Home
Class 12
MATHS
Evaluate: int(x^3tan^(-1)x^4)/(1+x^8)dx...

Evaluate: `int(x^3tan^(-1)x^4)/(1+x^8)dx`

Text Solution

Verified by Experts

The correct Answer is:
`((tan^(-1)x^(3))^(2))/(6)+C `
`I= int tan^(-1)x^(3)*x^(2)/(1+x^(6))dx`
` " Let " tan^(-1)x^(3)=t`
` :. dt=(3x^(2))/(1+x^(6))dx `
` :. I=(1)/(3)int tdt=(t^(2))/(6)+C=((tan^(-1)x^(3))^(2))/(6)+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(x^2tan^(-1)x^3)/(1+x^6)dx

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

Evaluate int_(0)^(1)(tan^(-1)x)/(1+x^(2))dx

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

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

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

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

Evaluate: int_(-1)^3(tan^(-1)x/(x^2+1)+tan^(-1)(x^2+1)/x)dx

Evaluate int tan^(3)x dx

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