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Evaluate the integrals by making appropriate u-substitutions and applying the formulas reviewed in this section$$\int \frac{d x}{\sqrt{x^{2}-4}}$$
Calculus 1 / AB
Calculus 2 / BC
Chapter 7
PRINCIPLES OF INTEGRAL EVALUATION
Section 1
An Overview of Integration Methods
Integrals
Integration
Integration Techniques
Trig Integrals
Trig Substitution
Missouri State University
Harvey Mudd College
University of Nottingham
Boston College
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Evaluate the integrals by …
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Evaluate the integrals.
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I know this question. We're going to be solving an indefinite integral using the method of you substitution to me of the integral of D X over the square root of X squared minus force. The first thing we're gonna do is we're gonna just rewrite this as the girl of D axe of the square root over the square root of, uh, X squared minus chief squared. And so from here, we're going to just set are X equal to you. So we're going toe, have, um, active equal to you dio. And then we're gonna take the driven SRD X is equal to do you. And now we can just rewrite this equation a plug the in for our d x r d u and for our X Are you going to have a couple of d do over the square root of you squinted fitness to to, uh, to square. Sorry on that. We're going to be using the equation that states that, um the integral of d you over the square root of you squared minus a squared is equal to the L on of you, plus the square root of you plus and a plus R E minus a squared plus C. So from here we can plug in for our values. So we're going to have our two is equal to R A. So we're going tohave the l n of you plus the square root of you squared minus two squared plus c And now all we have to do is plug in for are you and our view is equal to X So our final answer is going to be the L on of X plus the square root of X squared minus four plus C.
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