Problem 23 Easy Difficulty

Choose the correct answer.
$\int \frac{d x}{x\left(x^{2}+1\right)}$ equals
(A) $\log |x|-\frac{1}{2} \log \left(x^{2}+1\right)+C$
(B) $\log |x|+\frac{1}{2} \log \left(x^{2}+1\right)+C$
(C) $-\log |x|+\frac{1}{2} \log \left(x^{2}+1\right)+\mathrm{C}$
(D) $\frac{1}{2} \log |x|+\log \left(x^{2}+1\right)+C$

Answer

Related Courses

Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 7

Integrals

Section 5

Integration by Partial Fractions

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Video Transcript

We have another number 23 in which we need to find the integration of the X by X into X squared plus one. So we have to use parcel faction fall one by accent too Access squared plus one. Since this cannot be factories further so we can write by X Place B X blessed buyer Access squared plus one. Because geometry is quadratic. So one will be equal to in two X plus one. Blessed be X plus C into X. So let's write a place be. This will be the coefficient of X squared. Bless C. X plus A. Okay now if you create the coefficients A plus B will be equal to zero because there is no excess square here and Coefficient of C is zero Coefficient Back zero. So she will be equal to zero because there is no term of X in left hand side but equal to one. If equal to one. We will be equal to from here. We will be equal to -1. We have a we have been we have seen so let us plug in in our integration which is equal to a by X. So simply one by X. one by XDX plus bx plus C. So bx that is minus one X and C is zero. So two X plus X squared plus one dicks. Now this will be love of monarchs less. We should write minus uh X by Access Square Plus one. The now differentiation of X squared plus one is two X. So let us multiply and divide with two Will be getting a lot more artifacts -1 by to log off X squared plus one. Let's see. They should be the answer. Option Number is the correct one. Thank you.

Get More Help with this Textbook