# How do you use partial fraction decomposition to decompose the fraction to integrate #1/(1+e^x) #?

This is not really a partial fraction problem, but instead it's just a trick. Write:

This means

Therefore,

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To decompose the fraction 1/(1+e^x) using partial fraction decomposition, first, express it as a sum of simpler fractions. Start by assuming that 1/(1+e^x) can be expressed as A/(1+e^x) + B/(1+e^(-x)). Then, find the values of A and B by equating the numerators of the original expression and the decomposed expression. Finally, integrate each simpler fraction individually to obtain the integral of the original expression.

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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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