Integrating Trigonometric Functions is one of the major aspects of Integral Calculus, trigonometric functions have standard integral values on the table of integrals.
But the major problem of integrating trig functions is when you are being given multiple trig identity functions to integrate... Many mathematics students find it a little bit difficult because multiple angles are mostly not listed on the table of integrals..
Below is the standard formula for integrating multiple angles.
Integral of Multiple angle for sine and cosine functions 
Check some few examples below.
Don't forget to add your comments for any questions or suggestions.. .