Integral Help: $\int^t_0{se^{d(t-s)} ds}$

Question

I would like to know how to solve this integral, I have tried and I know the solution. Yet, I am not able at all to work around all the steps to get to the solution. I know this is a particular case, but I do not know how to achieve the right solution. The integral is the following (in case the format in the title does not work).

$$\int^t_0{se^{d(t-s)} ds}$$

Thanks for the help!!

Answer 1

Hint:

$$\int se^{d(t-s)}ds=e^{dt}\int se^{-ds}ds$$

and now integration by parts may be handy.

Answer 2

for your control the result is given by $$\frac{-d t+e^{d t}-1}{d^2}$$