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Evaluate: int1/((a^2+x^2)^2)dx...

Evaluate: `int1/((a^2+x^2)^2)dx`

Text Solution

Verified by Experts

I=`int1/((a^2+x^2)^2)dx`
let `x=atany`
`dx=asec^2ydy`
`I=int (asec^2ydy)/((a^2+(a^2tan^2y))^2`
`I=int (asec^2ydy)/(a^2(1+tan^2y)^2)`
`I=a/(a^4)int (sec^2dy)/(sec^2y)^2 `
...
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