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

Explanation

`frac{x}{(x-1)(x^{2}+4)}=frac{A}{x-1}+frac{B x+C}{x^{2}+4} ldots ldots ldots ldots(1)`



`A` can easily be obtained by using Heavyside's Cover-up Method:


`A=[frac{x}{x^{2}+4}]_{x=1}=frac{1}{5}`. Hence, with this `A`, from (1), we have,



therefore `frac{x}{(x-1)(x^{2}+4)}-frac{frac{1}{5}}{x-1}=frac{B x+C}{x^{2}+4} text {, i.e., }`




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