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Evaluate the integral.$$\int \frac{d x}{\sqrt{x^{2}-6 x+10}}$$

$\ln (x-3+\sqrt{(x-3)^{2}+1})+C$

Calculus 1 / AB

Calculus 2 / BC

Chapter 7

PRINCIPLES OF INTEGRAL EVALUATION

Section 4

Trigonometric Substitutions

Integrals

Integration

Integration Techniques

Trig Integrals

Trig Substitution

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Okay. Okay. So we have integral, uh, one over the square root of execute X squared minus six X plus 10. And so what we're dealing with here and something that almost looks like a square on the bottom. So let's complete the square. And in order to do that, you'll see the next minus six. X plus nine plus one is in equivalent expression to the denominator. And so that's equal to X minus three years squared, plus one. So what we're going to have is TX and let's let you so let's letting you equal X minus three. So you is equal to D X and so we can replace some of the things in here. So is the DS with the deal. This here is our denominator, and that's gonna be you. So you squared plus one. And now this Books like a trig. So So let's let u equal tangent data you equal to seek an squared leader. You see that? So you're going to get not just box these off and actually it's just moved on sub. So you've got the integral of you over the square root of you squared plus one that is equal to integral Seacon Square data over second theater because you swear so tangent squared plus one swear rooted. So you squared plus one equals 10 jin squared plus one. So that's people the second squared theater. So you can square root that just get Seacon So that is equal to the integral of seeking data the theater. So that is equal to the natural log of second theater atrocity engines. Vida. So moving along again then is equal to the natural log of the spirit of you plus one once, um, you so bringing that all the way back Thio X So we'll move over here. You're going to get X minus three squared once one expects minus three was she and

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