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

Evaluate: `int(x^2)/(x^6+a^6)\ dx`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(3)(1)/(2a^(3))"log"_(e)|(x^(3)-a^(3))/(x^(3)+a^(3))|+C`
`I=int(x^(2))/(x^(6)-a^(6))dx`
` "let "x^(3)=t`
` :. 3x^(2)dx=dt`
` :. I=(1)/(3)int(dt)/(t^(2)-a^(6))=(1)/(3)(1)/(2a^(3))"log"_(e)|(t-a^(3))/(t+a^(3))|+C`
`=(1)/(3)(1)/(2a^(3))"log"_(e)|(x^(3)-a^(3))/(x^(3)+a^(3))|+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.7|10 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.4|20 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^2)/(sqrt(1-x^6))dx

answer the foll. Questions: (ii)evaluate : int (x^4+1)/(x^6+1) dx

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

Evaluate : int (x^(2)dx)/(x^(6) -6x^(3) + 5)

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

Evaluate: int (x^(4) + 1)/(x^(6) + 1) dx

Evaluate : int(dx)/(50+2x^2.

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

Evalute int(x^4+1)/(x^6+1)dx .

Evaluate: int x^2 sin x dx