Hy. Can someone please explain me how can I resolve ∫ 0 ∞ e − ( s I − A ) t d t ? I must have the final result ( s I − A ) − 1 . I think it has the euler form, for beta integral but I don't know how can I get to that result.

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Hy. Can someone please explain me how can I resolve       ∫          0              ∞            e          −      (      s      I      −      A      )      t          d  t ? I must have the final result   (  s  I  −  A      )          −      1      . I think it has the euler form, for beta integral but I don&#039;t know how can I get to that result.

Savion Chaney · Accepted Answer

If you wrote the integral correctly, just use the fact that  ∫      e          k      t        =      k          −      1            e          k      t        +  Cwhere, of course,   k is a constant and   C is an arbitrary constant. There is no need for a fancy integral such as the beta integral. Finding the definite integral from that is easy, since the limit is easy.All this, of course, depends on   s,   I, and   A being real or complex numbers.

Hy. Can someone please explain me how can I resolve int^infty_0 (e^(−(sI−A)t)dt) ? I must have the final result (sI−A)^(−1). I think it has the euler form, for beta integral but I don't know how can I get to that result.

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