Question

∫cos2x/(1+sinxcosx) dx 求详解.

Answer 1

Let u = 1 + sin(x)cos(x) = 1 + (1/2)sin(2x)

and du = cos(2x) dx → dx = du/cos(2x)

So ∫ cos(2x)/(1+sin(x)cos(x)) dx

= ∫ 1/u du

= ln|u| + C

= ln| 1 + sin(x)cos(x) | + C

or = ln| sin(2x) + 2 | + C