Home
Class 12
MATHS
Evaluate: int(x-1)/((x+1)sqrt(x^3+x^2+x)...

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

Text Solution

Verified by Experts

The correct Answer is:
`2"tan"^(-1)sqrt(x+(1)/(x)+1)+C`
`I=int((x-1)dx)/((x+1)sqrt(x^(3)+x^(2)+x))`
`=int((x^(2)-1))/((x^(2)+2x+1)sqrt(x^(3)+x^(2)+x))`
`=int((1-(1)/(x^(2)))dx)/((x+(1)/(x)+2)sqrt(x+(1)/(x)+1))`
`"Putting " x+(1)/(x)+1=u^(2),`
`I=int(2udu)/((u^(2)+1)*u)=2 "tan"^(-1)u+C`
`=2"tan"^(-1)sqrt((x+(1)/(x)+1))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.8|7 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.9|15 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.6|6 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(x+1)/((x-1)sqrt(x+2))dx

Evaluate: int(x^2-1)/((x^2+1)sqrt(x^4+1))dx

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

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

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

Evaluate: int1/((x-3)sqrt(x+1))dx

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

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

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

Evaluate: int(x+1)/((x-1)(x+3))dx