НГ
Нина Гончаренко
Ответ. 1. INT((5*x^2+6*x+9)/((x-3)^2*(x+1)^2)*dx=INT(1/2*(x+1)^2)+9/(2*(x-3)^2)*dx=-0,5/(x+1)-4,5/(x-3)+C;
2. INT(x^2-8*x+7)/((x^2-3*x-10)^2)*dx=INT((27/49)*(x+2)^-2-(30/343)*(x+2)^-1+(30/343)*(x-5)^-1-(8/49)*(x-5)^-2)*dx=-(27/49)*(x+2)^-1-(30/343)*Ln(x+2)+(30/343)*Ln(x-5)+(8/49)*(x-5)^-1+C;
1290.
(2x-3) / (x^2 -3x +2)^3 dx = d(x^2 -3x +2)/ (x^2 -3x +2)^3
==> integral (2x-3) / (x^2 -3x +2)^3 dx = -1/2 * 1/(x^2 -3x +2)^2 + C