I have alreday gotten the result and want to know how Maple was doing this calculation.

Would you like to tell me the way. Thanks.

eq12 := `assuming`([invlaplace(exp(-sqrt(s))*sqrt(s)/((sqrt(s)+a1)*sqrt(s+a2)*(s+a3)), s, t)], [a1 > 0, a2 > 0, a3 > 0])

We know it's true that the Inverse Laplace Transform of two functions' multiplication is the convolution of every function's Inverse Laplace Transform. I think the case can be upgraded to multiple functions, i.e.

L^(-1)(f[1]*f[2]***f[n])=L^(-1)(f[1])∗L^(-1)(f[2])∗∗∗L^(-1)(f[n])

I take the Inverse Laplace Transform on a specific function and the shown result is still an integral.

Would you like to explain it to me?

Thanks.

I can't take the inverse laplace transform of one kind of functions.

Would you like to help me?

Thanks.