Home
Class 12
MATHS
Evaluate: Evaluate: intx^(-11)(1+x^4)^(-...

Evaluate: Evaluate: `intx^(-11)(1+x^4)^(-1/2)dx`

Text Solution

Verified by Experts

`I=int (dx)/(x^(11)(1+x^(4))^(1//2))=int (dx)/(x^(11)*x^(2)(1+1//x^(4))^(1//2))`
Let `1+(1)/(x^(4))=t^(2) " or " (-4)/(x^(5))dx=2tdt`
`:. I=int(dx)/(x^(13)(1+1//x^(4))^(1//2 ))`
`=-(1)/(4)int(2tdt)/(x^(8)t)`
`=-(1)/(2)int(t^(2)-1)^(2)dt`
`=-(1)/(2)int(t^(4)-2t^(2)+1)dt`
`= -(1)/(2)[(t^(5))/(5)-(2t^(3))/(3)+t]+C, " where " t=sqrt(1+(1)/(x^(4)))`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXAMPLE|18 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.1|9 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(1+x^4)/((1-x^4)^(3/2))dx

Evaluate: intx^(13/2) (1+x^(5//2) )^(1/2) dx

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

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

Evaluate: inte^(3logx)(x^4+1)^(-1)dx

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

Evaluate: int1/(x^4-1)dx

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

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

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