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Evaluate the integrals that converge.$$\int_{-1}^{+\infty} \frac{x}{1+x^{2}} d x$$

$+\infty($ divergent $)$

Calculus 1 / AB

Calculus 2 / BC

Chapter 7

PRINCIPLES OF INTEGRAL EVALUATION

Section 8

Improper Integrals

Integrals

Integration

Integration Techniques

Trig Integrals

Trig Substitution

Campbell University

Oregon State University

University of Michigan - Ann Arbor

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the improper integral here. Nickel going negative one to infinity of X over one plus x squared DX. So we go ahead and we take the limit. Um, as well as be approaches infinity of the inner grow. Now from negative one to be lips, um, to pee of, well, X over one plus x squared dx. Okay, so we're just gonna go. This is equal to the limit, as be approaches infinity. Um uh, well of one half times the integral from negative one to be of two X over one plus x square the x. Okay. Um, so now, well, this is equal to the limit as be approaching infinity of well, we get. So again, we have the limit here. Right? Okay, are going limit limit has be approaches. Infinity of well of one half times is integral becomes the natural log of one plus x squared. And then we are evaluating from negative one to be so this is equal Chew, um, one half times the limit, as be approaches infinity. Um, off. Well, the natural log of one plus b squared minus one half times the natural log, um of to write, which is which is equal to infinity. So we see here that delimited here approaches infinity. Therefore, the given improper integral is die a virgin. So we are divergent and we cannot compute it because, well, we are governed.

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