Home
Class 12
MATHS
Integrate the functions1/(x(logx)^m), x ...

Integrate the functions`1/(x(logx)^m), x >0`

Text Solution

Verified by Experts

Given,`1/(x(logx)^m), x >0`
Putting `logx=t`
=`1/x​dx=dt`
⇒`∫1/[x(logx)^m]​dx=∫dt/(t)^m​`
=`[t^((−m+1)​)]/(1−m)+C`
=`[logx^((−m+1)​)+]/(1−m)+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.4|25 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.8|6 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

Integrate the functions (1)/(x+x log x)

Integrate the functions (1)/(x-x^(3))

Integrate the functions (x^(2)+1)log x

Integrate the functions (1)/(x-sqrt(x))

Integrate the function (1)/(x-x^(3))

Integrate the functions (1)/(1+cot x)

Integrate the functions ((1+log x)^(2))/(x)

Integrate the functions (2x)/(1+x^(2))

Integrate the functions (1)/(1-tan x)

Integrate the functions xsqrt(1+2x^2)