Question

cat este integrala din 4x^2-3x+2/4x^2-4x+3 dx ...hellppp

Answer 1

(4x²-3x+2)/(4x²-4x+3)  =adui   si   scazi   1   la  numarator  .Obtii
(4x²-3x+3)/(4x²-4x+3)-1/(4x²-4x+3)=1-1/(4x²-4x+3)/integrezi
F(x)=∫dx-dx/(4x²-4x+3)=x-∫dx/(4x²-4x+3)
la   numitor  e   o   functie   de   grd   2/o   scrii   sub  forma  canonica
F1(x)=∫dx/(4x²-4x+3)=∫dx[4*(x-1/2)²-(-8/4)
Substutie
x-1/2)=y    dx=dy
F1(y)=∫dy/(y²+8/4)=∫dy/(y²+2)=∫dy/(y²+√2²)=1/√2 arctgy/(1/√2)=revii  la  substitutie
F1(x)=√2/2arctg√2/2*(x-1/2)
F(x)=x-F1(x)=x-√2/2arctg√2/2*9x-1/2)
trecerea   la   forma   canonica
ax²+bx+c=a*(x+b/2a)²-Δ/4a