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$$\frac{1}{x\left(x^{n}+1\right)} \text { [Hint: multiply numerator and denominator by } x^{n-1} \text { and put } x^{n}=t \text { ] }$$

Calculus 2 / BC

Chapter 7

Integrals

Section 5

Integration by Partial Fractions

Integration Techniques

Campbell University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

01:53

In mathematics, integratio…

27:53

In mathematics, a techniqu…

00:54

Divide as indicated.$\…

01:20

$$\text { Divide } x^{3 n}…

04:51

perform the indicated oper…

00:49

$\frac{1}{x^{4}+x^{3}+2 x^…

03:15

Simplify.$$\frac{x}{1-…

01:37

Simplify $: \frac{\frac{1}…

00:44

Multiply the numerator and…

Perform the operations and…

00:29

simplify.$$e^{x}\left(…

01:10

Simplify.$$\frac{\frac…

02:23

$$\text { Simplify: }\left…

00:50

Simplify the compound frac…

Simplify.$$\frac{x…

02:00

Simplify.$$\left[\…

00:58

Simplify each expression.<…

01:35

Divide and, if possible, s…

02:29

Simplify.$$\frac{1…

00:56

Evaluate $\lim _{x \righta…

00:35

Write each expression with…

Number 16 in which we need to integrate one by accent too X. raised to the power endless one. So first of all let us multiply and divide with access to the power and mines one Access to about N -1. So this will become actually to the power and -1 by this. And this will make access to power end And to access the parent plus one. And now we have to just integrated. So let us substitute access to the power and equal to T which is equal to N X. Raised to the power and minus one dx equal to DT after differentiating. So our integration will become okay so let us multiply and divide by one by N. So that this whole thing will become a culture DT. So one by N. One by the T plus one DT. So we have to use partial fraction to solve this. So let us take it out one by tion to T plus one. Let us write one by a by T plus B. Bye deep list one. So they should be Donald when equal to a. and two. Deep list one plus bt. We have to find the value of A. And B. For this value. Making the terms one by +01 by one. So let us plug into equal to minus one. The storm will be zero minus B. So be equal to -1 Now if equal to zero. So one will be equal to a. Is one. So this become equal to a bit one by T one by deep list one. Let us plug in here. So This will become equal to one by N. one by T minds. one by deep list one and GT. So one by and log the minus Love. D. Plus one policy. Okay This is one by end Love B. Bye. D plus one model list. Let's see. No value of T. Is value teach accept foreign. So this will become one by N. Not actually the power and My access to power and plus one plus C. So they should be the answer. Thank you. So.

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Simplify each expression.$$n^{x+2} \div n^{x}$$

Divide and, if possible, simplify.$$\frac{x^{2}-1}{x} \div \frac{x+1}{x-…

Simplify the compound fractional expression.$$\frac{1-\frac{1}{x^{2}…

Simplify.$$\frac{1}{1+(1+x)^{-1}}$$

Evaluate $\lim _{x \rightarrow 1} \frac{x^{m}-1}{x^{n}-1}$ for any numbers $…

Write each expression without using negative exponents, and simplify the res…

03:39

Integrate the rational functions.$$\frac{x^{3}+x+1}{x^{2}-1}$$

01:38

Integrate the functions.$x \sin x$

04:06

For each of the differential equations in Exercises 11 to 14 , find a partic…

05:06

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06:20

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04:00

Integrate the functions.$$x \cos ^{-1} x$$

00:48

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01:34

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11:38

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02:59

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