10.4.14 Laplace Transform

Condition: using the coagulation theorem, find the original of the first functions, to find the originals in the rest, use the result, or the differentiation theorem, or the theorem of integrating the original. The answer to the latter of the specified examples to check, either finding its image according to the original, or finds the original in another way. a) \ (\ frac {p} {(p+1) \ left (p^{2} +1 \ right)} \) \ (\ frac {1} {(p+1) \ leftt (p^{2} +1 \ right) \) \ ( \ frac {1} {p (p+1) \ left (p^{2} +1 \ right)} \).