Home
Class 12
MATHS
(1+log x)^(2)/(x)...

`(1+log x)^(2)/(x)`

Text Solution

Verified by Experts

` int ((1+ log x)^(2))/(x) dx " " underset( rArr (1)/(x) dx=dt)(" Let " 1+ log x=t)`
` = int t^(2) dt = (1)/(3) t^(3) +c` lt brgt `(1)/(3) (1+ log x)^(3)+c`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.3|24 Videos
  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.4|25 Videos
  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.1|22 Videos
  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos
  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

int_(1)^(2) (dx)/(x(1+log x)^(2))

The value of int _(-1)^(1) log ((2-x)/(2+x)) d x is equal to

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

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

int((1+(log)_e x)^2)/(1+(log)_e x^(x+1)+((log)_e x^(sqrt(x)))^2)dx=

solve int_(1)^(2)(log x)/(x^(2))dx

Evaluate int_(-1)^(1) log ((2-x)/( 2+x)) dx

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

Evaluate : int [ log (log x) +(1)/((log x)^(2)) ] dx

If int x log (1+x^(2))dx= phi (x) log (1+x^(2))+x(Psi)+C , then