Question

Помогите ,пожалуйста,А1(4)

Answer 1

$\int{\frac{1}{(5x-1)^4}dx}=\int{(5x-1)^{-4}dx}$
Замена: $5x-1=t, 5dx=dt, dx=\frac{dt}{5}$
$\int{t^{-4}}\frac{dt}{5}=\frac{1}{5}\int{t^{-4}dt}=\frac{1}{5}\frac{t^{-3}}+C{-3}=\frac{-1}{15t^3}+C=\frac{-1}{15(5x-1)^3}+C$