Home
Class 12
MATHS
(sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(...

`(sqrt(x^(2)+1)[log(x^(2)+1)-2logx])/(x^(4))`

Text Solution

Verified by Experts

`=int (sqrt(x^2+1)[log(x^2+1)−2logx])/(x^4) dx`
`=int (sqrt(x^2+1)log((x^2+1)/(x^2)))/(x^4)dx`
`=int sqrt((x^2+1)/(x^2))log((x^2+1)/(x^2))×1/(x^3)dx`
put `int sqrt((x^2+1)/(x^2))=t, (x^2+1)/(x^2)=t^2`
...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.3|24 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|46 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.5|23 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

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

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

If y sqrt(x^(2)+1)= log (sqrt(x^(2)+1)-x) , prove that (x^(2)+1)(dy)/(dx) +xy+1=0 .

Solve: 4(log)_(x/2)(sqrt(x))+2(log)_(4x)(x^2)=3(log)_(2x)(x^3)dot

Find the domain of the functions f(x) = (1)/(sqrt( 4x^(2)-1)) +log _e (x(x^(2) -1))

Find the value of x satisfying the equation, sqrt((log_3(3x)^(1/3)+log_x(3x)^(1/3))log_3(x^3))+sqrt((log_3(x/3)^(1/3)+log_x(3/x)^(1/3))log_3(x^3))=2

The value of int_(-1)^(1) (log(x+sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(x) dx-int_(-1)^(1) (log(x +sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(-x)dx ,

The integral int_(2)^(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx is equal to

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

(1/2)^(logx^2)+2> 3.2^(-"log"(-x))