Question

Evaluate \[\int\frac{x^{2}+1}{x^{2}-5x+6}\,dx\].

Options

• \[x-5\log|x-2|+10\log|x-3|+\mathrm{C}\]

• \[x-\frac{5}{x-2}+\frac{10}{x-3}+\mathrm{C}\]

• \[x+5\log|x-2|-10\log|x-3|+\mathrm{C}\]

• \[-5\log|x-2|+10\log|x-3|+\mathrm{C}\]

Answer 1

Use \[1-\frac{5}{x-2}+\frac{10}{x-3}\] and integrate each term separately. The integral of \[\frac{1}{x-a}\] is \[\log|x-a|\], followed by \[+\mathrm{C}\].