Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Integral of a special trigonometic functions

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Integral special trigonometic | Date |
---|---|

I Integration by parts | Dec 12, 2017 |

Special Integrals Hermite(2n+1,x)*Cos (bx) and e^(-x^2/2) | May 31, 2015 |

Integration and special functions. | Apr 14, 2015 |

Is the definite integral a special case of functionals? | Jan 31, 2015 |

Solving special exponential integral | Feb 2, 2014 |

**Physics Forums - The Fusion of Science and Community**