Home
Class 12
MATHS
int(x dx)/((x-1)(x-2)equal (A) log|((x-1...

`int(x dx)/((x-1)(x-2)`equal
(A) `log|((x-1)^2)/(x-2)|+C` (B) `log|((x-2)^2)/(x-1)|+C`(C) `log|((x-1)^2)/(x-2)|+C` (D) `log|(x-1)(x-2)|+C`

A

`log|((x-1)^2)/(x-2)|+C`

B

`log|((x-2)^2)/(x-1)|+C`

C

`log|((x-1)^2)/(x+2)|+C`

D

`log|(x-1)(x-2)|+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Option `B` is the correct answer
Given `int(x dx)/((x-1)(x-2)`
By partial fraction we have
`(x )/((x-1)(x-2))=A/(x-1)+B/(x-2)`
...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT ENGLISH|Exercise MISCELLANEOUS EXERCISE|44 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.3|24 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise Exercise 7.11|20 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT ENGLISH|Exercise Solved Examples|13 Videos

Similar Questions

Explore conceptually related problems

int(dx)/(x(x^2+1) equal(A) log|x|-1/2log(x^2+1)+C (B) log|x|+1/2log(x^2+1)+C (C) -log|x|+1/2log(x^2+1)+C (D) 1/2log|x|+log(x^2+1)+C

int (dx)/((x+1)(x-2))=A log (x+1)+B log (x-2)+C , where

The integral int (xdx)/(2-x^2+sqrt(2-x^2) equals: (A) log|1+sqrt(2+x^2)|+C (B) xlog|1-sqrt(2+x^2)|+C (C) -log|1+sqrt(2-x^2)|+C (D) xlog|1-sqrt(2-x^2)|+C

d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}] equals (a) (x^2-1)/(x^2-4) (b) 1 (c) (x^2+1)/(x^2-4) (d) e^x(x^2-1)/(x^2-4)

int(log(x+1)-log x)/(x(x+1))dx= (A) log(x-1)log x+(1)/(2)(log x-1)^(2)-(1)/(2)(log x)^(2)+c (B) (1)/(2)(log(x+1))^(2)+(1)/(2)(log x)^(2)-log(x+1)log x+c (C) -(1)/(2)(log(x+1)^(2))-(1)/(2)(log x)^(2)+log x*log(x+1)+c (D) [log(1+(1)/(x))]^(2)+c

int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a) 1/2(ln((x-1)/(x+1)))^2+C (b) 1/2(ln((x+1)/(x-1)))^2+C (c) 1/4(ln((x-1)/(x+1)))^2+C (d) 1/4(ln((x+1)/(x-1)))^2+C

int_(1)^(2) (dx)/(x(1+log x)^(2))

intdx/(x(1+x^10))= (A) 1/10 log((1+x^10)/x^10)+c (B) 1/10 log(x^10/(1+x^10))+c (C) 1/(1+x^10)^2+c (D) none of these

int(x^3)/(x+1)\ dx is equal to (a) x+(x^2)/2+(x^3)/3-log|1-x|+C (b) x+(x^2)/2-(x^3)/3-log|1-x|+C (c) x-(x^2)/2-(x^3)/3-log|1+x|+C (d) x-(x^2)/2+(x^3)/3-log|1+x|+C

Find y(x) , if it satisfies the following differential equation (dy)/(dx)=(x-y)^2 , and given that y(1)=1 (A) -ln|(1-x+y)/(1+x-y)|=2(x-1) (B) ln|(2-y)/(2-x)=x+y-1 (C) ln|(1-x+y)/(1+x-y)|=2(x-1) (D) 1/2ln|(1-x+y)/(1+x-y)|+ln|x|=0