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int((x+1)^(2)x)/(x(x^(2)+1)) is equal to...

`int((x+1)^(2)x)/(x(x^(2)+1))` is equal to

A

`log_(e)x+c`

B

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

C

`log_(e).(1)/(x^(2)+1)+c`

D

`log_(e){x(x^(2)+1)}+c`

Text Solution

Verified by Experts

The correct Answer is:
B
`int((x+1)^(2))/(x(x^(2)+1))dx=int(x^(2)+1+2x)/(x(x^(2)+1))dx`
`=int(x^(2)+1)/(x(x^(2)+1))dx+2int(x)/(x(x^(2)+1))dx`
`=int(dx)/(x)+2int(d)/(x^(2)+1)=log_(e)x+2 tan^(-1)x+c`
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