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

Evaluate: `int(ddx)/(sqrt(1+x^2)+sqrt((1+x^2)^3))`

Text Solution

Verified by Experts

The correct Answer is:
`1+sqrt(1+t^(2))+c`
`I=int(xdx)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))))`
`=int(xdx)/(sqrt((1+x^(2))(1+sqrt(1+x^(2)))))`
` "Let " 1+sqrt(1+x^(2))=t^(2)`
` :. 2tdt =(x)/(sqrt(1+x^(2)))dx`
` :. I=int2t=t+c=1+sqrt(1+t^(2))+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.3|16 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(xdx)/(sqrt((1+x^2)+sqrt((1+x^2)^3)))

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

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

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

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

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

Evaluate: int(x^2)/(sqrt(1-x^6))dx

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

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

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