Home
Class 12
MATHS
Evaluate: int1/(xlogx(2+logx)\ dx...

Evaluate: `int1/(xlogx(2+logx)\ dx`

Text Solution

Verified by Experts

`I=int frac{d x}{x log x(2+log x)}`
Putting `log x=t`
`Rightarrow frac{1}{x} d x=d t `
`therefore I=int frac{d t}{t(t+2)} `
`text { Let } frac{1}{t(t+2)}=frac{A}{t}+frac{B}{t+2} `
`Rightarrow frac{1}{t(t+2)}=frac{A(t+2)+B t}{t(t+2)} `
`Rightarrow 1=A(t+2)+B t`
...
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int1/(xlogxlog(logx))dx

int(1)/(xlogx(2+logx))dx=

Evaluate : int(1)/(xlogxlog(logx))dx

Evaluate: int(logx)/((1+logx)^2)\ dx

Evaluate int[1/logx-1/(logx)^2]dx

Evaluate : int(logx)^(2)dx .

Evaluate int(logx)/((1+logx)^(2))dx .

Evaluate : int_1^3 cos( logx )/x dx

int7^(x logx)(1+logx)dx=

Evaluate: int1/x[x(logx)^2+2logx]e^xdx