∫ (1+cos^2 x)/cos^2 x dx = 我的算法：∫ (1+cos^2 x)/cos^2 x dx = 1/cos^2 x + 1 = 2/(cos2x +1 ) + 1 = 2（cos2x+1)^-1 +1=这么变成了 2(cos2x+1)^0/(0) 不对啊 ==
问题描述：
∫ (1+cos^2 x)/cos^2 x dx =
我的算法：∫ (1+cos^2 x)/cos^2 x dx = 1/cos^2 x + 1 = 2/(cos2x +1 ) + 1 = 2（cos2x+1)^-1 +1=这么变成了 2(cos2x+1)^0/(0) 不对啊 ==
答
原式=∫(1/cos²x+1)dx
=∫(sec²x+1)dx
=∫d(tanx)+∫dx
=tanx+x+C (C是积分常数)
答
∫ (1+cos^2 x)/cos^2 x dx =∫1/cos^2 x + 1dx
=∫1/cos^2 xdx+x
=∫1d（tanx)+x
=tanx+x+c