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Integrate each of the given functions.$$\int_{1}^{3} \frac{3 x^{3}+8 x^{2}+10 x+2}{x(x+1)^{3}} d x$$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 10

Integration by Partial Fractions: Other Cases

Integrals

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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in the problem we have been given integration one and three three x cubed plus eight x square Plus 10 x plus two bon X into X plus one to the power three dicks. This is equal to Dress in 1, 2 3, one upon x plus one Plus three upon x plus one whole square plus to opponents dicks. No, this is regionals. Ellen marks plus one plus three into x minus one. So the X plus one to the power -2 upon -2 plus twice. Ellen mod X one and three. So this is equal to Ellen Marred X-plus one minus three upon two into one upon X plus one. Well it's quite mhm Plus to Ellen marks one and 3, the limits putting the limits we have the answer. S Ellen 4 -3 upon 32 Plus to Ellen Model three minus Ellen this is Ellen mod two Plus three upon 8. So further this equals to 3.17162. So this is the answer.

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