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

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

A

`(x^(3))/(3) + x - tan^(-1) x + C`

B

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

C

`(x^(3))/(3)0 + x - 2 tan^(-1) x +C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
On dividing `(x^(4) + 1)` by `(x^(2) +1)`, we get
`((x^(4)+1))/((x^(2) + 1)) = (x^(2) - 1) + 2/((1+x^(2)))`.
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