Home
Class 12
MATHS
int(x)/((x^(2)-a^(2))(x^(2)-b^(2)))dx is...

`int(x)/((x^(2)-a^(2))(x^(2)-b^(2)))dx` is equal to

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int(xdx)/((x^(2)-a^(2))(x^(2)-b^(2)))`
Put `" "x^(2)=t" "rArr" "xdx=(1)/(2)dt`
`therefore" "l=(1)/(2)int(dt)/((t-a^(2))(t-b^(2)))`
`=(1)/(2)int{(dt)/((a^(2)-b^(2))(t-a^(2)))-(dt)/((a^(2)-t^(2))(t-b^(2)))}`
`=(1)/(2(a^(2)-b^(2)))log|(t-a^(2))/(t-b^(2))|+C`
`rArr" "l=(1)/(2(a^(2)-b^(2)))log|(x^(2)-a^(2))/(x^(2)-b^(2))|+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)|78 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

Similar Questions

Explore conceptually related problems

int(dx)/((x^(2)+a^(2))(x^(2)+b^(2))) equals.

Find int(dx)/((x^(2)+a^(2))(x^(2)+b^(2))) equals

int(x^(2))/(x(x^(2)-1))dx is equal to

int(dx)/(a^(2)sin^(2)x+b^(2)cos^(2)x) is equal to

int x^(2)dx is equal to:

int(x^2e^(x))/((x+2)^(2))dx is equal to

int(x^(2)+1)/(x(x^(2)-1))dx is equal to

int((x+1)^(2))/(x(x^(2)+1))dx is equal to:

int x^(2)(ax+b)^(-2)dx is equal to

int(x)/((x^(2)+1)(x^(2)+2))dx is equal to