Question

интеграл (5x+6)dx/ x^2+8x+20

Answer 1

$\displaystyle \int\frac{5x+6}{x^2+8x+20}dx=\frac{5}{2}\int\frac{2x+8-\frac{28}{5}}{x^2+8x+20}dx=\frac{5}{2}\int\frac{d(x^2+8x+20)}{x^2+8x+20}-\\-14\int\frac{d(x+4)}{(x+4)^2+4}=\frac{5}{2}ln|x^2+8x+20|-7arctg\frac{x+4}{2}+C\\\\\\(x^2+8x+20)'=2x+8$