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Evaluate the integrals by making appropriate u-substitutions and applying the formulas reviewed in this section.$$\int \frac{e^{\tan ^{-1} x}}{1+x^{2}} d x$$

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

Boston College

Lectures

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In mathematics, a trigonom…

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In mathematics, trigonomet…

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Evaluate the integrals by …

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I. So, in this question, we're going to be solving the indefinite integral using the method of the substitution. So first thing we're going to do is we're going to set are tan of the arc Tanne. So I should say X is equal to you. Ongoing take derivative of both sides derivative of the ark 10 of acts is just equal to one over x squared, plus one d x. So now we're going to plug in tow our equation. So we're gonna plug in Ah, for the tan of, uh, for the ark 10. I'm sorry of acts, are you? And then we're going to plug in for our ah, one over x squared plus one d x r d you So we're just gonna have the integral of e to the U D you, which is just going to be equal to the Inter to Ah, you plus C on from here. All we have to do is plug in for are you and are you is equal to the arc Tanne? Uh, axe. I'm sorry. This is we have e to the u is what the, um integral of each of the U is equal to And so from here we're going tohave e to the Ark tan of X plus C on That is our final answer.

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