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

`int[(sqrt(x^2+1)(ln(x^2+1)-2lnx)))/(x^4) dx`

A

`((x^(2)+1)^(3//2))/(x^(3))[(2)/(3)-ln((x^(2)+1)/(x^(2)))]+C`

B

`((x^(2)+1)^(3//2))/(3x^(3))[ln((x^(2)+1)/(x^(2)))-(2)/(3)]+C`

C

`((x^(2)+1)^(3//2))/(3x^(3))[(2)/(3)-ln((x^(2)+1)/(x^(2)))]+C`

D

`(sqrt(x^(2)+1))/(3x^(3))(ln.(x^(2)+1)/(x^(2))-(2)/(3))+C`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int(sqrt(x^(2)+1).[ln(x^(2)+1)-2 In x])/(x^(4))dx`
`=int sqrt(1+(1)/(x^(2))).(1)/(x^(3)).ln (1+(1)/(x^(2)))dx =-(1)/(2)int sqrt(t)` ln t dt
on applying integration by parts, we get
`=-(1)/(2)[ln t.(2t^(3//2))/(3)-int (1)/(t).(2)/(3)t^(3//2)dt]`
`=-(1)/(3)t^(3//2)ln t +(2)/(9)t^(3//2)+C`
`=((x^(2)+1)^(3//2))/(3x^(3)){(2)/(3)- ln((x^(2)+1)/(x^(2)))}+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

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

Find:int(sqrt(x^(2)+1)(log(x^(2)+1)-2log x))/(x^(4))dx

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

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

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

int sqrt(x)(log x)^(2)dx

Evaluate int(sqrt(x^(2)+1){log_(e)(x^(2)+1)-2logx}dx)/(x^(4)) .

int (x^(x)(x^(2x)+1)("ln"x+1))/(x^(4x)+1)dx