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Evaluate: int1/((x^2+1)(x^2+4))\ dx...

Evaluate: `int1/((x^2+1)(x^2+4))\ dx`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

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