We started integrals not too long ago, I understand it for the most part but I always have a problem figuring out how to solve ones involving trig identities. Like this:
$$\int \frac{1+\cos^{2}x}{1+\cos2x}$$
Indefinite integral of $$\frac{ 1 + \cos^2(x)}{ 1 + \cos(2x) }.$$
I tried changing the denominator to $2\cos^2(x)$ but I still can't make a u substitution.
$$1+\cos{2x}=2 \cos^2{x}$$
$$1/\cos^2{x}=\frac{d}{dx} \tan{x}$$
That should get you across the finish line.