Home
Class 12
MATHS
Evaluate: int(log(1+1/x))/(x(1+x))dx...

Evaluate: `int(log(1+1/x))/(x(1+x))dx`

Text Solution

Verified by Experts

The correct Answer is:
` -((log(1+(1)/(x)))^(2))/(2) + C`
Let `log(1+(1)/(x))=t`
` :. (0-(1)/(x^(2)))/(1+(1)/(x)) dx=dt `
` implies (-dx)/(x(x+1))=dt `
` implies int(log(1+(1)/(x)))/(x(1+x))dx=-int t dt `
`=- (t^(2))/(2) +c `
` = -((log(1+(1)/(x)))^(2))/(2) + c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.3|16 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

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

Evaluate: int(log(1+x^(2)))/(x^(3))dx

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

Evaluate: int log(x+1)dx

Evaluate: int log(x+1)dx

Evaluate: int x log(1+x)dx

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

Evaluate int(log(1+x))/(1+x)dx on (-1,oo)

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

int(log(1+x))/(1+x)dx