to a number then I can find the integral with mathematica easily. For general case with symbolic ##\alpha##, I cannot find the integral like this kind from any table and mathematica won't give the result as well. I am trying to apply the following relation to simplify the integrand
##
\cos[\alpha x] = 2\cos x \cos[(\alpha-1)x] - \cos[(\alpha-2)x]
##
it doesn't help to compute the integral. Any idea is welcomed. Thanks.