Question

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

Options

• \[\frac14\log|2x^2+6x+5|+\tan^{-1}(2x+3)+C\]

• \[\frac14\log|2x^2+6x+5|+\frac12\tan^{-1}(2x+3)+C\]

• \[\frac12\log|2x^2+6x+5|+\frac14\tan^{-1}(2x+3)+C\]

• \[\frac14\log|2x^2+6x+5|+\frac12\sin^{-1}(2x+3)+C\]

Answer 1

The derivative-related part gives \[\frac14\log|2x^2+6x+5|\]. Completing the square in the remaining integral gives \[\tan^{-1}(2x+3)\], multiplied by \[\frac12\].