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Evaluate the integral.
$ \displaystyle \int e^{x + 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
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University of Michigan - Ann Arbor
Idaho State 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.
01:23
Evaluate the integral.…
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evaluate Integral
before we do a U substitution. Let's rewrite this in a girl using the laws of exponents as either the ex times e to the e to the x power. So that's just using your laws of exponents. A B a C is into b plus c. So then here, let's do it. You So you girls eat of x deal either the ex so than here. When we put this in, we just have you you do you The eating of the yoo is this term here and then the d u is giving us the e x, the X and asked what's left over up here. So this just verifies that we have the right integral in terms of you and Ray Tous. We know that's just either you pussy and then there we just replace you with even X from our use. Um so eat to the e to the X power plus see? And that's your final answer
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