Re: [積分] 一題奇怪的積分

[Frobenius (▽．(▽×▽φ)=0)]

※ 引述《TaiBeiGuo (台北國)》之銘言：
: ※ [本文轉錄自 trans_math 看板 #1E5mjzg2 ]
: 作者: TaiBeiGuo (台北國) 看板: trans_math
: 標題: [積分] 一題奇怪的積分
: 時間: Fri Jul  8 21:51:53 2011
:  π ln(1+πcosx)dx
: ∫ --------------
:  0     cosx
: 好像不是用t=π/2-x那招...

NIntegrate[Log[1 + \[Pi] Cos[x]]/
 Cos[x], {x, 0, 1.8947424337268773392122745222685641814}]

4.55959

NIntegrate[Log[1 + \[Pi] Cos[x]]/Cos[x], {x, 0, ArcCos[-1/\[Pi]]}]

4.55959 - 3.2099*10^-17 I

NIntegrate[Log[1 + \[Pi] Cos[x]]/Cos[x], {x, 0, \[Pi]}]

NIntegrate::slwcon: Numerical integration converging too slowly; suspect one
of the following: singularity, value of the integration is 0, highly
oscillatory integrand, or WorkingPrecision too small. >>

NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after
9 recursive bisections in x near {x} = {1.89595}. NIntegrate obtained
4.93435\[VeryThinSpace]-5.6891 I
 and 0.004227575773339409` for the integral and error estimates. >>

4.93435 - 5.6891 I

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