Question

cos2x/sin^2xcos^2x的不定积分

cos 2x /sin^2 x*cos^2 x不定积分
答案是“-tanx-cotx+c"我要过程....

Answer 1

∫cos2xdx/(sin^2xcos^2x)
= 4∫cos2xdx/(2sinxcosx)^2
=4 ∫cos2xdx/(sin2x)^2
=2 ∫cos2xd(2x)/(sin2x)^2
=2 ∫d(sin2x)/(sin2x)^2
=-2*1/(sin2x)+c
=-2csc2x+c.