Question

Решить интеграл (4x-1)/(x^(2)-8x+25)

Answer 1

$int frac{4x-1}{x^2-8x+25}dx=int frac{4x-1}{(x-4)^2+9}dx=[, t=x-4,; x=t+4,; dx=dt, ]=\\=int frac{4t+15}{t^2+9}dt=2int frac{2t, dt}{t^2+9}+15int frac{dt}{x^2+9}=[, 2t, dt=d(t^2+9), ]=\\=2, ln|t^2+9|+15cdot frac{1}{3}cdot arctgfrac{t}{3}+C=\\=2cdot ln|x^2-8x+25|+15cdot arctg frac{x-4}{3}+C$