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Evaluate: int((2x+1))/((x^(2)+4x+1)^(3//...

Evaluate: `int((2x+1))/((x^(2)+4x+1)^(3//2))dx`

A

`(x^(3))/((x^(2)+4x+1)^(1//2))+C`

B

`(x)/((x^(2)+4x+1)^(1//2))+C`

C

`(x^(2))/((x^(2)+4x+1)^(1//2))+C`

D

`(1)/((x^(2)+4x+1)^(1//2))+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(2x+1)/((x^(2)+4x+1)^(3//2))dx=int(2x+1)/(x^(3)(1+(4)/(x)+(1)/(x^(2))))dx`
`=int(2x^(-2)+x^(-3))/((1+(4)/(x)+(1)/(x^(2))))dx`
Now put `(1)/(x^(2))+(4)/(x)+1=t^(2)`
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