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Marias325
a fost răspuns

integrala de la 0 la 1 din x/(x^2+x+1)

Răspuns :

Lennox
x²+x+1=(x+1/2)²+3/4
I=∫dx/(x+1/2)²+3/4   x∈[0,1]
(x+1/2)=y
Schimbarea limitelor  de   integrare
x=0   y=1/2
x=1  y=3/2
I=∫dy/(y²+3/4=∫dy/[y²+(√3/2)²]=2/√3arctg √3/2y/0↑1=2/√3arctg√3/2-2/√3artgo=
2/√3  arctg√3/2=2√3/3*arctg√3/2

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