# How do you integrate #int e^x/(4-e^x)# using substitution?

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This is a common integral:

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To integrate ( \frac{e^x}{4 - e^x} ) using substitution, let ( u = 4 - e^x ). Then, ( du = -e^x dx ).

Now substitute ( u ) and ( du ) into the integral:

[ \int \frac{e^x}{4 - e^x} dx = -\int \frac{1}{u} du ]

This simplifies to:

[ -\ln|u| + C ]

Substitute back for ( u ) to get the final answer:

[ -\ln|4 - e^x| + C ]

where ( C ) is the constant of integration.

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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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