quirk involving trig substitution?

Question

I have reduced the following trig identity to the following which is correct.

$$\int \cos^2(x)\tan^3(x)dx = \int \tan(x) - \sin(x)\cos(x)dx$$

However this next step changes the value of my equation.. i.e False

$$\int \cos^2(x)\tan^3(x)dx = \int \tan(x) dx - \int\sin(x)\cos(x)dx$$

Why can i not do this?

proof below http://www.wolframalpha.com/input/?i=integral%28cos^2x*tan^3x%29+%3D+integral%28tanx%29+-+%28sinxcosx%29

http://www.wolframalpha.com/input/?i=integral%28cos%5E2x%2Atan%5E3x%29+%3D+integral%28tanx%29+-+integral+%28sinxcosx%29

Answer 1

The two integrals that Wolfram gets are not equal (so the equation is false), but the two integrals do differ by a constant, so both are correct indefinite integrals.