# Evaluate #int \ e^(-st)sint \ dt #?

# int \ e^(-st)sint \ dt = -(e^(-st)(s sint +cost ))/(s^2+1) + C #

We seek the integral:

We can then apply Integration By Parts:

Then plugging into the IBP formula:

We have:

Now consider the integral given by:

We will now need to apply IBP again:

Then plugging into the IBP formula we have::

And so combining the results we find that:

And not forgetting the constant of integration,

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The integral of ( e^{-st} \cdot \sin(t) , dt ) is ( \frac{s}{s^2 + 1} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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