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Evaluate: int8/((x+2)(x^2+4))\ dx...

Evaluate: `int8/((x+2)(x^2+4))\ dx`

Text Solution

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`I=int frac{8}{(x+2)(x^{2}+4)} d x`

Let `frac{8}{(x+2)(x^{2}+4)}=frac{A}{x+2}+frac{B x+C}{x^{2}+4}`

`Rightarrow 8=A(x^{2}+4)+(B x+C)(x+2) `

`Rightarrow 8=(A+B) x^{2}+(2 B+C) x+(4 A+2 C)`

On comparing the terms, we get

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