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

$\frac{33}{784}$

Calculus 1 / AB

Chapter 25

Integration

Section 4

The Definite Integral

Integrals

Campbell University

University of Michigan - Ann Arbor

Idaho State University

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Hello. We have to value their given definite integral. That is given Money is 1-2 eight x managed to upon to access square minus X plus one. To the power of three the X. So we will substitute to prescribe you Well we can it can be integrated with their but the substitution of the excess carbon is X plus one as it goes to you. So now we will do defense here differentiation of this with respect to X. So this will be four X -1. Yeah because too do you upon the X. four X -1 of the X. Because who do you so we can add it And then x equals to one is 1. Then you will be consumed two and two minus one squared minus of minus one plus one. So there's a little bit too Plus one Plus 1. That is the cost of four. And then actually closer to You will be two into two square minus of two plus one. So this will be he had managed to that is six plus one, that is seven. So these are the new limits so you can buy it 4 to 7. Okay. Goes off four X -1 DX so we can like it's a cause to be you upon Here to the power of three. Okay, so this will be cause to integration of this will be goes off you believe our ministry plus one upon monastery plus one 4 to 7. So this will be considered to myself, You two departments to upon managed to four per seven. So this will be a cost to- of 75 I -2- of 4 to the power monastery. So this will be a question 7 to the power of manage to- of 4 to the power of manage to so that we request to minus of 33 upon 784. So this will be a question 33 upon 784 So this is the has it And it will be close 0.04-1. Okay, so this is the answer. Mhm. I hope you understood things.

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