I didn't understand how the last step was derived from a differential equation problem in postgraduate mathematics, from f'(t) to f(t).
The general solution formula of first-order linear differential equation y'+P(x)y = Q(x) is adopted.
y=e^(-∫p(x)dx)(∫q(x)e^(∫p(x)dx+c)
Only he omitted the brackets and worked out ∫P(x)dx first.