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Integrate the functions.$$\frac{6 x+7}{\sqrt{(x-5)(x-4)}}$$

Calculus 2 / BC

Chapter 7

Integrals

Section 4

Integrals of some Particular Functions

Integration Techniques

Missouri State University

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:00

Find the indefinite integr…

04:18

Use integration tables to …

03:41

Evaluate the integral.…

01:12

00:57

Evaluate the following int…

01:43

02:42

01:52

Determine these indefinite…

05:29

Evaluate the integral.

01:27

06:58

Evaluate the integrals.

01:25

Find the antiderivative.

03:25

Use substitution to find e…

01:20

01:53

01:06

Find the most general anti…

00:41

01:34

05:21

So we have question number 19 in which we need to solve. Uh Well to find the International six x plus seven divided by underwrote X minus five in two x minus four. Okay so let us rewrite it as six X plus seven. They went by Access choir -9 x plus 20 under the square root. So there's his six x plus seven divided by if he just All right it is is it too So no problem. We'll be using the matter. Mhm of integration as six X plus seven will be writing it six X plus seven equal to a D by D X. Access Choir -9 x plus 20 plus B. Now six X plus seven will be equal to mm two x -9 plus B. So this is to A X Plus B -98. Now let's equate The coefficient of accent constant terms from these two. So if you create coefficient of X it will become too equal to six so equal to three. And if you quit the constant term uh we will be having B -9 equal to seven so we will be equal to seven plus nine A. That is 34. So He becomes equal to 34. So our integral print will look like well look like yeah uh E DVD X X squared minus minus plus 20. So it is three D V D X means differentiation of this thing. So two x -9 and a bless 34. Mhm Offly 34, divide by access squad -9 x plus 20 under the squad shoot K. D. X. So if you separate it out it will become three and 2 two weeks -9 by access Choir minus nine X plus 20 under the square root DX. 34 into one by Access choir -9 x plus 20 under the square road dx. Now if just write it at the end of we know that we have differentiation of this In the numerator. So this could be simply written as three one by T DT after substituting x squared minus nine X plus 20 equal to T. Okay plus 34 that is completely square here. X -3. Old Square Plus 20-9 dx under the square root. So here it will become clear departments one x 2 so teachers to department minus one by two plus one -1 x two Plus 1. And plus hear 34 if we assume x minus three equal to Y. So this whole thing will become equal to do you? I buy why square minus Until 11 whole square into the square root. Yeah so there's not quantity 2 -1 so six and 2 And the rooty place 34 and we have formula for this log. Why minus I'm sorry. Plus Y squared minus access Choir. This constant of integration. See so why square minus X. Is quiet log. So we have formula access squared minus his question. Yes six under T. T. Is simply that's a square minus nine X plus 20 Access choir plus nine x plus 20 Plus 34 Log. This is why why it means x minus three X -3 plus under root all those things that is X -5 and two x minus four. Okay and policy that should be the answer. Okay exercise three yes 34. Yes. Let's see. This should be the answer. Thank you.

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