Do i have to find the equivalent L and use this equation?i(t)1/L* integrate(v(t) dt+i(t_0),i(t),i(t_0))
Your equation looks correct, but I don't understand the stuff after dt+. (The i(t_0) looks like it might be initial conditions, but the other terms don't make sense.) In your circuit and equation i(t) and L can be either i1(t) or i2(t) and L1 or L2. The current add to get i(t).