Question Number 101985 by I want to learn more last updated on 06/Jul/20

∫ ((3x^5  − x^4  + 9x^3  − 12x^2  − 2x  +  1)/((x^3  − 1)^2 )) dx

Answered by 1549442205 last updated on 06/Jul/20

∫(((3x^5 −x^4 +9x^3 −12x^2 −2x+1)/((x^3 −1)^2 )))dx=∫{((3x^2 )/(x^3 −1))−(1/(x^2 +x+1))−(9/((x^2 +x+1)^2 ))   +(1/(3(x−1)))−(((x+2))/(3(x^2 +x+1)))+((7(x+2))/((x^2 +x+1)^2 ))−(4/(9(x−1)))+(2/(9(x−1)^2 ))+((2(x+3))/(9(x^2 +x+1)))+((6(x+1))/(9(x^2 +x+1)^2 ))}dx  ∫((3x^2 )/(x^3 −1))dx=ln∣x^3 −1∣,∫(1/(x^2 +x+1))dx= _(x+(1/2)=u)     ∫(dx/((x+(1/2))^2 +(((√3)/2))^2 ))=(2/(√3))arctan((2x+1)/(√3))

Commented byI want to learn more last updated on 07/Jul/20

Thanks sir.