Evaluate: `int(4x^4+3)/((x^2+2)(x^2+3)(x^2+4))\ dx`

Explanation

`I=int frac{(4 x^{4}+3) d x}{(x^{2}+2)(x^{2}+3)(x^{2}+4)}`

Putting `x^{2}=t`

Then,



`frac{4 x^{4}+3}{(x^{2}+2)(x^{2}+3)(x^{2}+4)}=frac{4 t^{2}+3}{(t+2)(t+3)(t+4)} `

`text { Let } frac{4 t^{2}+3}{(t+2)(t+3)(t+4)}=frac{A}{t+2}+frac{B}{t+3}+frac{C}{t+4} `

`Rightarrow frac{4 t^{2}+3}{(t+2)(t+3)(t+4)}=frac{A(t+3)(t+4)+B(t+2)(t+4)+C(t+2)(t+3)}{(t+2)(t+3)(t+4)} `

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