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int(2x^2-1)/((x^2+4)(x^2-5))dx=...

`int(2x^2-1)/((x^2+4)(x^2-5))dx=`

A

`(1)/(5)tan^(-1)((x)/(2))+(1)/(2sqrt(5))log|(x+sqrt(5))/(x-sqrt(5))|+c`

B

`(1)/(5)tan^(-1)((x)/(2))+(1)/(2sqrt(5))log|(x-sqrt(5))/(x+sqrt(5))|+c`

C

`(1)/(5)tan^(-1)((x)/(2))+(1)/(sqrt(5))log|(x+sqrt(5))/(x-sqrt(5))|+c`

D

`(1)/(5)tan^(-1)((x)/(2))+(1)/(sqrt(5))log|(x-sqrt(5))/(x+sqrt(5))|+c`

Text Solution

Verified by Experts

The correct Answer is:
B
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