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int(dx)/((x^2+4x+5)^2) is equal to 1/2...

`int(dx)/((x^2+4x+5)^2)` is equal to `1/2[tan^(-1)(x+1)+("x"+2)/("x"^2+4"x"+5)]+"c"` `1/2[tan^(-1)(x+2)-("x"+2)/("x"^2+4"x"+5)]+"c"` `1/2[tan^(-1)(x+1)-("x"+2)/("x"^2+4"x"+5)]+"c"` `1/2[tan^(-1)(x+2)+("x"+2)/("x"^2+4"x"+5)]+"c"`

A

`(1)/(2)[tan^(-1)(x+1)+(x)/(x^2+4x+5)]+C`

B

`(1)/(2)[tan^(-1)(x+2)-(x+2)/(x^2+4x+5)]+C`

C

`(1)/(2)[tan^(-1)(x+1)-(x+2)/(x^2+4x+5)]+C`

D

`(1)/(2)[tan^(-1)(x+2)+(x+2)/(x^2+4x+5)]+C`

Text Solution

Verified by Experts

The correct Answer is:
D
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