Home
Class 12
MATHS
int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1)...

`int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1))dx` is equal to

A

`2sqrt(2-(2)/(x^(2))+(1)/(x^(4)))+C`

B

`2sqrt(2+(2)/(x^(2))+(1)/(x^(4)))+C`

C

`(1)/(2)sqrt(2-(2)/(x^(2))+(1)/(x^(4)))+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let l`=int((x^(2)-1)dx)/(x^(3)sqrt(2x^(4)-2x^(2)+1)),`
`" "["dividing numerator and denominator by x"^(5)]`
`=int(((1)/(x^(3))-(1)/(x^(5)))dx)/(sqrt(2-(2)/(x^(2))+(1)/(x^(4))))`
`"Put "2-(2)/(x^(2))+(1)/(x^(4))=t`
`rArr" "((4)/(x^(3))-(4)/(x^(5)))dx=dt`
`therefore l=(1)/(4)int(dt)/(sqrtt)=(1)/(4).(t^(1//2))/(1//2)+C=(1)/(2)sqrt(2-(2)/(x^(2))+(1)/(x^(4)))+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

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

Evaluate: int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx

What is int(x^(4)-1)/(x^(2)sqrt(x^(4)+x^(2)+1))dx equal to ?

int(1)/(sqrt(8+2x-x^(2)))dx is equal to

int(x^(2)-1)/((x^(2)+1)sqrt(x^(4)+1)) dx is equal to -

int(1)/(sqrt(9x-4x^(2)))dx is equal to

int((x^(2)-1))/((x^(2)+1)sqrt(x^(4)+1))dx is equal to