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0-1-e-x-1-dx-




Question Number 151761 by talminator2856791 last updated on 22/Aug/21
                        ∫_0 ^( ∞)  (1/( (√(e^x +1)))) dx
01ex+1dx
Answered by mindispower last updated on 22/Aug/21
∫_0 ^∞ ((e^(−(x/2)) dx)/( (√(1+(e^(−(x/2)) )^2 ))))=−2∫_0 ^∞ (de^(−(x/2)) /( (√(1+(e^(−(x/2)) )^2 ))))  =−2[argsh(e^(−(x/2)) )]_0 ^∞   =2argsh(1)=ln(3+2(√2))
0ex2dx1+(ex2)2=20dex21+(ex2)2=2[argsh(ex2)]0=2argsh(1)=ln(3+22)

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