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int(1)/(x^(2)+4x+13)dx is equal to...

`int(1)/(x^(2)+4x+13)dx` is equal to

A

`log(x^(2)+4x13)+C`

B

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

C

`log(2x+4)+C`

D

`(2x+4)/((x^(2)+4x+13)^(2))+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(dx)/(x^(2)+4x+13)=int(dx)/(x^(2)+4x+4+9)`
`=int(dx)/((x+2)^(2)+3^(2))=(1)/(3)tan^(-1)((x+2)/(3))+C`
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