Laplace transform of the integral of the solution

Question

I have the following differential equation $y'+4y=11t^7$ with the initial condition $y(0)=3$

I need to find the following laplace transform $$L\left\{\int_0^t y(\mathcal{T}) d\mathcal{T}\right\}$$

I'm unsure of what to use for $y(\mathcal{T})$ and how to then start it off

Can anyone provide any help?

Answer 1

Hint: we have $$\mathscr{L}\left(\int_0^t f(\tau)\,d\tau\right)=\frac{F(s)}{s},$$ where $F(s)=\mathscr{L}(f(t))$.