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

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

Text Solution

Verified by Experts

The correct Answer is:
`3tan^(-1)(x^(1//3))+C`
`I=int(dx)/(x^(2//3)(1+x^(2//3)))`
` " Let " t^(3)=x, " then " dx=3t^(2) dt `
`:. I=int(3t^(2)dt)/(t^(2)(1+t^(2))) `
`=3int(dt)/(1+t^(2))=3tan^(-1)(t)+C `
`=3tan^(-1)(x^(1//3))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.3|16 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(dx)/(x^(1/2)+x^(1/3))

Evaluate int(dx)/(2x^(2)+x+3) .

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

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

Evaluate int(4x)/(x^(2)-3x+2)dx

Evaluate: int(dx)/(x^2(x^4+1)^(3/4))

Evaluate: int(dx)/(x^2(x^4+1)^(3/4))

Evaluate: int(dx)/(x^2(x^4+1)^(3/4))

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

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