I do not know how to calculate [uv]

Please give me a full explanation

Let's nd a reduction formula for the indenite integral In = / sec"(x)dx. If n 2 2 then we can rewrite this integrai as In = f (1 + m2(x)) seen2(x)dx = In_2 + / tanz (x) sewn20:) dx. Now use integration by parts to get / tan2 (5:) seen20:) dx = / uv' dx = [W] / u'v dx with u = tan(x) and v, = tan(x) seen20:). This gives - [uv]= \"and - u'v= \"- Hence. without further integration we have the reduction formula mm: :n- Use this to evaluate In = sec\"_2(x) tan(x) + g(n)In_2 I4: +C