神马作文网求∫sinxcosx/(sinx^4+cosx^4 )dx
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/23 18:33:25
求∫sinxcosx/(sinx^4+cosx^4 )dx
sinxcosx/[sinx^4+cosx^4]
=1/2sin2x/[(sinx^2+cosx^2)^2-2sinx^2cosx^2]
=1/2sin2x/(1-(sin2x)^2/2)
=sin2x/(2-(sin2x)^2)
=sin2x/(1+(cos2x)^2)
∫[sinxcosx]dx/[sinx^4+cosx^4]
=∫sin2xdx/[1+(cos2x)^2]
=-1/2∫dcos2x/(1+(cos2x)^2)
= -1/2arctan(cos2x)+C
=1/2sin2x/[(sinx^2+cosx^2)^2-2sinx^2cosx^2]
=1/2sin2x/(1-(sin2x)^2/2)
=sin2x/(2-(sin2x)^2)
=sin2x/(1+(cos2x)^2)
∫[sinxcosx]dx/[sinx^4+cosx^4]
=∫sin2xdx/[1+(cos2x)^2]
=-1/2∫dcos2x/(1+(cos2x)^2)
= -1/2arctan(cos2x)+C
求不定积分 sinxcosx/1+sinx^4 dx
求不定积分∫[sinxcosx/(sinx+cosx)]dx
∫sinxcosx/(1+sin^4x)dx
求不定积分∫(cos x)^2 /sinx dx
求不定积分∫(1+sinx) / cos^2 x dx
求不定积分 ∫ sinx（cos∧5)x dx.
求不定积分∫(cos^4x)dx,
求不定积分 sinx/cos^3x dx
求不定积分 cos^3x/sinx dx
求函数f(x)=(sinx+cos^4x+sin^2xcos^2x)/2-2sinxcosx-1/2sinxcosx+1
∫sinxcosx/(sinx+cosx)dx
已知2sin²x-cos²x+sinxcosx-4sinx+2cosx=0求(sin2x+1)/(1