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int (x^(4) + x^(2) + 1)/(x^(2) - x +1) ...

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

A

`(x^(5))/(5) + (x^(3))/(3)` + x + c

B

`(x^(3))/(3) - (x^(2))/(2)` + x + c

C

`(x^(3))/(3) - (x^(2))/(2)` + c

D

`(x^(3))/(3) + (x^(2))/(2)` + x + c

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

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

    A
    `(x^(3))/(3) + tan^(-1)`x +C
    B
    `(x^(3))/(3) - tan^(-1)`x +C
    C
    `(x^(3))/(2) + tan^(-1)`x +C
    D
    `(x^(3))/(2) + tan^(-1)`x +C

  • 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 +1)/(x^(2) + 1) dx =

    A
    `(1)/(2)" log "|x^(2) - 1| + cos^(-1) ` x + c
    B
    `(1)/(2)" log "|x^(2) - 2| + tan^(-1) ` x + c
    C
    `(1)/(2)" log "|x^(2) + 1| + tan^(-1) ` x + c
    D
    `(1)/(2)" log "|x^(2) - 1| - tan^(-1) ` x + c

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    int (x^(2) + 1)/(x^(4) + 7x^(2) + 1) dx is equal to

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