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int(3x^(2)+2x)/(x^(6)+2x^(5)+x^(4)+2x^(3...

`int(3x^(2)+2x)/(x^(6)+2x^(5)+x^(4)+2x^(3)+2x^(2)+5)dx=`

A

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

B

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

C

`sin^(-1)((x^(3)+x^(2)+1)/(2))+c`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(3x^(2)+2x)/((x^(3)+x^(2)+1)^(2))dx`
Put `x^(3)+x^(2)+1=t`
`therefore" "I=int(1)/(t^(2)+4)dt`
`=(1)/(2)tan^(-1)((t)/(2))+c`
`=(1)/(2)tan^(-1)((x^(3)+x^(2)+1)/(2))+c`
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