We use Laplace to go into complex or frequency domain and do our analysis of system. So what does the trigonometric substitution of tan(x) cos(x) or sin(x) shows while integrating some complex function. Although that simply our integral but what is that domain be which we are working on.
2026-03-31 15:45:01.1774971901
What is the logic behind the trigonometric substitution method in integration?
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When you make a u-substitution, you are not working with a new variable, but a variable that is dependant on the old variable. As such, you aren't changing the space, but changing the form of the integral. Solving this will give you an answer in terms of your original variable.
Instead, when you do a Laplace transform, you are changing which variable the problem is working with. $s$ is not related to $x$ in any way. As such, it can be said you're working in a different domain.