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

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

Text Solution

Verified by Experts

I=`int(x^3)/((x^2+1)^3)dx`
let `(1+x^2)=t`
`2xdx=dt`
Thus,
`I=int(x**x^2dx)/(1+x^2)^3`
`I=int (t-1)/(t^3) (dt)/2`
`I=1/2(int (1/t^2-1/t^3)dt)`
`I=1/2(-1/t+(1/t^2))`
...
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

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

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

" 1.Evaluate "int(x^(3)/(1+x^(2)))dx

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

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