Question

Пожалуйста!!!!!!!!!!!!!!!!!!

Answer 1

$\int \frac{4x+2}{x^2+8x+7}\, dx=\int \frac{4x+2}{(x+4)^2-9}=\Big [\, t=x+4,\; dt=dx,\; x=t-4\, \Big ]=\\\\=\int \frac{4t-14}{t^2-9}\, dt=2\int \frac{2t\, dt}{t^2-9}-14\int \frac{dt}{t^2-9}=2\, ln|t^2-9|-14\cdot \frac{1}{2\cdot 3}\, ln\Big |\frac{t-3}{t+3}\Big |+C=\\\\=2\, ln|x^2+8x+7|-\frac{7}{3}\cdot ln\Big |\frac{x+1}{x+7}\Big |+C\; .$