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

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

Text Solution

Verified by Experts

`I=int(dx)/(x^(2)sqrt(1+x^(2)))=int(dx)/(x^(3)sqrt(1+(1)/(x^(2))))`
Let `t=sqrt(1+(1)/(x^(2))) " or " (dt)/(dx)=(1(-(2)/(x^(3))))/(2sqrt(1+(1)/(x^(2))))`
or `(dx)/(x^(3))= -t dt`
or `I= -int(tdt)/(t)= -t +C= -sqrt(1+(1)/(x^(2))) +C`
`= - (1)/(x)sqrt(1+x^(2))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXAMPLE|18 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.1|9 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(dx)/((1+x^(2))sqrt(1-x^(2))).

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

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

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

Evaluate: int(dx)/((x^2+4)sqrt(x^2-4))

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

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

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

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

Evaluate: int_0^(1)x(dx)/(sqrt(1-x^(2)))