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

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

Text Solution

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`I=int frac{d x}{(x^{2}+1)(x^{2}+4)}`
Putting `x^{2}=t`
Then, `frac{1}{(x^{2}+1)(x^{2}+4)}=frac{1}{(t+1)(t+4)}`
`text { Let } frac{1}{(t+1)(t+4)}=frac{A}{t+1} `
`Rightarrow 1=A(t+4)+B(t+1)`
Putting `t+4=0`
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