Home
Class 12
MATHS
I=int \ loge (logex)/(x(loge x))dx...

`I=int \ log_e (log_ex)/(x(log_e x))dx`

Text Solution

Verified by Experts

The correct Answer is:
`((log_(e)(log_(e)x))^(2))/(2)+C`
`intlog_(e)(log_(e)x)*(1)/(x log_(e)x)dx`
`=int log_(e)(log_(e)x)*(log_(e)(log_(e)x))'dx`
`=((log_(e)(log_(e)x))^(2))/(2)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.4|20 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.2|7 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Find the range of f(x)=(log)_e x-((log)_e x)^2/(|(log)_e x|)

Evaluate: int(log_(e x)e*log_(e^2x)e*log_(e^3x)e)/x dx

Evaluate int(1+x^(2)log_(e)x)/(x+x^(2)log_(e)x)dx

The value of int(e^(5log_(e)x)+e^(4log_(e)x))/(e^(3log_(e)x)+e^(2log_(e)x))dx is

Evaluate int(x+1)/(x(x+log_(e)x))dx

If f(x)=log_(e)(log_(e)x)/log_(e)x then f'(x) at x = e is

"If "log_(e)(log_(e) x-log_(e)y)=e^(x^(2_(y)))(1-log_(e)x)," then find the value of "y'(e).

The number of real solution(s) of the equation 9^(log_(3)(log_(e )x))=log_(e )x-(log_(e )x)^(2)+1 is equal to

If int((log_(ex)e)(log_(e^(2)x)e)log_(e^(3)x) e))1/x dx = Alog |1+logx|+B log |2+log x|+C log |3+ logx| +D then A-B+C is equal to

Compute the area of the region bounded by the curves y=e x(log_e x) and y=(log_e x)/(e x)