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

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

Text Solution

Verified by Experts

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