Help with easy integral?

Question

∫ e^( (r + i - 1)*log(t) - t ) dt

where r and i are constants

Answer 1

S e^( (r + i - 1)*log(t) - t ) dt ........................S means integral here.

= e^( (r + i - 1)*Slog(t)dt - St  dt

= e^( (r + i - 1)(tlogt - t) - (t^2)/2 +c

as r and i are constants e^() can be taken out and what remains is formal integration

Answer 2

Since r and i are constants, let's write k=(r+i-1) for simplicity. And I'm going to assume your log is to base e since you never state the base.

e^(klog(t) - t )

= e^(klog(t)) * e^(-t)

= e^log(t^k) * e^(-t)

= t^k * e^(-t)

You've to state whether r and i are integers or not. If they are not integers, there is no closed form solution.