求不定积分∫[1/(sin^2 cos^2(x)]dx

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 04:08:38

求不定积分∫[1/(sin^2 cos^2(x)]dx
求不定积分∫[1/(sin^2 cos^2(x)]dx

求不定积分∫[1/(sin^2 cos^2(x)]dx
原式= ∫{ [(sin x)^2 +(cos x)^2 ] /[(sin x)^2 (cos x)^2 ] }dx
= ∫[ (sec)^2 ]dx +∫[ (csc)^2 ]dx
= tan x -cot x +C
= sin x /cos x -cos x /sin x +C
= [ (sin x)^2 -(cos x)^2 ] / (cos x sin x) +C
= -cos 2x / [ (1/2)sin 2x ] +C
= -2 cot 2x +C,(C为任意常数).
解法二：原式= ∫dx / [(1/4) (sin 2x)^2]
= 4 ∫[ (csc 2x)^2 ] dx
= 2 ∫[ (csc 2x)^2 ] d(2x)
= -2 cot 2x +C,(C为任意常数).
= = = = = = = = =
以上计算可能有误,你最好检查一下.
正负是个大问题.
注意：
sec x =1/ cos x,
csc x =1/ sin x.
(tan x)' =(sec x)^2,
(cot x)' = -(csc x)^2.

求不定积分∫[1/(sin^2 cos^2(x)]dx 求不定积分∫[1/sin^2cos^2 (x)]dx 求不定积分 ∫ sin^4/cos^2 dx 求不定积分 ∫ (ln sin x) / (cos^2 x) dx 求不定积分sin^2cos^4 ∫(1-sin/x+cos)dx不定积分求不定积分：$(sin x +cos x)/(1+cos^2x) dx 求不定积分∫(cos2x)/(sin^2x)(cos^2x)dx∫(cos2x)/(sin^2x)(cos^2x)dx 求不定积分 ∫ sin∧4x/cos∧2x dx求不定积分 ∫ sin∧4x/cos∧2x dx 求不定积分：∫(sin x/cos^3 x)dx 求不定积分：∫(sin x/cos^3 x)dx cos^2/sin^2 2xdx 求不定积分求不定积分：| ( sin^2 x / cos^3x ) dx 求不定积分：(根号cos(x))/(sin^2(x)) 求sin^2(t)*cos^4(t)dt的不定积分求不定积分cos^4x/sin^2xdx 求不定积分∫(cos2x)/(sin^2x)(cos^2x)dx求不定积分,∫(cos2x)/(sin^2x)(cos^2x)dx,∫cos二倍x除以sin平方x 乘cos平方x dx 求不定积分∫sin^2dx与∫cos^2dx