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

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

Text Solution

Verified by Experts

`"Let I"=int (2x^(2)-1)/((x^(2)+4)(x^(2)-5))dx`
`=int ((x^(2)-5)+(x^(2)+4))/((x^(2)+4)(x^(2)-5))dx`
`=int ((1)/(x^(2)+4)+(1)/(x^(2)-5))dx`
`=int(1)/(x^(2)+2^(2))dx+int (1)/(x^(2)-(sqrt5)^(2))dx`
`=(1)/(2)tan^(-1)((pi)/(2))+(1)/(2sqrt5)log""|(x-sqrt5)/(x+sqrt5)|+c`\
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