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Integrate each of the given functions.$$\int \frac{d T}{T^{2}+2 T+2}$$

$\tan ^{-1}(T+1)+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 6

Inverse Trigonometric Forms

Integrals

Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

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we want to evaluate the following integral. The integral of D T over t squared plus two T. Plus to this question is showing their understanding of how to utilize trig and metric intervals in particularly testing our newfound knowledge of inverse trig metric into rules on the left, we have one integral, d'you over a square minus U squared Is our exciting you over a plus. See on the right to integral, D'you over a squared plus B squared is one over A. Are changing over a plus C. Thus we must have because we have no square roots are denominated for integral that we're using integral to now identify you. Do you end A? We see that you is one plus T do U S D T and A is one so we can rewrite are integral and solved too. And certainly to the US we have the integral. DT over one plus one plus t squared gives us for one over a arch. And you were able to see Arc tangent one plus 2 plus see the constant of integration in this problem.

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