Home
Class 12
MATHS
Evaluate: int(sqrt(1+x^2))/(1-x^2)dx...

Evaluate: `int(sqrt(1+x^2))/(1-x^2)dx`

Text Solution

Verified by Experts

Let,
`x=tan theta`

`dx=sec^2 theta d theta`

`=-int(sqrt(1+x^2))/(x^2-1)dx`

`=-int(sqrt(1+tan^2 theta))/(tan^2 theta -1) sec^2 theta d theta`

`=-int(sqrt(sec^2 theta))/(tan^2 theta -1) sec^2 theta d theta`

`=-int(sec^3 theta)/(tan^2 theta -1) d theta`

Converting into `cos theta` and `sin theta`

...
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 int sqrt(1-x^2) dx

Evaluate: int sqrt(1+x-2x^(2))dx

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

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

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

Evaluate: int1/(sqrt(2x-x^2))\ dx

Evaluate: int sqrt(1+2x-3x^(2))dx

Evaluate: int1/(x^2sqrt(1+x^2))\ dx

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

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