This will be about integrating product of trigonometric functions with no powers involved for example,

\int sin6xcos21x dx or \int cosxcos5x dx.

The simple trick here is to use the product to sum to formulas that can be found here.
For convenience, I’ll insert them here.


So very conveniently,

\int cosxcos5x dx=\int \frac{1}{2}(cos4x+cosx) dx = \frac{1}{2}(\frac{sin4x}{4}+sinx).
Now you see the usefulness of the product to sum formula! Better learn how to find them!

For trigonometric functions with powers involved, you can refer to part 1 to part 5.


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