10.4.14 Laplace transform

Condition: Using the convolution theorem, find the original of the first of the given functions, to find the originals in the rest, use the result obtained, either the differentiation theorem, or the integration theorem of the original. Check the answer to the last of the given examples, either by finding its image from the received original, or by finding the original itself in another way. a) \( \frac{p}{(p+1)\left(p^{2}+1\right)} \) b) \( \frac{1}{(p+1)\left(p^{2}+1\right)} \) c) \( \frac{1}{p(p+1)\left(p^{2}+1\right)} \).