Laplace Transform Homework: Proving Informally

jakncoke
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Homework Statement



supposed to prove informally that

f(x)=Integral 0-->infinity (cosxt/(t^2+1))dt == Pi/2*Exp[-x]


Homework Equations





The Attempt at a Solution


no clue, need some hints to get started
 
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Is that (cos x) t or cos(xt)?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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