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Evaluate the integral.
$ \displaystyle \int \sqrt{\frac{1 + x}{1 - x}}\ dx $
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 5
Strategy for Integration
Integration Techniques
Oregon State University
Baylor University
University of Michigan - Ann Arbor
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 indicated int…
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Evaluate the integral.…
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Evaluate the following int…
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Find the Integral of \int …
Let's start off by just multiplying the intolerant by something else from multiply top and bottom by one plus X inside the radical. So go ahead and multiply out those name raiders on top one plus x, the radicals cancel in the denominator and we can go ahead and split this into two. You may remember this first inner rule And for the second for the first General, if you haven't memorized, you can take X to be signed here. That's it. Drinks up. And then when you integrate this, you get it. Send in for sex, Slim. Now, over here, we can do a use up. So then, there you have it to you. Oh, from the negative two equals X t x. So this in a girl becomes negative would have used to the negative one have to you. So go ahead and use the power ruler and and simplify and we get negative. You too, the one half. So let's just go ahead and negative. You too, the one half and then replace you back in terms of X from this equation here. So that's minus new to the one half. So that's one minus X square to the one half power. And then at our constancy, finally, and that's our final answer
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