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Evaluate int (2x)/((x^2+1)(x^2+3))dx...

Evaluate `int (2x)/((x^2+1)(x^2+3))dx`

Text Solution

Verified by Experts

We have,
`I=int frac{2 x d x}{(x^{2}+1)(x^{2}+3)}`
Putting `x^{2}=t`
`Rightarrow 2 x d x=d t `
`therefore I=int frac{d t}{(t+1)(t+3)}`
Let `frac{1}{(t+1)(t+3)}=frac{A}{t+1}+frac{B}{t+3}`
`Rightarrow frac{1}{(t+1)(t+3)}=frac{A(t+3)+B(t+1)}{(t+1)(t+3)}`
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