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Evaluate the integral.

$ \displaystyle \int \frac{e^{2x}}{1 + e^x}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Integration Techniques

Missouri State University

Campbell University

Baylor University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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Evaluate the integral.…

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evaluate Integral

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Evaluate the given integra…

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Let's try to use a use for this one. Let's take you to be either the ex deal also even X then here. So firstly, for under the use of all, rewrite this. Yeah, So you can see here. That is our to you. So we have you have here one plus you down there. And then we also see this. This is just our do you. So it's already there. So the next step here would be to do polynomial division. So go ahead and do your division here. You could do synthetic if you need to. Quotient is one and then the remainder is minus one. So we write in this form Integrate this and then finally easier use up toe back. Subutex. We could drop the absolute value here since eat of the X Plus one is positive and that's your final answer.

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