# Tagged Questions

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### How to derive laplace formula for given integral of laplace transform? [closed]

As stated in title how to derive formula directly from definition? $$\int_0^ \infty te^te^{-st} dt$$
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### Contour integration with branch points inside the contour.

In my scientific research I ran into an unpleasant situation with specific type of contour integrals. Being more specific I have problems not with integrals themselves (I can use various numeric ...
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### Laplace transform quick answer check :) using second shift theorem

I want to get $L((t-4)^2u(t-4))$ I say this is a second shift with $g(t)=(t^2-4t)$ and my friend says "NO you are wrong, you are dumb!!!!!! $g(t)$ is MOST CERTAINLY equal to $t^2$" Mine gives me ...
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### Evaluating Laplace Transform

I have a Laplace transform function of the following form and I'm trying to evaluate it. From my research I think I need to take the Inverse Laplace Transform and then integrate, but I'm having ...
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### Convergence integral causal function

I have an exercise where there is the following given: $f$ is a causal function. $f$ is Laplace transformable:$\int_{0}^{\infty} f(t)e^{-zt} \, dt = L(z)$ with $Real(z)> -1$ I have to ...
### How do I evaluate $\lim_{h \to \infty} e^{h(1-s)}$?
I'm messing around with Laplace, and was trying to find the transform of $e^{t}$ and I have to evaluate $$\lim_{h \to \infty} e^{h(1-s)}$$ I figure if $s=1$, the limit is $1$. If $0≤s<1$, the ...
### Find the Laplace transform of $g(t) = 1+cos^2(2t)$ by direct integration
I'm having trouble finding out how to directly integrate the function $f(t)$ because of the $\cos^2(2t)$ term. I understand that $\cos^2(2t) = \frac{1}{2} + \frac{1}{2}\cos(4t)$ but I don't ...