Integrate the functions.
$$
\sqrt{x^{2}+4 x+6}
$$

Answer

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Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 7

Integrals

Section 7

Definite Integral

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Video Transcript

we have fallen number three in which we need to integrate. Access squared plus four X plus six. Access Choir plus four X plus six under the square root. Okay so this could build an as by completing the square method X plus two whole square plus six minus two square. And the route so X plus to hold square plus six minus four to Okay now this is I so we have to integrate it the X. Now we have to substitute let us say explodes to equal to why? So D X will be equal to Dy so this becomes Y squared plus let us right through two whole square and D way. So we have formula for this formula is if uh like access choir plus a squared on the route DX So this will be one by two accent too. Access square plus it's quiet place is quite by to log. Love of X place access square place is square under the root. Let's think we will be using the same formula we're here. So this is one by two in a place of access to it. Why Access square plus a square? So this will be simply Y squared plus two plus a squared by two. That is two by two. Because A is route to here, log X means Y plus X squared plus a square. That is Y squared plus two plus. Now that is plaguing the value of this, Y as X plus two. We will be getting one by two. X plus two in to access square players four X plus six. If you plug in where I could expose to we're going to get it. We're going to get this. So there's a log X plus two. Place access square Place four X plus six plus C. So this should be the answer. Okay, so they should be answered for third number questions. Thank you so much.

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