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

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

Text Solution

Verified by Experts

`=int((x-1)/(x+1))^4\ dx`

Let, `x+1=t`
`dx=dt`

`=int((t-2)^4)/(t)^4\ dx`

`=int(t^4 – 8t^3 + 24t^2 – 32t +16)/(t^4)\dx`

`=int(1 – 8/t + 24t^(-2) – 32t^(-3) +16t^(-4))\dx`

`=t-lnt-24/t+(16)/(t^2)-(16)/(3t^3)+C`

`=(x+1)-ln(x+1)-24/(x+1)+(16)/((x+1)^2)-(16)/(3(x+1)^3)+C`

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(1)/(x(x-1))dx

Evaluate: int1/(x(x-2)(x-4))\ dx

Evaluate int (3x)/(4x+1)dx

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

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

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

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

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

Evaluate: int1/(x\ (x^n+1))\ dx (ii) int1/(x(x^5+1))\ dx

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