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find-x-2-dx-x-3-2x-1-




Question Number 133123 by abdomsup last updated on 19/Feb/21
find ∫  ((x^2 dx)/(x^3 −2x+1))
findx2dxx32x+1
Answered by Ñï= last updated on 19/Feb/21
∫(x^2 /(x^3 −2x+1))dx  =(1/3)∫((3x^2 −2+2)/(x^3 −2x+1))dx  =(1/3)ln∣x^3 −2x+1∣+(2/3)∫(dx/((x−1)(x^2 +x−1)))  =(1/3)ln∣x^3 −2x+1∣+(2/3)∫((1/(x−1))−((x+2)/(x^2 +x−1)))dx  =(1/3)ln∣x^3 −2x+1∣+(2/3)ln∣x−1∣−(1/3)∫((2x+1+3)/(x^2 +x−1))dx  =(1/3)ln∣x^3 −2x+1∣+(2/3)ln∣x−1∣−(1/3)ln∣x^2 +x−1∣−(1/( (√5)))ln∣((x+(1/2)−(√(5/4)))/(x+(1/2)+(√(5/4))))∣+C
x2x32x+1dx=133x22+2x32x+1dx=13lnx32x+1+23dx(x1)(x2+x1)=13lnx32x+1+23(1x1x+2x2+x1)dx=13lnx32x+1+23lnx1132x+1+3x2+x1dx=13lnx32x+1+23lnx113lnx2+x115lnx+1254x+12+54+C
Commented by mathmax by abdo last updated on 19/Feb/21
thNks sir
thNkssir

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