Home
Class 12
MATHS
Evaluate: int(dx)/(x^2(x^4+1)^(3/4))...

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

Text Solution

Verified by Experts

The correct Answer is:
`-(1+(1)/(x^(4)))^(1//4)+C`
`int(1)/(x^(2)(x^(4)+1)^(3//4))dx=int (1)/(x^(5)(1+(1)/(x^(4)))^(3//4))dx`
`= -(1)/(4)int(1)/(t^(3//4))dt " where "t=1+(1)/(x^(4))`
`= -(1)/(4)(t^(1//4))/(1//4)+C= -t^(1//4)+C`
` = -(1+(1)/(x^(4)))^(1//4)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.5|9 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.3|16 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE ENGLISH|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

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

int1/(x^2(x^4+1)^(3/4)) dx

int1/(x^2(x^4+1)^(3/4))dx

Evaluate: (i) int1/(x^2(x^4+1)^(3//4))\ dx (ii) int(sin^5x)/(cos^4x)\ dx

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

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

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

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

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

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