Home
Class 12
MATHS
Evaluate int((log x-1)/(1+(logx)^(2)))^...

Evaluate `int((log x-1)/(1+(logx)^(2)))^(2)dx`

Text Solution

Verified by Experts

The correct Answer is:
`(x)/(1+(logx)^(2))+C`
` "Put " log x=t, "i.e.," x=e^(t) " so that " dx=e^(t) dt`
`:. int(((t-1))/(1+t^(2)))^(2)e^(t)dt=int e^(t)[(1)/(1+t^(2))-(2t)/((1+t^(2))^(2))]dt `
`=e^(t)(1)/(1+t^(2))+C`
`=(x)/(1+(logx)^(2))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Single)|77 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.8|7 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 x)/((1+log x)^(2))dx

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

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

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

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

Evaluate : int {log(logx)+(1)/((logx)^(2))}dx

int (log x)/(1+logx)^2 dx

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

Evaluate int e^x(1/logx-1/(x(logx)^2)) dx

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