How do you evaluate the integral #int 3sinx+4cosxdx#?
This integral is easier than it looks!
The first thing that we need to realize is that we can break the integral up over the addition:
Then we can move the constants out of the integrals:
Now we can just sub in the antiderivatives for
You should have these memorized, they come up a lot!
so the final answer is:
because this is an indefinite integral, we stop here and do not need to evaluate further.
note: I combined the two constants of integration,