Question

Evaluate \[\int\frac{dx}{x^2-6x+13}\].

Options

• \[\sin^{-1}\left(\frac{x-3}{2}\right)+C\]

• \[\frac{1}{2}\log\left|\frac{x-3}{x+3}\right|+C\]

• \[\frac{1}{2}\tan^{-1}\left(\frac{x-3}{2}\right)+C\]

• \[\frac{1}{2}\tan^{-1}\left(\frac{x+3}{2}\right)+C\]

Answer 1

Write the denominator as \[(x-3)^2+2^2\] and put \[x-3=t\]. Applying the \[t^2+2^2\] standard form gives the inverse tangent result.