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Evaluate the integral? : # int e^(2x)/(1+e^(2x))^2 dx #

Answer 1

Christopher Agresta

# int \ e^(2x)/(1+e^(2x))^2 \ dx = -1/(2(1+e^(2x))) + C#

We want to find;

# int \ e^(2x)/(1+e^(2x))^2 \ dx #

Let #u =1+e^(2x) => (du)/dx = 2e^(2x) #

Substituting into the integral we get:

# int \ e^(2x)/(1+e^(2x))^2 \ dx = int \ (1/2)/u^2 \ du# # " " = 1/2int \ 1/u^2 \ du# # " " = -1/2 1/u + C# # " " = -1/(2(1+e^(2x))) + C#

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Answer 2

Ezekiel Alexander

The integral (\int \frac{e^{2x}}{(1+e^{2x})^2} dx) evaluates to (-\frac{1}{2(e^{2x} + 1)} + C), where (C) is the constant of integration.

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Answer from HIX Tutor

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.