Make
into
and using Sum-Difference formulas from here
Table of Trigonometric Identities
now simplify and integrate.
This problem I cannot seem to solve,I have the answer but i want to know how to get to it, i do not know if i used the table or do i integrate it by parts? Thank You!!
The problem:
Integrate[Sin[3 x] Cos[5 x], x]
and this is the answer:
8 (Cos[x]) ^(2)- Cos[8 x]
-------------------------
16
Make
into
and using Sum-Difference formulas from here
Table of Trigonometric Identities
now simplify and integrate.
You can also do this using the "cyclic method". (That's not it's official name; that's just what I call it.)
Let
and
and
The integration by parts formula gives:
and
and
Now we have:
Note that that last integral is just , so we have:
Solve for . (You should also check my math; make sure I didn't make any sign errors and whatnot.)
Remark: To get the answer into the format given to you in the answer key, you may need to use some trig identities.