I think I should use the identity:
...and rewrite the integral like this:
But then what I use for u to substitute? I tried using u = cos(10x) and I don't think that's right.
Can you point me in the right direction? Thank you!
I would like to start out by saying that I am completely against making u substutions for all integrals...
I would much rather recognize a pattern, guess at an antiderivative, and then put a correction factor out in front (I know most universities don't teach it like this, but let's give it a shot)
We know the integral of is
So let's "guess" that the integral is
Now if we take the derivative of that, we get , so we're off by a factor of 5, so let's put in front of our "guess" and we'll be good
So the answer is