![](https://i.imgur.com/rmGqHlb.jpg)
Re: [微積] 研究所考古題
![](https://i.imgur.com/rmGqHlb.jpg)
3π/4 1 π/2 1 3π/4 1
∫ ------------ dx = ∫ ------------ dx + ∫ ------------- dx
π/4 1+2^(cosx) π/4 1+2^(cosx) π/2 1+2^(cosx)
(令 u = π - x)
π/2 1 π/4 1
= ∫ ------------ dx + ∫ -------------- -du
π/4 1+2^(cosx) π/2 1+2^(-cosu)
π/2 1 π/2 2^(cosu)
= ∫ ------------ dx + ∫ -------------- du
π/4 1+2^(cosx) π/4 1+2^(cosu)
π/2 1 π/2 2^(cosx)
= ∫ ------------ dx + ∫ -------------- dx
π/4 1+2^(cosx) π/4 1+2^(cosx)
π/2
= ∫ 1 dx = π/4
π/4
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02/07 22:07, , 1F
02/07 22:07, 1F
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