Home
Class 12
MATHS
Evaluate: int(dx)/(x^2(1+x^7)^(6/7))...

Evaluate: `int(dx)/(x^2(1+x^7)^(6/7))`

Text Solution

Verified by Experts

The correct Answer is:
` -((1+x^(5))^(1//5))/(x)+C`
`I=int(dx)/(x^(2)(1+x^(5))^(4//5))=int(dx)/(x^(6)((1)/(x^(5))+1)^(4//5))`
` "Let " t=1+(1)/(x^(5)) " or " dt= -(5dx)/(x^(6))`
` :. I= -(1)/(5) int(dt)/(t^(4//5))= -t^(1//5)+C= -(1+(1)/(x^(5)))^(1//5)+C`
`= -((1+x^(5))^(1//5))/(x)+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(dx)/(x^2(x^6+1)^(5/6))

Evaluate: int(dx)/((2x-7)(x-7)

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

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

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

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

Evaluate : int (x^(7))/(x-1)dx

Evaluate : int dx/(7x - 10 - x^2)

Evaluate: int1/(x^2+6x+5)dx

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