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Evaluate the given integral.$$\int \frac{e^{2 x}}{e^{2 x}+1} d x$$

$$\frac{1}{2} \ln \left(e^{2 x}+1\right)+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Missouri State University

Campbell University

Baylor University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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Evaluate the integral.…

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Evaluate the integral.

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Evaluate the given integra…

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evaluate Integral

we can replace E to the two X plus one by using a use substitution, taking you to be each of the two x plus one. That way, this constant one disappears when we differentiate, because do you becomes two times each of the two x dx, which allows us to write this integral in terms of you to get 1/2 times the integral of one over you, which is equal to 1/2 times Ellen of the absolute value of you plus C. And now we can replace you with each of the two X plus one and we can drop the absolute value because e to the two X is greater than zero and that completes the problem.

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