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int (x^(2)-1)/(x^(2)+1)dx=...

`int (x^(2)-1)/(x^(2)+1)dx=`

A

x - `tan^(-1)x + c `

B

2x - `2tan^(-1)`x + c

C

x + `2tan^(-1)x + c `

D

`x - 2tan^(-1)` x + c

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • int (x^(5))/(x^(2)+1)dx=

    A
    `(x^(4))/(4)+(x^(2))/(2)+Tan^(-1)x+c`
    B
    `(x^(4))/(4)-(x^(2))/(2)+(1)/(2)log(x^(2)+1)+c`
    C
    `(x^(4))/(4)+(x^(2))/(2)+Tan^(-1)x+c`
    D
    `(x^(4))/(4)-(x^(3))/(3)-Tan^(-1)e`

  • int (x^(4))/(x^(2)+1)dx

    A
    `(x^(3))/(3)-x+"Tan"^(-1)x+c`
    B
    `(x^(5))/(5)+Tan^(-1)x+c`
    C
    `4x^(3)+Tan^(-1)x+c`
    D
    `(x^(4))/(4)+x+Tan^(-1)x+c`

  • int (x^(2))/(x^(4)+1)dx=

    A
    `(1)/(2sqrt(2))Tan^(-1)((x^(2)+1)/(sqrt(2)x))+(1)/(4sqrt(2))log |(x^(2)-sqrt(2)x+1)/(x^(2)+sqrt(2)x+1)|+c`
    B
    `(1)/(2sqrt(2))Tan^(-1)((x^(2)\1)/(sqrt(2)x))+(1)/(4sqrt(2))log |(x^(2)+sqrt(2)x+1)/(x^(2)-sqrt(2)x+1)|+c`
    C
    `(1)/(2sqrt(2))Tan^(-1)((x^(2)\1)/(sqrt(2)x))+(1)/(4sqrt(2))log |(x^(2)-sqrt(2)x+1)/(x^(2)+sqrt(2)x+1)|+c`
    D
    none

    • Similar Questions

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    int (x^(5))/(x^(2) + 1) dx =

    int (x +1)/(x^(2) + 1) dx =

    int (2x+1)/(x^(2)(x+1))dx=

    int (x^(4) + x^(2) +1)/(x^(2) + 1) dx =

    int (x^(2) + x)/((x^(2) + 1)(x - 1)) dx =

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