badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12

                        

Integrate:- {(1/(logx))-(1/(logx) 2 )} for upper limit e 2 and lower limit 0.

9 years ago

Answers : (4)

vikas askiitian expert
509 Points
							

I = {1/logx -1/(logx)2 }dx

multiply numerator & denominator by x

I = x{1/logx-1/(logx)2}dx /x

put logx = t

    dx/x = dt      & x=et

now

        I = et{1/t - 1/t2}dt       

        I = et{ f(t) + f1(t) }

we have a direct formula for ex{f(x) + f1(x)}dx = exf(x)

 so I = et f(t) 

        =et/t = (x / logx)       lim 0 to e2

        =0 - e2/2

9 years ago
Manav
13 Points
							
Take logx= t and x=e^t
dx=e^t × dt 
So integral becomes, integration [1÷t- 1÷t^2]× e^t
This is of the form e^x( f(x) +f'(x) )= e^x(f(x) )+c 
So answer becomes e^logx[ 1÷logx] +c
2 years ago
Sadhan Ganguly
15 Points
							
Integration dx/log x - integration dx/(log x)^2
Intigrating the first part by parts formula
1/log x integration 1 dx - integration ( d/dx (log x)^-1.integration 1 dx ) dx - integration dx/(log x)^2
x/log x  + integration dx/(log x)^2 - integration dx/(log x)^2= x/log x ans.
2 years ago
Kushagra Madhukar
askIITians Faculty
605 Points
							
Dear student,
Please find the solution to your problem below.
 
I = {1/logx -1/(logx)2 }dx
multiply numerator & denominator by x
I = x{1/logx-1/(logx)2}dx /x
put logx = t
    dx/x = dt      & x=et
now
        I = et{1/t - 1/t2}dt       
        I = et{ f(t) + f1(t) }
we have a direct formula for ex{f(x) + f1(x)}dx = exf(x)
so I = et f(t) 
        = et/t = (x / logx)       lim 0 to e2
        = 0 – e2/2
        = – e2/2
 
Thanks and regards,
Kushagra
4 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 51 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details