Problem

Integrate the rational functions. $$ \frac{3 x-1}…

02:27

Problem 13 Easy Difficulty

Integrate the rational functions.
$$
\frac{2}{(1-x)\left(1+x^{2}\right)}
$$

Answer

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Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 7

Integrals

Section 5

Integration by Partial Fractions

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Problem 1

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Video Transcript

following number again, in which we have to integrate the rational function to buy one minus six into one Plus Extra Square. Using parts infraction. So let us write it as one x 1 -1 because this cannot be factories further. So we should be writing a by one. Many sex. Let's be explicit Bye One plus access choir or access squared plus one. So we will be having to equal to into Access Choir Plus one. Let's be explicit into one mile sex. Now we have to find the value of B, B, C and A. So we'll be using technique of making each term equal to 01 by one. So if you plug in X equal to one it will be to equal to three a.m. Sorry to a. Because one is 11 plus 12 way To a. And this time will be zero even be equal to one. Similarly if you plug in X equal to anything all the supposed zero. So it will be to equal to a let's see. So she will be equal to two miners say that is one And if you plug in anything that was supposed to be equal to -1 so it will become to A to A And this is -2 x. So minus to B. It will be in place to be because -2. Okay and -2 c. So let us plug in equal to one. So this will be too plus two B minus two. These two will get cancelled out so B will be equal to one. So we are value B one C one equal to one. So mm to buy one minus X into one plus X square will build in as a by one minus X Is to one x 1 -6 plus B. One by a B X policy. So simply X plus one by one plus x esquire Now we have two integrated. Be explicit We have integrated D X D X. Dx. So this is if you take minus as common it will become minus log off X -1 integration place. Let us spit it out X by one plus access Choir D X plus one by one plus X. Choir Dx. So Differential of one places, squares to works so it is multiply and divide by two. So this will become minus love Model X -1 plus one by two log access quiet plus one is always positive. So let us right simply access quite plus one And bless 10 universe 10 universe X Policy. So they should be the answer for number 13 remember 13. Thank you. Yeah.

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