求积分,1/1+(cosx的二次方)dx.

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求积分,1/1+(cosx的二次方)dx.求积分,1/1+(cosx的二次方)dx.求积分,1/1+(cosx的二次方)dx.∫1/1+(cos^2x)dx=∫(sin^2x+cos^2x)/(sin

求积分,1/1+(cosx的二次方)dx.
求积分,1/1+(cosx的二次方)dx.

求积分,1/1+(cosx的二次方)dx.
∫1/1+(cos^2x)dx
=∫(sin^2x+cos^2x)/(sin^2x+cos^2x+cos^2x)dx
=∫(sin^2x+cos^2x)/(sin^2x+2cos^2x)dx (被积函数上下同除以cos^2x)
=∫(tan^2x+1)/(tan^2x+2)dx
=∫(sec^2x)/(tan^2x+2)dx
= ∫1/(tan^2x+2)dtanx
=1/√2*arctan(tanx/√2)+C