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

`int(dx)/(sqrt(1+4x^2))`

A

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

B

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

C

`log|2x+sqrt(4x^(2)+1)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int(dx)/(sqrt(1-4x^(2)))=int(dx)/(sqrt(4{((1)/(2))^(2)+x^(2)}))`
`=(1)/(2)int(dx)/(sqrt(x^(2)+((1)/(2))^(2)))=(1)/(2)log|x+sqrt(x^(2)+((1)/(2)))^(2)|+C_(1)`
`=(1)/(2)log|x+(sqrt(4x^(2)+1))/(2)|+C_(1)`
`=(1)/(2)log|2x+sqrt(4x^(2)+1)|-(1)/(2)log2+C_(1)`
`=(1)/(2)log|2x+sqrt(4x^(2)+1)|+C" "[C=(1)/(2)log2+C_(1)]`
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)/(sqrt(16-4x^(2)))=?

int(dx)/(sqrt(4x^2-5))=

The value of int(2dx)/sqrt(1-4x^(2)) is

int(dx)/(sqrt(4x^(2)+1))

int(x)/(sqrt(1-4x^(2)))dx

" (b) "int(dx)/(sqrt(4x^(2)-1))

int(dx)/(sqrt(4x^(2)+5))

int(dx)/(sqrt(9-4x^(2)))

int(dx)/(sqrt(4x^(2)+3))

int(dx)/(sqrt(4x^(2)-9))