Question

Неопределенный дробный интеграл.

Answer 1

$intlimits {[2(3x-5)/(x^2-6x+10) +1]} , dx =2 intlimits {(3x-5)/(x^2-6x+10)} , dx +$$intlimits {1} , dx =2 intlimits {[3(2x-6)/(2(x^2-6x+10) +4/(x^2-6x+10)]} , dx + intlimits {1} , dx$$=3 intlimits {(2x-6)/(x^2-6x+10)} , dx +8 intlimits {1/[(x-3)^2+1]} , dx + intlimits {1} , dx =$$3ln(x^2-6x+10)+8arctg(x-3)+x+C$