Re: [積分] 一題奇怪的積分
※ 引述《TaiBeiGuo (台北國)》之銘言：
: 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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