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Evaluate the given definite integrals.$$\int_{2}^{3} \frac{8\left(x^{2}+1\right)}{\left(x^{3}+3 x\right)^{2}} d x$$

$\frac{22}{189}$

Calculus 1 / AB

Chapter 25

Integration

Section 4

The Definite Integral

Integrals

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:43

Evaluate the integrals.

00:58

Evaluate the integrals…

04:32

$$\text {Evaluate the foll…

Evaluate the following int…

10:10

02:05

01:34

04:14

03:14

21:31

Hello Friends We have to evaluate their given definite integers. That is integration of book three head of X squared plus one upon Excuse Plus three X square of the X. Okay so this can it can be indicated with so now we will differentiate it with respect to X. So this will be three access well plus three because to do you upon the X. So we can I did Access couple is one of the x equals two. one of 1. three of new when actually cause you to the lower limit then lower limit of you will be To the power of 3-plus 3 into two. That is eight plus six. That is 14 When exposed to three. Then you will be into the power three Last three into 3. So that is the question nine plus 27 Plus nine. So that is a costume 36. Mhm. So integration will be 14 to 36 yet by three of the U upon U squared Get up on three of Indication of 14: 36. Your department is two of the U. C. Integration of this will be close to Hit up on three you two departments two plus one upon managed to plus one 14- 36. So this will because we ate up on three You two departments 7 upon -1 fought in 2 36 So does the U -1 half for it by three When upon 36 months one upon 14 so we can write it. So that's when we questioned you. And 36 to the power of minus one- of 14 to the power of -1 multiplied wade upon three. So this will be a cost to 22.189. Mhm. Okay and they said the costume 0.116 four. So this is the answer. I hope you are not sure. Thank you.

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