# How do you evaluate the integral #int 2^x/(2^x+1)#?

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To evaluate the integral ∫(2^x / (2^x + 1)) dx, you can use a substitution method. Let u = 2^x + 1. Then, du = 2^x ln(2) dx. Rearranging for dx, you get dx = (1 / (ln(2) * u)) du. Substituting these into the integral, you get ∫(1 / u) du. This integral is ln|u| + C, where C is the constant of integration. Finally, substituting back for u, the result is ln|2^x + 1| + C. Therefore, the integral of 2^x / (2^x + 1) dx is ln|2^x + 1| + C.

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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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